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GCSEREVISED REVIREVISED SED WJEC Eduqas GCSE in MATHEMATICS ACCREDITED BY OFQUAL SAMPLE ASSESSMENT REV MATERIALS Teaching from 2015 ISED ED REVISED REV This Ofqual regulated qualification is not available for candidates in maintained schools and colleges in Wales.

GCSE MATHEMATICS Sample Assessment Materials 1 © WJEC CBAC Ltd.



GCSE MATHEMATICS Sample Assessment Materials 3 Assessment grids 175 © WJEC CBAC Ltd.



GCSE MATHEMATICS Sample Assessment Materials 5 Candidate Name Centre Number Candidate Number 0 GCSE MATHEMATICS COMPONENT 1 Non-Calculator Mathematics Higher Tier SPECIMEN PAPER 2 hour 15 minutes ADDITIONAL MATERIALS For Examiner’s use only The use of a calculator is not permitted in this examination. A ruler, protractor and a pair of compasses may be required. Question Maximum Mark Mark Awarded INSTRUCTIONS TO CANDIDATES 1. 3 Write your name, centre number and candidate number in the 2. 4 spaces at the top of this page. 3. 4 4. 6 Answer all the questions in the spaces provided in this booklet. 5. 3 6. 4 Take π as 3∙14. 7. 4 8. 4 INFORMATION FOR CANDIDATES 9. 3 10. 5 You should give details of your method of solution when 11. 4 appropriate. 12. 5 13. 7 Unless stated, diagrams are not drawn to scale. 14. 6 15. 5 Scale drawing solutions will not be acceptable where you are 16. 10 asked to calculate. 17. 4 18. 4 The number of marks is given in brackets at the end of each 19. 2 question or part-question. 20. 5 21. 7 You are reminded of the need for good English and orderly, 22. 6 clear presentation in your answers. 23. 7 24. 8 No certificate will be awarded to a candidate detected in any TOTAL 120 unfair practice during the examination. © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 6 Formula list Area and volume formulae Where r is the radius of the sphere or cone, l is the slant height of a cone and h is the perpendicular height of a cone: Curved surface area of a cone = πrl Surface area of a sphere = 4πr2 Volume of a sphere  4 πr3 3 Volume of a cone  1 πr2h 3 Kinematics formulae Where a is constant acceleration, u is initial velocity, v is final velocity, s is displacement from the position when t = 0 and t is time taken: v  u  at s  ut  1 at2 2 v2  u2  2as © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 7 1. Given that a = 10, b = 3 and c = – 5, find the value of each of the following expressions. (a) b2 [1] ....................................................................................................................................... ....................................................................................................................................... (b) ab [1] c ....................................................................................................................................... ....................................................................................................................................... (c) 2bc [1] a ....................................................................................................................................... ....................................................................................................................................... 2. (a) Write 6·8 × 104 in decimal notation. [1] ....................................................................................................................................... (b) Write in standard form the value of 00000853. [1] ....................................................................................................................................... (c) Find in standard form the value of (3  102)  (5  106). [2] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 8 3. Cherry Blossom paint is made by mixing red and white paint in a certain ratio. 4 litres of red paint is used to make 9 litres of Cherry Blossom paint. The diagram below shows the relationship between the amount of red paint and the amount of white paint needed to make Cherry Blossom paint. Amount of red paint (litres) ..….. ……. ……. ……. ……. ……. 0 1 2 3 Amount of white paint (litres) Write down the correct scale on the ‘Amount of red paint (litres)’ axis. [4] You must put a value on each of the dotted lines on the axis. You must show all your working to support your answer. ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 9 4. Andy sometimes gets a lift to and from college. [2] When he does not get a lift he walks. The probability that he gets a lift to college is 0·4. The probability that he walks home from college is 0·7. Getting to college and getting home from college are independent events. (a) Complete the following tree diagram. (b) Calculate the probability that Andy gets a lift to college and walks home from college [2] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... (c) Calculate the probability that Andy does not get a lift to or from college. [2] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 10 5. Write 3600 as a product of prime factors using index notation. [3] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 11 6. Alex bought 3 tins of paint and 4 brushes at a total cost of £23. Brian bought 2 tins of paint and 3 brushes at a total cost of £16. Using an algebraic method, calculate the price of a single tin of paint and the price of one brush. [4] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... The price of a single tin of paint = ……………………………… The price of one brush = ……………………………………….. © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 12 7. Using ruler and compass construction, shade the region that satisfies both of the following conditions. (i) The points are less than 5 cm from P [4] (ii) The points are nearer to Q than to P PQ © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 13 8. Two brothers, Richard and Andrew, share a sum of money in the ratio 2 : 7. [4] Andrew gets £30 more than Richard. Calculate how much the brothers share. ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 14 9. Factorise the following expressions. [2] (a) 6x2 + 8x ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... (b) x2 – 100 [1] ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 15 10. Peter decides to cover the floor of a room with a striped carpet. A shop sells this striped carpet from a roll that is 3 m wide at a price of £25 per metre length. 3m Diagram not drawn to scale His floor is rectangular in shape with length 13 m and width 8 m. 8m 13 m Diagram not drawn to scale The carpet is laid to ensure that the stripes on the carpet are parallel to two of the sides of the room and lie in one direction only. Find the cost of the cheapest way of covering the floor, and state by how much it is cheaper. Show all your working. [5] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 16 ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 17 11. Vectors DF and DE are shown in the diagram below. F 2a + 5b D E 3a  2b Line PQ is 3 times the length of line EF. PQ is in the opposite direction to EF. Find PQ in the form ma + nb. [4] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 18 12. A building company used 24 workers to prepare a building site. The site measured 30 acres and the work was completed in 10 days. (a) The company is asked to prepare another site measuring 45 acres. [3] This work has to be completed in 15 days. Calculate the least number of workers the company should employ for this work. ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... (b) State one assumption you have made in your answer to part (a). [2] How would your answer to part (a) change if you did not make this assumption? ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 19 13. The line L1 is shown in the diagram below. The line L2, which is not shown, is perpendicular to L1. y 9 03 x L1 Diagram not drawn to scale (a) (i) Find the gradient of L1. [2] ....................................................................................................................................... ....................................................................................................................................... (ii) Write down the gradient of L2. [1] ....................................................................................................................................... ....................................................................................................................................... (b) The two straight lines L1 and L2 intersect at the point (1, 6). [4] Find the equation of L2 and write it in the form ax + by + c = 0. ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 20 14. On a journey from Dover to Sheffield, Liam drove at an average speed of 40 mph for the first three hours of his journey. The remaining 120 miles of his journey were completed at an average speed of 30 mph. Liam told his friend that he had completed the whole journey at an average speed of 35 mph. Check to see if Liam is correct. [6] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 21 15. Triangle ABC is isosceles with AB = AC. The line BP bisects AB^C. The line CQ bisects AC^B. A QP B C Diagram not drawn to scale Prove that triangle BCP and triangle CBQ are congruent. [5] You must give reasons to support your statements. ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 22 16. A survey was carried out to record the speeds of cars entering a village. The histogram illustrates the results of the survey. (mph) (a) Use the histogram to complete the grouped frequency table below. [2] Speed, s (mph) 0 < s  20 20 < s  30 30 < s  40 40 < s  50 50 < s  60 Frequency ....................................................................................................................................... ....................................................................................................................................... (b) 40% of the cars surveyed were fined for exceeding a certain speed as they entered the village. Calculate an estimate of this speed. [4] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 23 (c) A further survey was carried out after the placement of a speed camera warning sign. The results are summarised in the grouped frequency distribution below. Speed, s (mph) 0 < s  20 20 < s  30 30 < s  40 40 < s  50 50 < s  60 Frequency 60 40 20 15 5 Draw a histogram to illustrate the results of this survey. [3] ....................................................................................................................................... ....................................................................................................................................... (d) Compare the two histograms. Do you consider the speed camera warning sign to have been effective? Give a reason for your answer. [1] ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 24 17. y is inversely proportional to x. y = 16 when x  1 . 2 Write an expression for y in terms of x. [4] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 25 18. Simplify 3 7 [4] 4 7 ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 26 19. Express x2 12x 14 in the form (x  a)2  b , where a and b are whole numbers to be found. [2] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 27 20. (a) Express 0  78 as a fraction. [2] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... 1 [3] (b) Evaluate 32  92 , giving your answer as a recurring decimal. ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 28 21. The diagram below shows a composite shape formed by joining two rectangles. 4 cm x cm 12 cm (x + 2)cm Diagram not drawn to scale The area of the larger rectangle is 4 times the area of the smaller rectangle. Calculate the dimensions of the smaller rectangle. [7] You must justify any decisions that you make. ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 29 22. (a) The diagram shows a sketch of the graph y = f(x). The graph passes through the points (– 2, 0) and (6, 0). y ( 2, 0) O (6, 0) x Sketch the graph of y = f(x + 5) on the axes below. You must indicate the coordinates of the points of intersection of the graph with the x-axis. [3] y Ox (b) The diagram below on the left shows a sketch of the graph y = x2. [2] Sketch the graph of y =  x2 + 3 on the axes on the right. You must indicate the coordinates of the stationary point. y = x2 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 30 (c) The function f (x) has been translated, as shown in the diagram below. Explain why you cannot say exactly what translation was used. [1] y = f (x) y x O ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 31 23. (a) When Kayla shoots an arrow, the probability that she hits the target is 0·3. Each attempt is independent of any previous shot. (i) What is the probability that she hits the target for the first time on her third attempt? [2] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... (ii) Check whether or not there is more than a 50% chance of Kayla hitting the target once only on her first three attempts. [3] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... (b) (i) A fairground game consists of removing two balls at random from a box containing 15 blue balls and 5 red balls. A player wins the game if two red balls are removed. John calculates that the probability of winning the game is  1 2  1.  4  16 What assumption has John made for his answer to be correct? [1] ....................................................................................................................................... ....................................................................................................................................... (ii) If John’s assumption was not true, what effect would this have on the probability of winning the game? [1] ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 32 24. C 60 (x + 3) cm x cm BA The area of the triangle is 300 cm2. Calculate the length of AB. [8] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 33 Candidate Name Centre Number Candidate Number 0 GCSE MATHEMATICS COMPONENT 1 Non-Calculator Mathematics Foundation Tier SPECIMEN PAPER 2 hours 15 minutes ADDITIONAL MATERIALS For Examiner’s use only The use of a calculator is not permitted in this examination. Question Maximum Mark A ruler, protractor and a pair of compasses may be Mark Awarded required. 1. 4 2. INSTRUCTIONS TO CANDIDATES 3 Write your name, centre number and candidate number in the spaces at the top of this page. 3. 4 4. 4 Answer all the questions in the spaces provided in this 5. 2 booklet. 6. 11 7. 3 Take π as 3∙14. 8. 5 INFORMATION FOR CANDIDATES 9. 4 10. 2 You should give details of your method of solution when 11. 5 appropriate. 12. 3 13. 2 Unless stated, diagrams are not drawn to scale. 14. 5 Scale drawing solutions will not be acceptable where you 15. 6 are asked to calculate. 16. 4 17. 4 The number of marks is given in brackets at the end of 18. 3 each question or part-question. 19. 3 You are reminded of the need for good English and 20. 5 orderly, clear presentation in your answers. 21. 4 22. 3 No certificate will be awarded to a candidate detected in 23. 5 any unfair practice during the examination. 24. 6 25. 4 26. 4 27. 5 28. 2 29. 5 TOTAL 120 © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 34 Formula list Area and volume formulae Where r is the radius of the sphere or cone, l is the slant height of a cone and h is the perpendicular height of a cone: Curved surface area of a cone = πrl Surface area of a sphere = 4πr2 Volume of a sphere  4 πr3 3 Volume of a cone  1 πr2h 3 Kinematics formulae Where a is constant acceleration, u is initial velocity, v is final velocity, s is displacement from the position when t = 0 and t is time taken: v  u  at s  ut  1 at2 2 v2  u2  2as © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 35 1. From the numbers 9 10 48 8 27 13 write down ......................................... [1] a multiple of 5, ......................................... [1] a prime number, ......................................... [1] the value of 33, .......................................... [1] 64 . 2. (a) Write the number 7 500 000 in words. [1] ....................................................................................................................................... ....................................................................................................................................... (b) What is the value of the 9 in the number 239 815. [1] ....................................................................................................................................... ....................................................................................................................................... (c) Using all the digits 6 7 3 8 write down the smallest odd number. [1] ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 36 3. Some people took part in a book quiz. The number of points that each person scored in the quiz is shown below. 16 27 18 26 28 10 22 29 25 13 28 23 19 26 14 25 26 15 17 27 11 27 16 21 11 24 29 18 24 12 28 17 (a) A table is drawn to summarise these results and to show the number of medals that were awarded at the end of the competition. Complete the table below. You must make sure that all the intervals in the Points column are of [2] equal width. Points Number of Type of medal 10 to 14 competitors No medal 6 15 to 19 Bronze ........... to ........... Silver ........... to 29 Gold © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 37 (b) Using the squared paper below, draw a suitable bar chart that shows [2] how the medals were shared. Frequency No medal Bronze Silver Gold Type of medal © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 38 4. (a) Write 2187 correct to the nearest 10. [1] ....................................................................................................................................... (b) Write 54 478 correct to the nearest 1000. [1] ....................................................................................................................................... (c) Estimate the answer to 51 3∙9. [2] ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 39 5. Draw patterns like the given ones in each of the other 2 sections, so that the [2] completed pattern has rotational symmetry of order 4 about O. © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 40 6. The table shows the number of cars that used a town’s car park during a period of one week. Day Mon Tues Wed Thurs Fri Sat Sun TOTAL Number of 104 43 112 163 116 182 80 800 cars (a) How many cars used this car park during the weekend [1] (Saturday and Sunday)? ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... (b) One of the days between Monday and Friday is the town’s market day. On another day, between Monday and Friday, the shops are only open in the morning. Using the information given in the table, which days do you think they are? [2] Market day Morning opening only (c) The car park has space for 170 cars. Explain how it was possible for 182 cars to have used the car park on Saturday. [1] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 41 The charge for using this car park is displayed on the notice shown below. CAR PARK Monday to Friday: £2 per day Free parking on Saturday and Sunday (No time limit) (d) How much money was spent on parking at this car park for the week shown in the table? [2] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... (e) The town council is considering a new system for the way it charges for parking. The new system is  reducing the charge to £1.50 and  charging this amount on all seven days of the week and  allowing free parking for those who stay for less than one hour. That week, a quarter () of the cars stayed for less than one hour. Using this information, decide whether this new system would collect more or less money for the council. You must show all your working. [3] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 42 (f) State an assumption you have made in part (e) and explain how [2] your results would change if this assumption had not been made. ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 43 7. Each diagram represents a balance with the total weight on each side being equal. Find the values of A, B and C. [3] ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ....................................................................................................................................... A = ………………………kg B = ………………………kg C = ………………………kg © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 44 8. Points A and B are at the end of one of the longest straight roads in the USA. In the scale diagram below, 1 cm represents 10 km. AB (a) What is the actual distance between point A and point B? [3] ....................................................................................................................................... ....................................................................................................................................... (b) Would a bicycle travelling at an average speed of 40 km/h cover the distance from point A to point B in less than 2 hours? You must explain your answer. [2] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 45 9. Shari was asked to buy the following items from her local shop. Item Price Chicken curry £2.97 £3.04 Pizza £6.09 Washing powder £1.47 89 pence Butter Bread The shopkeeper tells Shari that the total cost is £102.23. Shari does not think that this is correct. (a) Show clearly how Shari could approximate each of these prices to [3] convince the shopkeeper that his total is not correct. ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... (b) What mistake do you think the shopkeeper made? [1] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 46 10. A piece of wood is 32 cm long. Alan wants to drill two holes in the wood at points A and B, where AB = 18 cm. The distance PA and QB must be equal. Diagram not drawn to scale Calculate the length PA. [2] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 47 11. Simplify each of the following. (a) 7a + 3b + 2a + 5b [2] ....................................................................................................................................... ....................................................................................................................................... (b) 3(y  2) [1] ....................................................................................................................................... ....................................................................................................................................... (c) 3y × 2y [1] ....................................................................................................................................... y6 [1] (d) y2 ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 48 12. Three identical rectangles, each measuring 7 cm by 3 cm, are placed together to make the shape shown in the diagram. Diagram not drawn to scale Calculate the perimeter of the shape. [3] ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.

GCSE MATHEMATICS Sample Assessment Materials 49 13. The following patterns have been made using shaded and unshaded squares. Pattern 1 234 Find the total number of squares in pattern 60. [2] ....................................................................................................................................... ....................................................................................................................................... © WJEC CBAC Ltd.