Snapshot 3- Questions

Name: ___________________________ GCSE (1 – 9) Averages Instructions • Use black ink or ball-point pen. • Answer all Questions. • Answer the Questions in the spaces provided – there may be more space than you need. • Diagrams are NOT accurately drawn, unless otherwise indicated. • You must show all your working out. Information • The marks for each Question are shown in brackets – use this as a guide as to how much time to spend on each Question. Advice • Read each Question carefully before you start to answer it. • Keep an eye on the time. • Try to answer every Question. • Check your answers if you have time at the end mathsgenie.co.uk

1 Here is a list of 10 numbers. 2344456677 (a) Work out the range. (b) Find the mode. ….......................... (1) (c) Calculate the mean. ….......................... (1) ….......................... (2) (Total for question 1 is 4 marks) 2 Here is a list of 5 numbers. 4 6 9 10 11 (a) Work out the range. (b) Write down the median. ….......................... (1) (c) Calculate the mean. ….......................... (1) ….......................... (2) (Total for question 2 is 4 marks)

3 Here are the heights, in cm, of 8 people. 155 171 164 171 167 188 190 151 (a) Work out the range. (b) Find the mode. ….......................… cm (1) (c) Calculate the mean. ….......................… cm (1) ….......................… cm (2) (Total for question 3 is 4 marks) 4 Here are the weights, in grams, of 6 potatoes 150 129 125 133 144 105 (a) Work out the range. (b) Work out the median weight. ….......................... (1) ….......................… g (2) (Total for question 4 is 3 marks)

5 Here are six cards. Each card has a number on it. 19 7 11 8 15 15 (a) Work out the range of the numbers on the cards. (b) Work out the mean of the numbers on the cards. ….......................... (1) ….......................... (2) (Total for question 5 is 3 marks) 6 Here is a list of 10 numbers. 1 4 4 5 6 8 11 11 11 14 (a) Work out the range. (b) Find the mode. ….......................... (1) ….......................... (1) (Total for question 6 is 2 marks)

7 Here are seven cards. Each card has a number on it. 12 5 10 18 12 11 9 (a) Work out the range of the numbers on the cards. (b) Work out the median of the numbers on the cards. ….......................... (1) (c) Work out the mean of the numbers on the cards. ….......................... (2) ….......................... (2) (Total for question 7 is 5 marks)

8 Here is a list of numbers. 864598 (a) Work out the median ….......................... (2) Here are six cards. There is a number on each card. Two of the numbers are hidden. 45?63? The mode of the six numbers is 4 The mean of the six numbers is 5 (b) Work out the two numbers that are hidden. .......................… , .......................... (2) (Total for question 8 is 4 marks)

9 Here is a list of numbers. ….......................... 14 19 15 20 11 14 19 (2) (a) Find the range (b) Calculate the mean Andrew says, ….......................... ”The median is the middle number, so the median is 20.” (2) (c) Andrew is incorrect, explain why. (1) (Total for question 9 is 5 marks) 10 Here is a list of seven numbers. One of the numbers is hidden. 11 6 7 10 7 9 ? The mean of the numbers is 9. Find the value of the hidden number. ….......................... (Total for question 10 is 2 marks)

11 The mean of eight numbers is 41. The mean of two of the numbers is 29. Work out the mean of the other six numbers. ….......................... (Total for question 11 is 3 marks) 12 Mark ran a mean distance of 13.2 km in five days. The next day Mark ran 20 km. Find the mean distance Mark ran in the six days. ….......................… km (Total for question 12 is 3 marks)

Name: Exam Style Questions Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser You may use tracing paper if needed Guidance 1. Read each question carefully before you begin answering it. 2. Donʼt spend too long on one question. 3. Attempt every question. 4. Check your answers seem right. 5. Always show your workings Revision for this topic

1.\" James has a spinner that has sections labelled 1 to 5. 1 \" He spins the spinner 10 times. \" Here are his scores. \" \" 1\" 4\" 4\" 2\" 3\" 4\" 5\" 1\" 4\" \" (a) Find the mode. ......................... (1) ! (b) Work out the mean. ......................... (2) ! (c) Work out the range. ......................... (2) 2.\" Simone records the number of minutes she spends on her mobile phone over \" 7 days. \" \" 8\" 5\" 13\" 6\" 24\" 19\" 10 \" Find the median.\" ! ...................minutes (2)

3.\" Here are the ages of 9 children at a birthday party. \" \" 10\" 12\" 13\" 10\" 11\" 14\" 15\" 10\" 12 \" \" \" (a) Find the mode. ......................... (1) ! (b) Find out the median. ......................... (2) ! (c) Work out the range. ......................... (2) ! (d) Work out the mean. ......................... (2)

4.\" A football team played six games. \" Here are the number of goals they scored in each game: \" \" 6\" 0\" 3\" 2\" 2\" 5 \" (a) Work out the median number of goals scored. ......................... (2) ! (b) Work out the mean number of goals scored. ......................... (2) \" The football team play one more game. \" The mean number of goals scored increases to 4. \" (c) Work out the number of goals scored in the seventh game. ......................... (2)

5.\" Miss Jones gives her class a test. ......................... \" The test is out of 40 marks. (1) \" Here are their scores. \" \" 31\" 29\" 20\" 35\" 32\" 38\" 32 ......................... \" (a) Work out the mode. (2) \" (b) Work out the median. ......................... (2) \" (c) Work out the range. \" The pass mark for the test is 75%. \" (d) How many students pass the test? ......................... (2)

6.\" Hannah is recording the number of letters in each word in an article. \" These are the first ten lengths. \" \" 3\" 4\" 5\" 6\" 2\" 4\" 3\" 7\" 3\" 6 \" (a) Work out the median. ......................... (2) ! (b) Calculate the mean. ......................... (2) ! The 11th word has 4 letters. \" (c) Tick the box which describes what affect this will have on the mean. (1) ! (d) Tick the box which describes what affect this will have on the median. (1)

7.\" Shown below are five cards which are arranged in order from smallest to largest \" The range of the cards is 4. \" The median of the cards is 8. \" The mean of the cards is 7. \" Work out the 4 missing numbers. ............., ............., ............. and ............. (4)

8.\" 8 boys and 8 girls from a class run 100m. \" The times taken, to the nearest second, for each girl are: \" \" 15\" 20\" 24\" 18\" 19\" 21\" 26\" 29 \" \" The mean of the boysʼ times is 25 seconds. \" The range of the boysʼ times is 14 seconds. \" Thomas says that “the boys in our class are faster than the girls.” \" Is he correct? (5)

9.\" A set of six numbers have a median of 5. \" All of the numbers are even. \" The range of the numbers is 6. \" The mode of the numbers is 4. \" Write down a possible set of six numbers. ............., ............., ............., ............., ............. and ............. (4)

Name: ___________________________ GCSE (1 – 9) Averages from Frequency Tables Instructions • Use black ink or ball-point pen. • Answer all Questions. • Answer the Questions in the spaces provided – there may be more space than you need. • Diagrams are NOT accurately drawn, unless otherwise indicated. • You must show all your working out. Information • The marks for each Question are shown in brackets – use this as a guide as to how much time to spend on each Question. Advice • Read each Question carefully before you start to answer it. • Keep an eye on the time. • Try to answer every Question. • Check your answers if you have time at the end mathsgenie.co.uk

1 The table shows information about the number of points scored in a game. Points Frequency 0 9 1 11 2 18 3 7 4 4 5 1 Work out the mean number of points per game. ….......................... (Total for question 1 is 3 marks) 2 The table shows information about the number of goals scored in a game by a football team. Points Frequency 0 10 1 12 2 x 3 7 0 4 or more The team scored a total of 55 goals. Find the value of x. ….......................... (Total for question 2 is 3 marks)

3 The table shows information about the number of goals a team scored in 38 games. Points Frequency 0 7 1 14 2 11 3 6 0 4 or more (a) Find the median number of goals scored. (b) Write down the mode ….......................... (c) Work out the total number of goals the team scored in all 38 games. (1) ….......................... (1) ….......................… (2) (Total for question 3 is 4 marks)

4 Adam is measuring the heights in cm of his tomato plants. Height (cm) Frequency 140 < h  150 7 150 < h  160 10 160 < h  170 15 170 < h  180 19 180 < h  200 9 (a) Estimate the mean height. Give your answer correct to 1 decimal place. ............................................cm (3) (b) Explain why your answer to part (a) is an estimate. ..........................................................................................................................................................… ..........................................................................................................................................................… (1) (Total for question 4 is 4 marks)

5 The table below gives information about the time taken for 20 people to run 5 km. Time (minutes) Frequency 15 < t  20 3 20 < t  25 6 25 < t  30 7 30 < t  40 4 (a) Find the class interval that contains the median. ............................................minutes (1) (b) Work out an estimate for the mean time. ............................................minutes (3) (Total for question 5 is 4 marks)

6 Michael recorded the maximum temperature every day in September. The table shows information about his results. Temperature (°C) Frequency 14 < t  18 4 18 < t  20 10 20 < t  22 8 22 < t  24 5 24 < t  28 3 Calculate an estimate for the mean maximum temperature. ............................................°C (Total for question 6 is 3 marks)

7 The frequency table shows the time taken for 100 people to travel to an event. Time (minutes) Frequency 0 < t  10 14 10 < t  20 16 20 < t  30 23 30 < t  40 29 40 < t  50 12 50 < t  60 6 (a) Find the percentage of people that travelled for more than 30 minutes to the event ..................................…% (1) (b) Find the class interval that contains the median. ..................................… minutes (1) (c) Find an estimate for the mean time taken for people to travel to the event. ..................................… minutes (3) (Total for question 7 is 5 marks)

8 The bar chart shows how many hours of homework 30 students did last week. 10 8 Number 6 of Students 4 2 0 3 to 5 6 to 8 9 to 11 12 to 14 0 to 2 Hours of Homework Calculate an estimate for the mean number of hours of homework. .........................................… hours (Total for question 8 is 3 marks)

Name: Exam Style Questions Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser You may use tracing paper if needed Guidance 1. Read each question carefully before you begin answering it. 2. Donʼt spend too long on one question. 3. Attempt every question. 4. Check your answers seem right. 5. Always show your workings Revision for this topic © CORBETTMATHS 2014

1. The table shows the ages of an under-21 rugby squad. \"\" \" Find the median age. ......................... (1) 2.\" A survey was taken of the amount of money spent at a greengrocers by 50 \" shoppers on a Saturday. The table shows the results. \"\" \" Which class interval contains the median? \" You must show your working. .................... < m ≤ .................... (1) © CORBETTMATHS 2014

3.\" George records the times taken by 20 students to complete a puzzle. \"\" \" Which time interval contains the median time taken to complete the puzzle? .................................................... (1) 4.\" A manager recorded how long each customer spent in his supermarket. \" The table shows his results. \"\" \" Which class interval contains the median? .................................................... (1) © CORBETTMATHS 2014

5.\" The table shows the heights of 100 students. \"\" \" Find the class interval in which the median lies. .................................................... (1) © CORBETTMATHS 2014

Name: ___________________________ GCSE (1 – 9) Sequences Instructions • Use black ink or ball-point pen. • Answer all Questions. • Answer the Questions in the spaces provided – there may be more space than you need. • Diagrams are NOT accurately drawn, unless otherwise indicated. • You must show all your working out. Information • The marks for each Question are shown in brackets – use this as a guide as to how much time to spend on each Question. Advice • Read each Question carefully before you start to answer it. • Keep an eye on the time. • Try to answer every Question. • Check your answers if you have time at the end mathsgenie.co.uk

1 Here are the first five terms of a sequence. 11 16 247 Write down the next two terms in the sequence. ......................… , ......................... (Total for Question 1 is 2 marks) 2 The first term in a sequence is 3. The term to term rule is add 5. Is 97 a term in the sequence? Give a reason for your answer. .................................................................................................................................................................. .................................................................................................................................................................. (Total for Question 2 is 2 mark) 3 Here are the first five terms of a Fibonacci sequence 5 8 123 Write down the next two terms in the sequence. ......................… , ......................... (Total for Question 3 is 2 marks) 4 The nth term of a sequence is 4n + 3 (a) Find the first two terms of this sequence. ......................… , ......................... (b) Is 35 a term in this sequence. You must show how you get your answer. .................................................................................................................................................................. .................................................................................................................................................................. (Total for Question 4 is 2 marks)

5 The nth term of a sequence is n2 + 1 (a) Find the first two terms of this sequence. (b) Is 35 a term in this sequence. ......................… , ......................… You must show how you get your answer. (1) .................................................................................................................................................................. ...............................................................................................................................................................… (1) (Total for Question 5 is 2 marks) 6 Here are the first 5 terms of a sequence. 11 8 5 17 14 (a) Find the next term of this sequence. The nth term of a different sequence is 10n² + 5 .....................…......................... (b) Work out the 5th term of this sequence. (1) 7 Here are the first four terms of a sequence. .....................…......................... 7 13 19 (1) (a) Write down the next term in the sequence. (Total for Question 6 is 2 marks) 25 (b) Explain how you got your answer ......................…......................... (1) .................................................................................................................................................................. (1) (Total for Question 7 is 2 marks)

8 Here are the first four terms of a number sequence. 2359 The rule to continue the sequence is multiply the previous term by 2 and then subtract 1 Work out the 5th term of this sequence. 9 Here are the first 5 terms of a Fibonacci sequence. ......................…......................... (Total for Question 8 is 1 mark) 22 4 Find the 8th term of this sequence. 6 10 10 The nth term of a sequence is n² + 3 .....................…......................... (a) Find the first three terms of this sequence. (Total for Question 9 is 2 marks) (b) Find the 10th term in this sequence. ...................… , ...................… , ...................... (2) .....................…......................... (1) (Total for Question 10 is 3 marks)

11 Here is a sequence of patterns made from white tiles and grey tiles. pattern number 1 pattern number 2 pattern number 3 (a) In the space below, draw pattern number 4. (1) (b) Work out the total number of tiles to make pattern number 7. .....................…......................... (2) Kyle says “There are 4 white tiles in pattern number 3 so there will be 8 white tiles in pattern number 6.” (c) Is Kyle right? You must give a reason for your answer. …........................................................................................................................................…...................... …........................................................................................................................................…...................... (1) (Total for Question 11 is 4 marks)

12 Here is a sequence of patterns made from grey counters. pattern number 1 pattern number 2 pattern number 3 (a) In the space below, draw pattern number 4. (b) Work out the total number of counters to make pattern number 10. (1) 13 Here are the first five terms of a sequence. .....................…......................... 31 27 23 (2) (a) Find the first negative term in the sequence. (Total for Question 12 is 3 marks) 19 15 (b) Is –30 a term in this sequence? ......................…......................… Give a reason for your answer. (2) .................................................................................................................................................................. ...............................................................................................................................................................… (1) (Total for Question 13 is 3 marks)

14 Here are the first 5 terms of an arithmetic sequence. -3 1 5 9 13 (a) Find an expression, in terms of n, for the nth term of this sequence. The nth term of a different arithmetic sequence is 2n – 3 .....................…......................... (2) (b) Is 101 a term in this sequence? Show how you get your answer. .....................…......................... (2) (Total for Question 14 is 4 marks) 15 Here are the first 5 terms of a sequence. 19 24 29 9 14 Find an expression, in terms of n, for the nth term of this sequence. .....................…......................... (Total for Question 15 is 2 marks) 16 Here are the first 5 terms of a sequence. 19 16 13 25 22 Find an expression, in terms of n, for the nth term of this sequence. .....................…......................... (Total for Question 16 is 2 marks)

17 Here are the first four terms of an arithmetic sequence. 4 11 18 25 Write down an expression, in terms of n, for the nth term of the sequence. ......................…......................... (Total for Question 17 is 2 marks) 18 Here are the first four terms of an arithmetic sequence. 35 31 27 23 Write down an expression, in terms of n, for the nth term of the sequence. ......................…......................... (Total for Question 18 is 2 marks) 19 Here are the first five terms of an arithmetic sequence. 21 27 33 39 45 Write down an expression, in terms of n, for the nth term of the sequence. ......................…......................... (Total for Question 19 is 2 marks) 20 Here are the first five terms of an arithmetic sequence. 2 7 12 17 22 Write down an expression, in terms of n, for the nth term of the sequence. ......................…......................... (Total for Question 20 is 2 marks)

Name: Exam Style Questions Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser You may use tracing paper if needed Guidance 1. Read each question carefully before you begin answering it. 2. Donʼt spend too long on one question. 3. Attempt every question. 4. Check your answers seem right. 5. Always show your workings Revision for this topic © CORBETTMATHS 2014

1.! Shown below is a rectangle. ! Work out the perimeter of the rectangle. ! Include suitable units. .................................... (2) 2.! Shown below is a square. ! Work out the perimeter of the square. .................................... ! Include suitable units. (2) © CORBETTMATHS 2014

3.! Shown below is an equilateral triangle. ! Work out the perimeter of the triangle. ! Include suitable units. .................................... (2) 4.! A rectangle has a perimeter of 32cm. ! Write down a possible pair of values for its length and width. Length: ..................cm Width: ..................cm (1) 5.! A rectangle has a perimeter of 20cm. ! Write down a possible pair of values for its length and width. Length: ..................cm Width: ..................cm (1) © CORBETTMATHS 2014

6.! Shown below is an isosceles triangle. ! Calculate the perimeter of the triangle. ............................cm 7.! (2) ! Calculate the perimeter of the shape above. ............................cm (2) © CORBETTMATHS 2014

8. ! Calculate the perimeter of the shape above. ............................cm 9.! Shown below is a rectangle. (2) ! Work out the perimeter. ................................cm ! Give your answer in centimetres. (2) © CORBETTMATHS 2014

10.! The perimeter of a parallelogram is 17cm. ! The length of each long side is 5cm. !! ! Work out the length of each short side. ................................cm (2) 11.! The perimeter of the rectangle and the square are the same. ! Find the width of the rectangle, x. ................................cm (3) © CORBETTMATHS 2014

12.! The length of a rectangle is 13.6 cm ! The perimeter of the rectangle is 37.8cm ! Calculate the width of the rectangle. ................................cm (3) 13.! The regular hexagon is drawn accurately. !! !!! ................................cm ! Find the perimeter of the hexagon. (3) © CORBETTMATHS 2014

14.! Shown below is an equilateral triangle with side length 6cm. ! (a) Find the perimeter of the triangle. ............................cm (1) ! Three equilateral triangles, each with side length 6cm, are put together to make ! one larger shape. ! Jemima says that the perimeter of the larger shape will be three times the ! perimeter of one of the triangles. ! (b) Explain why Jemima is wrong. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) © CORBETTMATHS 2014

15.! ! (a) Name the shape above. ......................... ! (b) Find the perimeter of the shape. (1) ! (c) The diagram shows a regular pentagon. ......................... (1) ! The perimeter of the pentagon is equal to the perimeter of the shape above. ! ! Work out the length of one side of the pentagon. ......................... (2) © CORBETTMATHS 2014

16.! Below is a table top. ! The length of the table is 40cm more than the width of the table. ! The perimeter of the table top is 4.2 metres. ! Find the size of the length and width of the table. length: .............................cm width: .............................cm (4) © CORBETTMATHS 2014

17.! Three regular hexagons are put together to make a larger shape. ! The perimeter of one of the regular hexagons is 18cm. ! Find the perimeter of the larger shape. ............................. (3) © CORBETTMATHS 2014

18.! Mr Jones is a chicken farmer. !! ! He wants to build a new fence around the chicken enclosure. ! Each metre of fencing will cost £7.99 ! Work out the cost of the new fence. ............................. (4) © CORBETTMATHS 2014

19.! A design is made from some identical rectangles and identical squares. ! Each rectangle is twice as long as each square. ! The perimeter of each square is 22cm. ! Calculate the perimeter of the design. .............................cm (4) © CORBETTMATHS 2014