MATHEMATICS 2 WORKBOOK

RELATIONS & FUNCTIONS RELATIONS AND FUNCDTIONS 1

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MATHEMATICS 2 FUNTIONS Evaluate each function. -a 2n 1) k ( a) = -3 × 5 ; Find k( 1) 2) f (n) = 4 + 3; Find f (0) 3) p(t) = 2t 2 - 2t; Find p(- 9 ) 4) f (t) = 4t + 2; Find f ( 10) 5) g( n) = n 2 - 2n; Find g(- 3 ) 6) f (n) = -3 ; Find f ( - 1 ) n 1 2 3 5 5 3 7) h(a) = a - a ; Find h( 2) 8) g( t) = - t + ; Find g ( ) 2 4 4 6 1 1 1 n + 3 9) f ( x ) = x + x 2 ; Find f ( ) 10) h( n) = × 5 ; Find h( 0) 2 6 2 Perform the indicated operation. 11) h( x) = -3x - 3 12) h( x) = 2x - 1 g( x ) = x 2 - 4x g( x) = x 2 + 4x Find ( h + g)(x ) h Find ( ) ( x ) g 13) g( x) = -2x - 5 14) f ( x) = 4x + 3 h( x ) = 2x 2 g( x) = 3x - 5 Find ( g × h)(x ) Find ( f × g)(x ) 15) g( x) = 2x - 4 16) h( a) = a 3 - 1 h( x ) = 3x g( a) = 4a - 2 Find ( g + h)(x ) Find (h + g)(a) 17) g( x) = -2x 2 + 3x 18) h( n) = 4n + 4 h( x ) = -x - 5 g( n) = -4n + 1 Find g( 9) ¸ h(9) Find h( g( - 5 )) 5 Worksheet by Kuta Software LLC

19) h(n) = n - 3 20) h( x) = 2x - 3 g( n) = n 2 - 4 + 2n g( x) = 2x ) ( hFind (h × g)(- 1 ) ) Find (- 2 g Find the inverse of each function. 9 x + 17 22) f ( x) = x 21) f ( x ) = 2 -15 + x 5 23) f ( x ) = 24) g( x) = x 5 4 3 x - 6 6 - x 25) f ( x ) = 26) g( x) = 7 3 27) g( x) = -x - 3 3 x + 9 28) f ( x) = 7 1 30) f ( x) = 2x - 4 29) g( x) = -2 - x 2 State if the given functions are inverses. - 5 x - 25 1 31) f ( x ) = 32) f ( x) = -2 - x 6 2 3 4 1 1 g( x) = - x + g( x) = - x - 5 5 2 2 4 16 34) g( x) = 2x + 4 33) f ( x ) = - x - 9 9 x - 4 f ( x) = 1 2 g( x) = 1 - x 2 6 Worksheet by Kuta Software LLC

SYSTEM OF EQUATIONS Solve each system by substitution. 35) y = 3x + 6 36) y = -2x - 5 y = 4x + 8 y = 3x + 5 37) y = x + 3 38) y = 4x y = -4x - 2 y = 3x + 1 39) y = x 40) y = 4x + 7 y = 3x + 4 y = -3x - 7 41) y = -1 42) y = 2x + 8 y = -2x + 5 y = -2x - 4 43) y = -3x + 1 44) y = x - 3 y = 1 y = 2x - 2 Solve each system by elimination. 45) 3 x + 2y = 2 46) - 5 x + 6y = -6 - 5 x - 2y = 2 - 5 x - 6y = 6 47) - 5 x + 2y = 0 48) - 2 x + 2y = -4 - 6 x - 2y = 0 - 5 x - 2y = 11 49) - 3 x + 4y = 15 50) - 5 x + 5y = 10 3 x - y = 3 4 x - 5y = -7 51) 7 x - 12y = 27 52) 2 x + 3y = -23 2 x + 3y = -18 4 x + 6y = -28 53) - 4 x + 2y = -20 54) 2 x - 10y = 6 6 x - 4y = 28 - 3 x + 20y = -9 7 Worksheet by Kuta Software LLC

Solve each system by graphing. 55) x = 42 + 7y 36 6 56) 2 x - - y = 0 8 5 5 3 - y = x 7 3 y - x = -6 y y 10 10 8 8 6 6 4 4 2 2 -10 -8 -6 -4 -2 2 4 6 8 10 x -10 -8 -6 -4 -2 2 4 6 8 10 x -2 -2 -4 -4 -6 -6 -8 -8 -10 -10 57) -10 + 9x = -2y 58) 4 y - 7x = 20 2 y = -10 + x y = -9 y y 10 10 8 8 6 6 4 4 2 2 -10 -8 -6 -4 -2 2 4 6 8 10 x -10 -8 -6 -4 -2 2 4 6 8 10 x -2 -2 -4 -4 -6 -6 -8 -8 -10 -10 8 Worksheet by Kuta Software LLC

QUADRATIC FUNCTIONS Solve each equation by factoring. 59) (n - 5)(n - 4) = 0 60) x( x + 3) = 0 61) (n - 5)(3n - 1) = 0 62) ( r + 3)(r + 4) = 0 63) (3k - 4)(k - 4) = 0 64) ( a + 5) 2 = 0 2 2 65) 8m - 336 = 8m 66) 4k + 20k = -16 67) 7m 2 - 14m = 245 68) n 2 = -14 + 9n Solve each equation by taking square roots. 69) 16p 2 = 25 70) n 2 + 3 = 49 2 2 71) v - 6 = 41 72) x - 8 = 56 73) - 8 p 2 = -64 74) b 2 - 8 = 1 75) 100k 2 - 1 = 8 76) 4n 2 - 1 = 219 9 Worksheet by Kuta Software LLC i

Sketch the graph of each function. 77) y = -2x 2 78) y = x 2 y y 1 5 4.5 -5 -4 -3 -2 -1 1 2 3 4 5 x 4 -1 3.5 -2 3 -3 2.5 -4 2 -5 1.5 1 -6 0.5 -7 -2 -1 1 2 3 4 x -8 -0.5 -9 -1 79) y = 3x 2 80) y = -x 2 y y 1 12 0.5 10 -3 -2 -1 1 2 3 x -0.5 -1 8 -1.5 6 -2 -2.5 4 -3 -3.5 2 -4 -4.5 -8 -6 -4 -2 2 4 6 x -5 81) y = 2x 2 82) y = 4x 2 y y 9 16 8 14 7 12 6 5 10 4 8 3 6 2 4 1 2 -3 -2 -1 1 2 3 4 5 6 7 x -14 -12 -10 -8 -6 -4 -2 2 4 x -1 10 Worksheet by Kuta Software LLC

83) f ( x ) = -( x - 4) 2 + 1 84) f ( x) = -3( x - 1) 2 + 1 y y 3 2 2 -4 -2 2 4 6 8 x 1 -2 1 2 3 4 5 6 7 x -4 -1 -6 -2 -8 -3 -4 -10 -5 -12 85) f ( x ) = 2( x + 3) 2 + 2 86) f ( x) = 2( x + 4) 2 - 2 y y 11 7 10 6 9 5 8 4 7 3 6 2 5 1 4 3 -9 -8 -7 -6 -5 -4 -3 -2 -1 x 2 -1 1 -2 -3 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 x 87) -( y + 4) = ( x + 4) 2 88) ( 1 y + 4) = ( x - 3) 2 y 2 -8 -7 -6 -5 -4 -3 -2 -1 1 x y -1 5 4 -2 3 -3 2 -4 1 -5 -5 -4 -3 -2 -1 1 2 3 4 5 x -6 -1 -7 -2 -8 -3 -9 -4 -5 11 Worksheet by Kuta Software LLC

EXPONENTIAL AND LOGARITHMIC FUNCTIONS Find the inverse of each function. 89) y = log ( 4 x ) 5 2 90) y = log x 6 91) y = log ( x - 4) 92) y = ln 3 x 6 93) y = -7log x 94) y = log ( x - 1) 4 95) y = log ( 3 x + 10) 96) y x - 5) 5 = log (2 4 97) y = 5log ( x - 3) 98) y = log ( x 5 + 1) 4 6 Solve each equation. x + 1 2 x + 1 3k 99) 5 = 5 100) 3 = 243 -2b 3 p - 1 101) 5 = 625 102) 3 = 81 2k -3n 3 103) 6 = 216 104) 4 = 4 -2b 2b + 3 -2x - 3 3 x 105) 4 = 4 106) 3 = 3 -2p - 3 3 p 3m + 2 2 107) 5 = 5 108) 6 = 6 -2x - 3 x 2 x -2x 109) 6 × 6 = 6 110) 125 = 625 -3n 4 -2m 111) 3 = 3 112) 64 × 16 = 1 12 Worksheet by Kuta Software LLC

36 x 1 -3x - 2 114) 5 2v × 25 = 5 -3v 113) -2x - 1 ( = ) ( ) 36 1 6 -3n 3n + 2 2 x - 3 115) 5 = 5 ( 1 ) -3x 1 116) × 8 = 16 2 -n 3 - n 3 117) 5 = 25 118) 16 = 2 Solve each equation. Round your answers to the nearest ten-thousandth. -9n n - 3.9 119) e - 10 = 87 120) 8 - 7 = 76.3 x + 3 n + 8 121) 10 - 9 = 46 122) 9 × 16 = 27 6n -3x 123) 20 - 7 = 55 124) - 9 e = -59 b + 4 n - 8 125) 14 - 9 = 69 126) 10 - 5 = 23 -9n 9 p 127) -4 × 10 = -58 128) 5 × 7 = 34.6 Expand each logarithm. 129) log ( x × y) 130) log u 4 u 132) log u 2 131) log v 3 5 133) log x 134) log x 6 135) log x 136) log x 13 Worksheet by Kuta Software LLC

Condense each expression to a single logarithm. 137) 18log a - 6log b log x log y log z 3 3 5 5 5 138) + + 3 3 3 139) 5 log x + 3log y log x log y 4 4 6 6 140) log z + + 6 2 2 log u log v 142) 4 log u - 8log v 7 7 2 2 141) log w + + 2 3 3 143) 6 log x + 18log y 144) log a + log b + 4log c 9 9 4 4 4 145) 6 log a - 18log b log x log y log z 2 2 7 7 7 146) + + 3 3 3 Solve each equation. 147) log ( - 3 n - 2) = log - n 148) log ( - 2 k - 3) = log ( - 3 k - 7) 149) log 20 = log ( x + 1) 150) log ( 4b - 2) = log ( 3b + 2) 151) log 10 = log ( - 2 k + 8) 152) log ( - 3 x - 2) = log ( 6 - x ) 153) log ( - 4 r - 2) = log ( 2r + 10) 154) log ( k + 5) = log (3k - 5) 155) log ( 3 x - 6) = log ( 2 x - 1) 156) log ( - 2 n + 8) = log ( 10 - 3n) 157) log ( 5n - 5) = log ( n + 3) 158) log ( - 5 n - 10) = log - 4 n 159) log ( 2 x + 7) = log ( 4 x + 5) 160) log ( 9 - 2k) = log (- 3 k - 5) 14 Worksheet by Kuta Software LLC i

Solve each Natural Logarithmic Equation. 161) ln 3m = ln (5m - 6) 162) ln ( 3 x + 4) = ln - x 163) ln ( 6 - a) = ln ( 3a + 2) 164) ln 11 = ln (9 - 2n) 165) ln ( 10 - 4v) = ln - 5 v 166) ln r = ln ( 4 - r) 167) ln ( 5 x - 8) = ln 27 168) ln - 4 x = ln ( 4 - 2x) 169) ln ( b + 9) = ln ( 1 - 2b) 170) ln ( - 3 v - 10) = ln ( - 2 v + 9) 171) 3 + log - 9 n = 6 172) 8 log ( a + 6) = 8 6 4 173) - 9 log ( n - 10) = -27 174) 8 + log 9b = 8 2 6 175) -1 + log ( n + 2) = 2 176) 5 + log ( v + 9) = 8 11 2 177) 2 log ( m - 4) = 2 178) log ( n - 2) - 6 = -7 7 179) -9 + log - p = -11 180) - 3 log 2m = 0 11 181) log 9 - log - x = 1 182) log ( x + 4) - log x = 2 8 8 2 2 183) ln x - ln ( x + 3) = 3 184) log - 5 x - log 3 = 1 5 5 185) log 5 - log ( x + 6) = log 33 186) log ( x 2 - 1) - log 7 = 1 4 4 4 9 9 187) log ( x + 21) + log x = log 72 188) log - 2 x - log 6 = 1 7 7 7 9 9 189) log 7 - log 3 x = 2 190) ln 3 + ln ( x 2 - 5) = ln 33 5 5 15 Worksheet by Kuta Software LLC

Eight circle theorems page The Eight Theorems: First circle theorem - angles at the centre and at the circumference. Second circle theorem - angle in a semicircle. Third circle theorem - angles in the same segment. Fourth circle theorem - angles in a cyclic quadlateral. Fifth circle theorem - length of tangents. Sixth circle theorem - angle between circle tangent and radius. Seventh circle theorem - alternate segment theorem. Eighth circle theorem - perpendicular from the centre bisects the chord Circle Theorem 1: Angles at the centre and at the circumference The angle at the centre is twice the angle at the circumference. (Note that both angles are facing the same piece of arc, CB) …. ............................................................................….................................. Circle Theorem 2: Angle in a semicircle The angle in a semi-cicle is 90°. (This is a special case of theorem 1, with a centre angle of 180°.) …. ............................................................................….................................. Circle Theorem 3: Angles in the same segment Angles in the same segment are equal. (The two angles are both in the major segment; I've coloured the minor segment grey) …. ............................................................................….................................. Circle Theorem 4: Angles in a cyclic quadlateral Opposite angles in a cyclic quadrilateral add up to 180°. [A cyclic quadrilateral has all 4 vertices (corners) touching a circle] …. ............................................................................….................................. 16

Circle Theorem 5: Length of tangents The lengths of the two tangents from a point to a circle are equal. CD = CE …. ............................................................................….................................. Circle Theorem 6: Angle between circle tangent and radius The angle between a tangent (eg DC) and a radius (eg AD) in a circle is 90°. …. ............................................................................….................................. Circle Theorem 7: Alternate segment theorem The angle (α) between the tangent (DC) and the chord (DF) at the point of contact (D) is equal to the angle (β) in the alternate segment*. ie α = β [This is a weird theorem, and needs a bit more explanation: Chord DF splits the circle into two segments. In one segment, there is an angle, β, 'facing' the chord, DF – this segment is called the alternate segment. Partly in the other segment, and partly outside the circle altogether, the angle α, is between the chord DF and the tangent DC] (*Thank you, BBC Bitesize, for providing me with wording for this theorem!) …. ............................................................................….................................. Circle Theorem 8: Perpendicular from the centre bisects the chord The perpendicular from centre A cuts the chord CD at E, the centre point of the chord, so that DE = EC 17

Circle Theorems NOTE: You must give reasons for any answers provided. All diagrams are NOT DRAWN TO SCALE. 1. (a) A, B and C are points on the circumference of a circle, centre, O. AC is the diameter of the circle. Write down the size of angle ABC. * (b) Given that AB = 6cm and BC = 8cm, work out (i) the diameter of the circle, (ii) the area of the triangle (iii) the area and circumference of the circle, leaving your answer in terms of (c) D is a point on the circumference of the circle above such that angle BDC = 60˚. (i) Write down the size of angle CAB. (ii) Work out the size of angle ACB. 18

2. P, Q, R and S are points on the circumference of a circle. Angle PRS = 65˚ and angle QSR = 44˚. Find the size of angle (i) PQS (ii) QPR 3. P, Q and R are points on the circumference of a circle, centre, O. PR is the diameter of the circle and ST is a tangent to the circle at the point R. Angle QRS = 58˚. (a) Work out the size of angle QRP. (b) Work out the size of angle QPR. 2 19

4. R 37 S T U O D O D D R, S and T are points on the circumference of a circle, centre O. ST is a diameter and Angle RST = 37. U is the point on ST such that angle RUS is a right angle. (a) Work out the size of angle URT. (b) Work out the size of angle ROT. (c) Work out the size of angle ORU. (d) Find the size of angle ORT. 20

B 5. A 48 O C D A, B, C and D are points on the circumference of a circle, centre O. BD is a diameter of the circle. Angle CAB = 48. (a) Write down the size of angle BCD. (b) Find the size of angle BDC. (c) Find the size of angle BOC. (d) Find the size of angle CAD. (e) Find the size of angle COD. (f) Find the size of angle OCB. 21

6. P, Q, R and S are points on the circumference of a circle, centre, O. TU is a tangent to the circle at the point S. Angle ROS = 64˚ and angle QSU = 58˚. (i) Find the size of angle: (a) OSQ (b) SQR (c) QPS (d) QRS (ii) Why are the lines QR and OS parallel? (iii) Find the size of angle (a) QRO (b) QSR 7. P, Q, R and S are points on the circumference of a circle, centre, O. PST is a straight line. PQ = PS Angle SOQ = 100˚ and angle RST = 78˚ Work out the size of angle: (a) QRS (b) PQS (c) OQS (d) PSO (e) SQR 22

THE LAW OF SINES Find each measurement indicated. Round your answers to the nearest tenth. 191) Find BC 192) Find AB C A 104° 15° 139° 16° A B B 30 C 20 193) Find AC 194) Find AC C C 29 29° 42° B A 89° 61° B 4 A 195) Find AB 196) Find AB A A 29 14° 91° 29 C B 47° 45° C B 197) Find BC 198) Find AB C C 11 141° 15° 33° B A 25° B 9 A 23 Worksheet by Kuta Software LLC

199) Find AC 200) Find BC C B 4 69° 12° A C 21° 101° B 19 A Solve each triangle. Round your answers to the nearest tenth. 201) m C = 34°, b = 17, c = 14 202) m C = 130°, b = 23, c = 28 203) m C = 52°, b = 30, c = 27 204) m C = 99°, m A = 20°, b = 23 205) m B = 42°, m A = 51°, a = 7 206) m C = 88°, b = 16, c = 15 207) In STR, m S = 16°, r = 40 km, s = 19 km 208) In B C A , m B = 71°, a = 39 km, b = 21 km 209) In YZX, m Y = 158°, x = 40 ft, y = 36 ft 210) In D E F , m E = 6.4°, m F = 136.6°, d = 32.4 m 24 Worksheet by Kuta Software LLC

THE LAW OF COSINES Find each measurement indicated. Round your answers to the nearest tenth. 211) Find BC 212) Find AB C 28 C B A 140° 117° 23 28 16 A B 213) Find AB 214) Find BC B B 28 A 105° 13 30 115° C 21 A C 215) Find AC 216) Find AB 15 C B A 34° 7 30 32° C 17 A B 217) Find BC 218) Find AB B A 19 131° 14 A 27 C 109° B C 13 219) Find BC 220) Find AB A 24 C B 130° 30 15 110° A C 28 B Solve each triangle. Round your answers to the nearest tenth. 221) 222) B B 15 km A 25 cm 13 cm 126° A C 10 km 11 km C 25 Worksheet by Kuta Software LLC

223) 224) A A 16 in 14 in 139° 13 in C 20 in B C 22 in B 225) 226) C B 15 yd 17 yd B A 28 yd 14 mi 13 mi A 9 mi C 227) In TRS, r = 28 in, s = 12 in, m T = 30° 228) In H P K , m H = 107°, k = 16 m, p = 25 m 229) In H P K , p = 19 m, k = 21 m, h = 18 m 230) In YZX, x = 6 m, z = 14 m, y = 9 m SIMPLE PROBABILITIES Represent the sample space using set notation. 231) A sandwich shop has four types of 232) A basket contains one apple, one peach, sandwiches: ham, turkey, chicken, and and one orange. You randomly pick a PB&J. piece of fruit. 233) When a button is pressed, a computer 234) A coffee shop offers French roast and program outputs a random even number Italian roast coffee. greater than 0 and less than 12. You press the button once. 235) The chess club must decide when to meet 236) A room in a house needs to be painted. for a practice. The possible days are The room can be painted white, yellow, or Tuesday or Wednesday. pink. 26 Worksheet by Kuta Software LLC

237) A spinner can land on either red, blue, or 238) The band must decide when to meet for a green. You spin twice. practice. The possible days are Tuesday or Wednesday. The possible times are 3, 4, or 5 p.m. 239) A spinner can land on either red, blue, 240) A coffee shop offers small, medium, and green, yellow, or purple. You flip a coin large sizes. Customers can choose and then spin the spinner. between French roast, Italian roast, and American roast. Find the number of possible outcomes in the sample space. 241) A sandwich shop has three types of 242) Four rooms in a house need to be painted. sandwiches: ham, turkey, and chicken. Each room can be painted white, yellow, Each sandwich can be ordered with white or pink. bread or multi-grain bread. Customers can add any combination of the eight available toppings 243) A softball player bats six times in a game. 244) When a button is pressed, a computer Each at-bat results in an out, getting on program outputs a random even number base, or hitting a home run. greater than 0 and less than 10. You press the button five times. Determine whether the scenario involves independent or dependent events. 245) A cooler contains twelve bottles of sports 246) A cooler contains fourteen bottles of drink: seven lemon-lime flavored and five sports drink: four lemon-lime flavored, orange flavored. You randomly grab a five orange flavored, and five fruit-punch bottle and give it to your friend. Then, flavored. You randomly grab a bottle. you randomly grab a bottle for yourself. Then you return the bottle to the cooler, You and your friend both get lemon-lime. mix up the bottles, and randomly select another bottle. Both times you get a lemon-lime drink. 27 Worksheet by Kuta Software LLC

247) You select a card from a standard shuffled 248) A bag contains six red marbles and five deck of 52 cards. You return the card, blue marbles. Another bag contains seven shuffle, and then select another card. Both green marbles and four yellow marbles. times the card is a diamond. (Note that 13 You randomly pick one marble from each of the 52 cards are diamonds.) bag. One marble is blue and one marble is yellow. 249) There are seven boys and six girls in a 250) A cooler contains thirteen bottles of sports class. The teacher randomly selects one drink: five lemon-lime flavored, three student to answer a question. Later, the orange flavored, and five fruit-punch teacher randomly selects a different flavored. You randomly grab a bottle. student to answer another question. The Then you return the bottle to the cooler, first student is a boy and the second mix up the bottles, and randomly select student is a girl. another bottle. The first time, you get a lemon-lime drink. The second time, you get a fruit-punch. Determine if the scenario involves mutually exclusive events. 251) A magazine contains fourteen pages. You 252) You roll a fair six-sided die. The die open to a random page. The page number shows an odd number or a number greater is seven or eight. than three. 253) A basket contains four apples, five 254) A jar contains six blue marbles numbered peaches, and three pears. You randomly one to six. The jar also contains four red select a piece of fruit. It is an apple or a marbles numbered one to four. You peach. randomly pick a marble. It is red or has an even number. 255) There are five nickels and seven dimes in 256) A bag contains four yellow tennis balls your pocket. Four of the nickels and three numbered one to four. The bag also of the dimes are Canadian. The others are contains four green tennis balls numbered US currency. You randomly select a coin one to four. You randomly pick a tennis from your pocket. It is a nickel or is US ball. It is green or has a number greater currency. than two. State if each scenario involves a permutation or a combination. Then find the number of possibilities. 257) The batting order for nine players on a 10 258) The student body of 70 students wants to person team. elect three representatives. 28 Worksheet by Kuta Software LLC

259) A team of 15 soccer players needs to 260) The student body of 165 students wants to choose three players to refill the water elect a president and vice president. cooler. 261) The student body of 45 students wants to 262) The student body of 185 students wants to elect a president, vice president, secretary, elect two representatives. and treasurer. 263) There are 270 athletes at a meeting. They 264) The batting order for ten players on a 11 each give a Valentine's Day card to person team. everyone else. How many cards were given? 265) 3 out of 15 students will ride in a car 266) A team of 10 basketball players needs to instead of a van choose three players to refill the water cooler. Find the probability of each event. 267) A technician is launching fireworks near 268) Elisa is carrying nine pages of math the end of a show. Of the remaining homework and five pages of English thirteen fireworks, ten are blue and three homework. A gust of wind blows the are red. If he launches ten of them in a pages out of her hands and she is only able random order, what is the probability that to recover nine random pages. What is the all of them are blue? probability that she recovers all of her math homework? 269) A nature preserve has a population of six 270) A chemistry lab requires students to black bears. They have been tagged #1 identify chemical compounds by using through #6, so they can be observed over various tests. Each student is given time. Two of them are randomly selected samples of three different compounds, and captured for evaluation. One is tested labeled A, B, and C. Each student is also for worms and one is tested for ticks. given a list of thirteen possible What is the probability that bear #3 is compounds. If a student does not perform tested for worms and bear #5 is tested for the tests and randomly chooses three from ticks? the list, what is the probability that he guesses all three correctly? 29 Worksheet by Kuta Software LLC

MATHEMATICS 2 STATISTICS Find the mode, median, mean, lower quartile, upper quartile, interquartile range, and sample standard deviation for each data set. 1) Academy Awards Movie # Awards Movie # Awards Movie # Awards Rebecca 2 Million Dollar Baby 4 How Green Was My Valley 5 Wings 2 Ordinary People 4 Terms of Endearment 5 Cavalcade 3 Rain Man 4 Forrest Gump 6 Annie Hall 4 Tom Jones 4 Lawrence of Arabia 7 Chariots of Fire 4 Unforgiven 4 Ben-Hur 11 Hamlet 4 2) Mens Heights (Inches) 3) Length of Book Titles 63 65 66 66 67 68 69 # Words Frequency 69 69 69 70 71 72 73 1 3 76 2 4 3 4 4 1 5 5 4) Age At Inauguration President Age President Age President Age President Age Theodore Roosevelt 42 Calvin Coolidge 51 George Washington 57 Andrew Jackson 61 John F Kennedy 43 Rutherford B Hayes 54 Thomas Jefferson 57 Dwight D Eisenhower 62 Grover Cleveland 47 George W Bush 54 James Madison 57 William H Harrison 68 James A Garfield 49 Woodrow Wilson 56 Harry S Truman 60 Ronald Reagan 69 30 Worksheet by Kuta Software LLC

5) Hours Slept 6) Length of Book Titles Hours Frequency # Words Frequency 4 1 1 1 4.5 1 2 4 5.75 1 3 7 7 2 4 1 7.25 2 5 2 7.5 4 7.75 1 8 4 7) Test Scores 8) Games per World Series 38 42 42 44 44 45 45 Games Frequency 45 45 45 46 46 46 49 4 2 52 54 54 6 5 7 8 9) Times Winning the Basketball Tournament Times WonFrequency 1 9 2 2 3 1 4 1 5 3 10) Games per World Series Games Frequency 4 1 5 3 6 5 7 8 31 Worksheet by Kuta Software LLC

Draw a histogram for each data set. 11) Games per World Series 12) Goals in a Hockey Game 4 4 4 4 5 6 6 7 3 3 3 3 5 5 5 5 7 7 7 7 7 7 13) Shoe Size 14) Boiling Point 6 7.5 7.5 8 8.5 8.5 9 Substance °C Substance °C 9.5 10 Ethanol 78.4 Magnesium 1,091 Nitric Acid 83 Lead 1,750 Sea Water 100.7 Silver 2,162 Phosphorus 280.5 Carbon 4,827 Zinc 907 15) Sales Tax 16) Hits in a Round of Hacky Sack State Percent State Percent 3 3 5 5 5 7 7 8 Montana 0 Nevada 6.85 12 Alaska 0 Minnesota 6.875 Oklahoma 4.5 Indiana 7 Ohio 5.75 Tennessee 7 West Virginia 6 Mississippi 7 Arkansas 6.5 32 Worksheet by Kuta Software LLC

Cumulative Frequency 1. 200 students took a test. The cumulative frequency graph gives information about their marks. 200 Cumulative frequency 160 120 80 40 0 10 20 30 40 50 60 Mark The lowest mark scored in the test was 10. The highest mark scored in the test was 60. Use this information and the cumulative frequency graph to draw a box plot showing information about the students’ marks. 10 20 30 40 50 60 Mark (Total 3 marks) 33

2. Daniel took a sample of 100 pebbles from Tawny Beach. He weighed each pebble and recorded its weight. He used the information to draw the cumulative frequency graph shown on the grid. (a) Use the cumulative frequency graph to find an estimate for (i) the median weight of these pebbles, .............................. grams (ii) the number of pebbles with a weight more than 60 grams. ......................................... (3) Cumulative Frequency 120 100 80 60 40 20 O 10 20 30 40 50 60 70 80 Weight (grams) 34

Daniel also took a sample of 100 pebbles from Golden Beach. The table shows the distribution of the weights of the pebbles in the sample from Golden Beach. Weight (w grams) Cumulative frequency 0 < w ≤ 20 1 0 < w ≤ 30 15 0 < w ≤ 40 36 0 < w ≤ 50 65 0 < w ≤ 60 84 0 < w ≤ 70 94 0 < w ≤ 80 100 (b) On the same grid, draw the cumulative frequency graph for the information shown in the table. (2) Daniel takes one pebble, at random, from his sample from Tawny Beach and one pebble, at random, from his sample from Golden Beach. (c) Work out the probability that the weight of the pebble from Tawny Beach is more than 60 grams and the weight of the pebble from Golden Beach is more than 60 grams ..................................... (4) (Total 9 marks) 3. 40 boys each completed a puzzle. The cumulative frequency graph below gives information about the times it took them to complete the puzzle. (a) Use the graph to find an estimate for the median time ............... seconds (1) 40 Cumulative 30 frequency 20 10 O 10 20 30 40 50 60 Time in seconds 35

For the boys the minimum time to complete the puzzle was 9 seconds and the maximum time to complete the puzzle was 57 seconds. (b) Use this information and the cumulative frequency graph to draw a box plot showing information about the boy’s times. 0 10 20 30 40 50 60 Time in seconds (3) The box plot below shows information about the times taken by 40 girls to complete the same puzzle. 0 10 20 30 40 50 60 Time in seconds (c) Make two comparisons between the boys’ times and the girls’ times. ............................................................................................................................................... ............................................................................................................................................... (2) (Total 6 marks) 4. The cumulative frequency diagram below gives information about the prices of 120 houses. (a) Find an estimate for the number of houses with prices less than £130 000. …………………………… (1) (b) Work out an estimate for the interquartile range of the prices of the 120 houses. £ …………………………… (2) (Total 3 marks) 36

Cumulative frequency 130 120 110 100 90 80 70 60 50 40 30 20 10 0 60 000 80 000 100 000 120 000 140 000 160 000 180 000 200 000 Prices of houses (£) 5. The table shows information about the number of hours that 120 children used a computer last week. Number of hours Frequency (h) 0 < h ≤ 2 10 2 < h ≤ 4 15 4 < h ≤ 6 30 6 < h ≤ 8 35 8 < h ≤ 10 25 10 < h ≤ 12 5 (a) Work out an estimate for the mean number of hours that the children used a computer. Give your answer correct to two decimal places. ………………hours (4) 37

(b) Complete the cumulative frequency table. Number of hours Cumulative frequency (h) 0 < h ≤ 2 10 0 < h ≤ 4 0 < h ≤ 6 0 < h ≤ 8 0 < h ≤ 10 0 < h ≤ 12 (1) 140 120 100 Cumulative frequency 80 60 40 20 2 4 6 8 10 12 Number of hours ( )h (c) On the grid, draw a cumulative frequency graph for your table. (2) (d) Use your graph to find an estimate for the number of children who used a computer for less than 7 hours last week. …………………… (2) (Total 9 marks) 38

6. The table shows information about the heights of 40 bushes. Height (h cm) Frequency 170 ≤ h < 175 5 175 ≤ h < 180 18 180 ≤ h < 185 12 185 ≤ h < 190 4 190 ≤ h < 195 1 (a) Complete the cumulative frequency table. Height Cumulative (h cm) Frequency 170 ≤ h < 175 170 ≤ h < 180 170 ≤ h < 185 170 ≤ h < 190 170 ≤ h < 195 (1) (b) On the grid, draw a cumulative frequency graph for your table. 40 Cumulative frequency 30 20 10 0 170 175 180 185 190 195 Height ( cm)h (2) (c) Use the graph to find an estimate for the median height of the bushes. ……………………… cm (1) (Total 4 marks) 39

PROBABILITY TREES 1. Hannah is going to play one badminton match and one tennis match. 9 The probability that she will win the badminton match is 10 2 The probability that she will win the tennis match is 5 (a) Complete the probability tree diagram. (2) (b) Work out the probability that Hannah will win both matches. (2) ........................................................................... (4 marks) 40

2. There are only red marbles and green marbles in a bag. There are 5 red marbles and 3 green marbles. Dwayne takes at random a marble from the bag. He does not put the marble back in the bag. Dwayne takes at random a second marble from the bag. (a) Complete the probability tree diagram. (2) (b) Work out the probability that Dwayne takes marbles of different colours. ..................................... (3) (5 marks) 41

3. Wendy goes to a fun fair. She has one go at Hoopla. She has one go on the Coconut shy. The probability that she wins at Hoopla is 0.4 The probability that she wins on the Coconut shy is 0.3 (a) Complete the probability tree diagram. (2) (b) Work out the probability that Wendy wins at Hoopla and also wins on the Coconut shy. .............................................. (2) (4 marks) ______________________________________________________________________________ 42