枫叶国际学校入学测试数学模拟试题 (2).doc

MATH PROFICIENCY TESTName_ Date_Record your answer on the answer sheet provided.1. Simplify: (2x4y5) 9. Evaluate 2a3b 4a4 for a= 3 and b= 2a) 6x12y15 b) 2x12y15 c) 8x64y125a) 432 b) 432 c) 128 d)144 e) 144d) 8x12y15 e) 8x7y810. Solve: 3x 7 222. Rewrite 4 3 using positive exponents only andevaluate the result.a) x 5 b) x 5 c) x 28 d) x 5 e) x 531 1a)= b) 3 41 = 12 c) 43 =644 643d) 43 = 64 e) 43 =1211. Solve:15 2x3 18 b) x 18 c) x 3 e) x 33 Evaluate:1 2 4 49 12. Simplify: (4x 8xy+2y ) (9x 4xy 7y )a) 5x 4xy 5y b) 5x 4xy + 9ya)72b)7 c)227d)2 e)7249c) 5x + 12xy + 4y d) 5x + 4xy + 9ye) 5x 12xy + 9y4 Simplify and rewrite using only positive exponents: 13. How long is BC? 24x2 32y ( )a)x44y6b)4y6x4c)4y6x2d)1y6e) y6a) 22x - 19x- 23 b) -16x +8x -5c) 16x -8x - 5 d) 16x -24x+55. Write an algebraic equation for the following After 7 e) 16x -8x +5is added to a number the sum is divided by4. The result is12. 14. Simplify:( 7a 19c) ( 12a+30c) ( 21a 11c)7n n 7a) =12 b) + 4 =12 c) n + =124 7 4n n + 7d) 7 12 12+ = e) =4 4a) 26a 38c b) 26a 22c c) 16a 60cd) 2a + 22c e) 26a + 38c15. When 6x y 10x y is completely factored, oneof the factors will be_6. Solve for x given 4(3x 7)= 7 a) 3x 5y b) 2xy c) 2xya)76b) 0 c)35 d)1274e)3512d) 3x 5y e) 3x 516. Simplify: ( 2x4y ) (6x y )7. Solve for x given 4 2(3x 4)=1 (5x+4).a) 12x12y6 b) 12x7y5 c) 12x4y3a) 9 b) 1 c) 15 d) 3 e) 7d) 8x12y6 e) 8x7y58. What is the value of the expression 3x2 +4xwhen x= 5 ?17. Simplify:24x 30x + 6x66xa) 55 b) 95 c) 50 d) 95 e) 55a) 4x5 5x +x b) 4x6 5x3+1 c) 4x5 5x +1 d) 4x5 5x e) 18x5 36xPage 1 of 518. When (4x 1) (2x +7) is expanded and written in 26. Factor completely: xy 5y 2x + 10the form Ax +Bx + C, what is the value of A + B + C? a) (x + 5) (y 2) b) (x 5) (y + 2)a) 31 b) 27 c) 12 d) 27 e) 31 c) (x + 2) (y + 5 d) (x 5) (y 2)e) (x 2) (y 5 ) x x 19. Expand and simplify: 7 9 + 2 2 27. Find the area of the figure, in square meters, to 1decimal place.a)x 2 1 b)x 6 34 2x24+ x6 3a) 935.6mb) 1691.1mc)x24 d)x 6 3x2 x 63c) 362.2md) 557.8me)x22 x6 3e) 271.1m28. Find the volume, in cubic centimeters, of the solid20. Multiply: (4x 3) (3x 5x +3) shown where h =12cm, s=7cm, and d=8cm.Express a) 12x4 9x 20x 27x 9b) 12x4 9x 20x + 27x 9your answer to two decimal places.a) 2077cm b) 435.63cm c) 12x4 + 9x 20x + 27x 9 d) 12x4 9x + 20x + 27x 9e) 12x4 + 9x + 20x + 27x 9c) 1742.54cm d) 217.82cme) 1258.96cm29. In the diagram shown, A B C is the image of21. Expand and simplify: (3x+4) 3(x+5) ABC. Which type of transformation is shown in thea) 9x + 18x + 1 b) 9x + 21x + 1 illustration?c) 9x + 9x + 1 d) 9x + 21x + 31 a) dilatione) 9x + 9x + 31 b) translationc) slide22. Factor: x 4x 12 d) rotationa) (x + 6) (x 2) b) (x + 12) (x 1) e) reflectionc) (x + 2) (x 6) d) (x + 7) ( x 3)e) (x 4) (x + 3) 30. Find the length of side x.a) 2023. Factor: 2x 7xy 15y b) 34a) (2x + 3y) (x 5y) b) (2x 3y) (x + 5y) c) 26c) (2x y ) (x 15y) d) (2x 5y) (x + 3y) d) 25e) (2x+ 5y) (x 3y) e) 3524. When 6x + x 15 is factored completely, one of 31. A triangle has vertices A( 5, 2), B( 3, 5), andthe factors will be _ C( 2, 1). Which of the following translations willa) 2x + 5 b) 2x + 3 c) 2x 3 d) 2x 5 e) 3x 5 place the image triangle in the fourth quadrant?a) 5 units left, 7 units down25. When (4x 7) 10(4x 7)+24 is factored b) 6 units right, 7 units downcompletely, one of the factors will be_ c) 4 units left, 7 units upa) 4x + 13 b) 4x + 3 c) x + 6 d) x + 4 e) 4x 11 d) 6 units right, 7 units upe) 4 units right, 7 units downPage 2 of 532. In the diagram shown, ABC DEF, c = 5, e = 7,and f= 9. Find a.d) r = 15cos25 e) r =15cos 2534a) c)2312e)3158 b)d)3 69 2538. A 2.5 metre ladder leans against a house forming a30 angle with the house. Exactly how far is the base ofthe ladder from the house?a) 1.35m b) 1.50mc) 2.25m d) 1.75m33. Given the DEF is congruent to PQR, find the e) 1.25mangle that is congruent to Ra) P b) F 39. The scale shown on a map of Canada is 1cm=c) D d) Q 120km. On the map the distance between Winnipeg ande) E Saskatoon is 5.7cm. How far apart are Winnipeg andSaskatoon to the nearest kilometre?34. Express tan A as a ratio of the variables given in a) 444km b) 516km c) 684kmABC. d) 276km e) 660kma)d)caacb)e)c babc)ba1a) 34 b) c)3422534d) 34 e)34225140. Evaluate: (3 + 5 )2 212 1335. In ABC, which of the following is equal to a) sinCb) tan Cc) cosA?41. Evaluate:43 38 3( )534( )d) cosCe) tan Aa) 1 b) 6 c)127d)13e) 936. Which of the following equations can be used to 42. Find the value of x in this diagram.find the length of x? a) 8.8 b) 12.8a) cos35 =d) cos35 =e) sin35 =20x x20x1414b) sin35 =xc) tan55 =x30c) 9.6 d) 10.2e) 7.243. Find the area of the shaded region where S = 12.a) 12.65 unitsb) 30.90 unitsc) 43.56 units37. Which equation can be used to correctly determine d) 3.90 unitsthe length of side r? e) 115.73 unitsa) r = 15tan25b) r = 15sin25 44. A right triangle has one leg of length a and ac) r =15sin 25hypotenuse of length c. Express the area of this trianglein terms of a and c.Page 3 of 5a)d) + a c a 2 2= b) 2A acA = e) 2 AAa c a( )= c)2=a c a2 2 a c a2A=c a c2 221 1a) (2x 3)= 28 b) x(x 3)= 28 2 21c) x(x + 3)= 28 d) x(x + 3)= 2821e) (2x + 3)= 28245. If Ax + 7x + Bx +30 is evaluated for x = 1 theresult is 54. When the expression is evaluated for x = 2the result is 6. What is the value of A?a) 3 b) -3 c) 2 d) -2 e) 451. Simplify:1a) b)23x + 5 6x 64 8 +12x 5c) 16 d) 2 e)103x246. The perimeter of a rectangle is 18x + 24 and the 52. Solve ax+ b = cx + d for x.width is 2x - 9. What is the length?a) 7x 3 b) 7x + 3 c) 16x 15d) 7x +21 e) 16x + 33a) x=d) x=b d+a c+d bc ab) x=e) x=d ba cd ba c+c) x=d b+a c47. A guy wire attached to the top of an 84m radioantenna is bolted to the ground 52m from the base of 53. The radius of the circle is 12cm. What is the area ofthe tower. If the wire is tight, how long is the wire? the shaded region?Express your answer to the nearest hundredth of a a) 46.8cm b) 41.1cmmetre. c) 76.8cm d) 68.2cma) 98.79cm b) 93.30cm e) 86.4cmc) 95.56cm d) 89.35cme) 136.00cm54. There are 3 dots in the first figure and 7dots in the48. A rectangle has both of its sides increased by 20%. second figure. If this pattern is continued, how manyBy what percent dose its area increase? dots will be in the nth Figure?a) 40% b) 44% c) 140%d) 84% e) 144%49. A cone with radius r = 3cm and height h = 9cm justfits inside a cylinder with the same height and radius. 55. If the pattern shown is continued, then what is the How many cubic centimetres are in the space betweennumber at the end of the 30th row?the two figures. Round your answer to 2 decimal 1places. 2 3a) 85cm b) 113cm 4 5 6c) 236cm d) 170cm 7 8 9 10e) 57cm50. The base of a triangle is 3units more than the height,the area of the triangle is 28 square units. If the heightis represented by x, which equation could be used tofind the measure of the height of the triangle?Page 4 of 5Fill in