枫叶国际学校入学测试数学模拟试题

.

MATH PROFICIENCY TEST

Name _________________________

Date _____________________

Record your answer on the answer sheet provided.

1. Simplify: (2x 4y 5) 9. Evaluate −2a 3b −4a 4 for a= −3 and b= −2 a) 6x 12y 15 b) 2x 12y 15 c) 8x 64y 125

a) 432

b) −432

c) −128 d)144

e) −144

d) 8x 12y 15

e) 8x 7y 8

10. Solve: 3x −7 ≥ −22 2. Rewrite 4 −

3

using positive exponents only

and

evaluate the result.

a) x ≤ 5 b) x ≤ −5 c) x ≤ 28 − d) x ≥ −5 e) x ≥ 5 3

1 1 a)

=

b) −3 41 = −12

c) 43 =64

4

64

3

d) − 43 = −64

e) 43 =12

11. Solve: 15 2x −

3

< 7 a) x > 18

b) x < 18

c) x < −3 d) x> −3 e) x < 3

3

Evaluate:

1

2 4

−

49

12. Simplify: (4x −8xy+2y ) −(9x −4xy −7y ) a) −5x −4xy −5y b) −5x −4xy + 9y

a)

7 2

b) 7 − c)

2

2 7 d) 2 − e)

7

− 2 49 c ) −5x + 12xy + 4y d) −5x + 4xy + 9y

e) −5x −12xy + 9y 4 Simplify and rewrite using only positive exponents:

13. How long is BC?

− 2

4x 2

3

2y

( )

a) x 4 4y

6

b) 4y 6 x

4

c) 4y 6

−

x

2

d) 1 y 6

e) y 6

a) 22x - 19x- 23 b) -16x +8x -5 c) 16x -8x - 5 d) 16x -24x+5

5. Write an algebraic equation for the following " After 7 e) 16x -8x +5 is added to a number the sum is divided by4. The result is 12." 14. Simplify:( −7a −19c) −( −12a+30c) −( −21a −11c)

.

7n n

7 a)

=12 b) + 4 =12

c) n + =12

4 7 4

n

n + 7

d)

7 12 12 + = e) = 4 4

a) 26a −38c

b) −26a −22c c) −16a

−60c d) 2a + 22c e) 26a + 38c

15. When 6x y −10x y is completely factored, one

of the factors will be_____ 6. Solve for x given 4(3x −7)= −7 a) 3x −5y b) 2xy c) 2xy

a) 7 6

b) 0 c) 35 − d) 12

7 4 e) 35

12

d ) 3x −5y e) 3x

−5

16. Simplify: ( 2x 4y ) (6x y )

7. Solve for x given 4 −2(3x −4)=1 −(5x+4). a) 12x 12y 6

b) 12x 7y 5

c) 12x 4y 3

a) −9

b) −1

c) 15

d) 3

e) 7

d) 8x 12y 6

e) 8x 7y 5

8. What is the value of the expression − 3x 2 +4x

when x= −5 ?

17. Simplify: 24x −30x ³ +

6x

6

6x

a) −55

b) −95

c) 50 d) 95

e) 55 a ) 4x 5

−5x +x

b) 4x 6 −5x 3+1 c) 4x 5 −5x

+1

d ) 4x 5 −5x e) 18x 5 −36x

Page 1 of 5

18. When (4x −1) (2x +7) is expanded and written in 26. Factor completely: xy −5y −2x + 10 the 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 1 decimal place.

a) x 2

1 −

−

b)

x

6 3

4 2 x 2 4

+

− x

6 3

a) 935.6m

b)

1691.1m c) x 2

4

− −

d) x 6 3 x 2 − x − 63

c)

362.2m d)

557.8m e) x 2

2

−

− x

6 3

e)

271.1m

28. Find the volume, in cubic centimeters, of the solid 20. Multiply: (4x −3) (3x −5x +3) shown where h =12cm, s=7cm, and d=8cm.Express

a ) 12x 4 −9x −20x −27x −9 b) 12x 4 −9x −20x + 27x −9 y our answer to two decimal places.

a) 2077cm b) 435.63cm

c ) 12x 4 + 9x −20x + 27x −9

d ) 12x 4 −9x + 20x + 27x −9 e) 12x 4 + 9x + 20x + 27x −9

c) 1742.54cm

d) 217.82cm

e) 1258.96cm

29. In the diagram shown, A' B' C is the image of

21. Expand and simplify: (3x+4) −3(x+5) ABC. Which type of transformation is shown in the

a) 9x + 18x + 1 b) 9x + 21x + 1 illustration? c) 9x + 9x + 1 d) 9x + 21x + 31 a) dilation e) 9x + 9x + 31 b) translation c) slide

22. Factor: x −4x −12 d) rotation a) (x + 6) (x −2) b) (x + 12) (x −1) e) reflection

c) (x + 2) (x −6) d) (x + 7) ( x −3)

e) (x −4) (x + 3)

30. Find the length of side x. a) 20 23. Factor: 2x −7xy −15y b) 34 a) (2x + 3y) (x −5y) b) (2x −3y) (x + 5y) c) 26 c) (2x −y ) (x −15y) d) (2x −5y) (x + 3y) d) 25 e) (2x+ 5y) (x −3y)

e) 35