ACT math practice test 12

1. In the complex numbers, where i2 = –1, what is the value of 5 + 6imultiplied by 3 – 2i?

F. 27
G. 27i
H. 27 + 8i
J. 15 + 8i
K. 15 – 18i

2. In the following figure, is a chord of the circle centered at O,with . If KL= 12 and MO= 6, what is the area of the circle?

A. 36π
B. 48π
C. 72π
D. 96π
E. 144π

3. Eldridge opened a savings account with an initial balance of $1,000. After that, every month for 8 months, she made one deposit to the account, always for the same amount. During that time, she made just one withdrawal.

Which of the following graphs accurately describes these transactions over an 8-month period?

F.
G.
H.
J.
K.

4. Eldridge opened a savings account with an initial balance of $1,000. After that, every month for 8 months, she made one deposit to the account, always for the same amount. During that time, she made just one withdrawal.

If each of Eldridge’s 8 deposits was in the amount of $200 and her withdrawal was $350, how much money did her account have at the end of 8 months?

A. $850
B. $1,550
C. $2,250
D. $2,350
E. $2,950

5. Martha picked out a pair of shoes she wanted and brought them to the front of the store to pay. The cashier told her that the shoes were on sale for 30% off the original price. She rang up the sale price plus 5% sales tax, so Martha ended up paying $58.80 for the shoes. What was the original price for the shoes?

F. $70
G. $75
H. $80
J. $85
K. $90

6. Which of the following is equivalent to ?

A. 1
B. sin n
C. cos n
D. cot n
E. csc n

7. In the following figure, the large quadrilateral is a square. What is the area of the shaded region in terms of xand y?

F.
G.
H.
J.
K.

8. If and , what is the ratio of f:h?

A. 1:06
B. 1:08
C. 1:10
D. 1:12
E. 1:20

9. If , then y=

F.
G.
H.
J.
K.

10. In the following figure, the base of the pyramid has the same area as the base of the cylinder, and the cylinder is twice the height of the pyramid. What is the ratio of the volume of the pyramid to the volume of the cylinder?

A. 1 to 3
B. 1 to 6
C. 2 to 3
D. 3 to 2
E. 6 to 1

11. Which of the following is a possible solution for x in terms of k for the equation ?

F.
G.
H.
J.
K.

12. If ,what is the value of ab?

A. 1
B. –1
C. 2
D.
E.

13. Which of the following functions has a range of f(x) 4?

F. f(x) = |x+ 4|
G. f(x) = |x– 4|
H. f(x) = |x+ 4| – 4
J. f(x) = |x– 4| + 4
K. f(x) = |x– 4| – 4

14. If , then a=

A.
B. b
C. b2
D. b4
E. b8

15. The following figure shows a regular octagon inscribed in a circle. The arc length from Ato Bis 6π. What is the area of the shaded region of the circle?

F. 8π
G. 16π
H. 24π
J. 36π
K. 64π