ACT Math Practice Test 70

1. In ΔXYZ below, the length of XY is 12 centimeters. How long is YZ, to the nearest tenth of a centimeter? (Note: The law of sines states that in ΔABC with sides length a, b, and c opposite ∠A, ∠B, and ∠C, respectively, .) (Note: sin53° ≈ 0.799, sin59° ≈ 0.857, sin68° ≈ 0.927)

F. 9.6
G. 10.3
H. 11.1
J. 12.9
K. 13.9

2. Jacob used the quadratic equation to find that the solutions to an equation are x = 3±, where c is a positive real number. Which of the following expressions gives these solutions as complex numbers?

A. 3±1ci
B. 3±2ci
C. 3±4ci
D. 3±8ci
E. 3±16ci

3. Points C and D are on the circle with center O as shown in the figure below. The length of CD is 12 millimeters and the measure of is 60°. What is the length of the diameter of this circle?

F. 12
G. 16
H. 20
J. 24
K. 28

4. Anylon cord is stretched from the top of a playground pole to the ground. The cord is 25 feet long and makes a 19° angle with the ground. Which of the following expressions gives the horizontal distance, in feet, between the pole and the point where the cord touches the ground?

A.
B.
C. 25tan19°
D. 25sin19°
E. 25cos19°

5. What are the coordinates of the center of the circle with the equation x2 + 8x + y2 -2y + 8 = 0 in the standard (x,y) coordinate plane?

F. (-4, 1)
G. (-1,-4)
H. ( 1,-4)
J. ( 4,-1)
K. ( 4, 1)

6. Scott's swimming pool has a depth of 8 feet and holds 13,000 gallons of water when full. Because of the warm weather, 10% of the water in the pool evaporates each day. Scott fills the pool with water and comes back the next day to measure the amount of water remaining in the pool. He considers this "Day 1" because it was taken 1 day after the pool was filled, and he labels his measurement as such. The next day, he measures the amount of water again, and he labels the results "Day 2" because it is now 2 days after he filled the pool. If Scott continues, on which day will he measure the pool that it is less than half full?

A. 5
B. 6
C. 7
D. 8
E. 9

7. If = ad - bc, then = ?

F. 2 da - 2cb
G. 2 db - 2ca
H. 4 da - 4cb
J. 4 db - 4ca
K. ad - bc

8. The figure below shows 4 congruent circles, each tangent to 2 other circles and to 2 sides of the square. If the length of a side of the square is 24 inches, then what is the area, in square inches, of 1 circle?

A. 9
B. 9π
C. 36
D. 36π
E. 144

9. Andy has 30 collectible comic books, which he bought in 2005 for $28.95 each. These comic books are currently valued at $34.35 each. Andy will sell these 30 comic books when their combined value is exactly $600.00 more than he paid for them. How much more will the average value per comic book have risen when Andy sells these 30 comic books?

F. $ 14.60
G. $ 12.72
H. $ 10.05
J. $ 7.84
K. $ 5.40

10. Circles with centers G and K intersect at points C and F, as shown below. Points B, G, H, J, K, and D are collinear. The lengths of AC, CE, and HJ are 18 cm, 10 cm, and 3 cm, respectively. What is the length, in centimeters, of BD?

A. 22
B. 25
C. 26
D. 28
E. 29

11. A parabola with vertex (-3,-2) and axis of symmetry y = -2 crosses the y-axis at (0, -2 + 3). At what other point does the parabola cross the y-axis?

F. No other point
G. (0,2 + 3)
H. (0,2 - 3)
J. (0,-2 - 3)
K. Cannot be determined from the given information

12. If z ≠ 4 and z ≠ -4, then which of the following is equivalent to the expression

A.
B.
C.
D.
E.

13. The sides of the angle with measure θ are the positive x-axis and a portion of the line y = -x, as shown in the standard (x,y) coordinate plane below. What is the value of tan θ ?

F. 1
G.
H.
J. -
K. -1

14. The nth term of an arithmetic sequence, an, is given by an = a1 + dn - d, where a1 is the 1st term, and d is the common difference between terms. Which of the following expressions gives d in terms of an, a1, and n ?

A.
B.
C.
D.
E. an - a1 - n

15. For all real positive values of x and y, 2 × 3 = 12y. What is x in terms of y?

F. 2y
G. 3y
H. 4y
J. 6y
K. 7y