ACT Math Practice Test 17
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A rectangular kitchen is 8 feet longer than it is wide. Its area is 240 square feet. How long, in feet, is it?
12
16
20
24
30
What is the equation of the circle in the standard (x, y) coordinate plane that has a radius of 4 units and the same center as the circle determined by x2 +y2 −6y+4 = 0?
x2 + y2 = −4
(x + 3)2 + y2 = 16
(x − 3)2 + y2 = 16
x2 + (y + 3)2 = 16
x2 + (y − 3)2 = 16
The perimeter of a square is 36 units. How many units long is the diagonal of the square?
8
9√2
16
18
18√3
If y ≠ z, what are the real values of x that make the following inequality true?
< 0
All negative real numbers
All positive real numbers
−1⁄3 only
1⁄3 only
3 only
What is cos given that = π⁄4 + π⁄6 and that cos(α + β) = (cos α)(cos β) − (sin α)(sin β)? (Note: You may use the following table of values.)
1⁄4
1⁄2
What is the solution set of |3a − 3| ≥ 12?
a ≥ 5 and a ≤ −5
a ≥ 5 and a ≤ −3
a ≥ −5 and a ≤ 5
a ≥ −5 and a ≤ 3
a ≤ 5 and a ≥ −5
Which of the following calculations will yield an even integer for any integer a?
2a2 + 3
4a3 + 1
5a2 + 2
6a4 + 6
a6 − 3
For what value of b would the following system of equations have an infinite number of solutions?
3x + 5y = 27
12x + 20y = 3b
9
27
36
81
126
If r and s are constants and x2 + rx + 12 is equivalent to (x + 3)(x + s), what is the value of r?
3
4
7
12
Cannot be determined from the given information
A certain rectangle is 5 times as long as it is wide. Suppose the length and width are both tripled. The perimeter of the second rectangle is how many times as large as the perimeter of the first rectangle?
3
5
6
12
15
A triangle, ΔABD, is reflected across the line y = x to have the image ΔA’B’D’ in the standard (x, y) coordinate plane: thus A reflects to A’. The coordinates of point A are (m, n). What are the coordinates of point A’?
(−m, n)
(m, −n)
(−m, −n)
(n, m)
Cannot be determined from the given information.
In the right triangle below, YZ = 10 units, and XZ = 4 units. What is sin Z?
A computer repair person charges $50.00 per hour, plus an additional mileage fee. The charge for mileage varies directly with the square root of the number of miles traveled. If one hour plus 25 miles traveled costs $140.00, what is the total amount charged for one hour plus 36 miles traveled?
$218.00
$196.92
$179.60
$158.00
$143.60
For some real number n, the graph of the line y = (n + 1)x + 6 in the standard (x, y) coordinate plane passes through (4,8). What is the value of n?
−3⁄2
−1⁄2
1⁄2
3⁄2
2
Which of the following expresses the number of miles a runner must travel in a 4-lap race where the course is a circle of radius m miles?
4m
4πm
4πm2
8πm
16πm
When graphed in the standard (x, y) coordinate plane,the lines x = −5 and y = x − 5 intersect at what point?
(−5,−10)
(−5,−5)
(−5,0)
(0,−5)
(0,0)
A horse eats 12 bales of hay in 5 days. At this rate, how many bales of hay does the horse eat in 5 + x days?
12 +
12 + x⁄5
+ x
The picture shown below has a uniform frame-width of 5⁄8 inches. What is the approximate area, in square inches, of the view able portion of the picture?
426.25
481.56
510.40
510.75
540.00
If 38x = 813x−2, what is the value of x?
−2
0
2
3
4
What is the slope of a line that is parallel to the line determined by the equation 5x − 4y = 8?
−4
−5⁄4
5⁄4
2
4
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