Pre-Algebra
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ACT Math Section General
Formulas
100
A radio station offers free competitions. Normally, one in every twenty contestants wins the free competition. What is the probability of losing the free competition?
A. 1/20 B. 1/19 C. 19/20 D. 19/1 E. 20/19
C. 19/20
100
What is the value of x when 2x + 3 = 3x – 4 ?
A) -7 B) -1/5 C) 1 D) 1/5 E) 7
(E) 7
100
Consider the following matrices:
A = [[-1,4],[-2,2]] and B = [[-3,2],[-2,8]]
What is A + B?
[[-4,6],[-4,10]]
100
The slope of the line that goes through the points (−5, 4) and (3,−12) is?
-2
100
If a circle has a diameter of 12, what is the circumference of the circle? (leave your answer in terms of pi)
12pi
100
How many questions are on the Math section of the ACT?
45 Questions
100
What is the formula in order to find the area of a Circle?
pir^2
200
Write as a decimal.
0.12×10^-3
.00012
200
Which of the following equations is equal to √45?
A. 1 ÷ 45. B. 5√9. C. 9√5. D. 3√5 E. 5√3
D. 3√5
200
x and y are real numbers. ai and bi are imaginary numbers. When does ai + x = bi + y ?
A. When a = b
B. When x = y
C. When a = x and b = y
D. When a = y and b = x
E. When a = b and x = y
E. When a = b and x = y
200
In the standard (x, y) coordinate plane, what are the coordinates of the midpoint of a line segment whose endpoints are (-3, 0) and (7, 4)?
(A) (2, 2) (B) (2, 4) (C) (5, 2) (D) (5, 4) (E) (5, 5)
A. (2,2)
200
Consider a cone with a height of 12 inches and a radius at its base of 3 inches. What is the volume of this cone? The formula for area of a cone is
A = 1/3pir^2h
(leave your answer in terms of pi)
36pi
200
True / False:
It is best to answer ONLY the questions you know. DO NOT GUESS!
False, It is important to answer all of the questions in each section of the ACT exam.
200
What is the Distance Formula?
sqrt((x2-x1)^2+(y2-y1)^2)
300
A company purchases cell phones at a cost of x and sells the cell phones at four times the cost. What equation below represents the profit made on each cell phone?
A. x. B. 3x. C. 4x. D. 3 - x. E. 4 - x
B. 3x
300
An internet provider sells internet packages based on low monthly rates. The price for the internet service depends on the speed of the internet connection. The chart above indicates the prices of the various internet packages. Which equation represents the prices of these internet packages?
A. P = (S - 5) +5. B. P = (S + 5) x 5.
C. P = 5 ÷ S. D. P = S x 5. E. P = S ÷ 5
D. P = S x 5
300
If
f(x) = 5x-2
and
g(x) = x^2 +3x
, then what is the value of g(f(-3))?
A. -340. B. -17. C. -2. D. 0. E. 238
E. 238
300
What is the slope of a line that is perpendicular to the line
4𝑥−2𝑦=12?
-1/2
300
If one leg of a triangle is 5cm and the other leg is 12cm, what is the measurement of the hypotenuse of the triangle?
A. 5√12cm
B. 12√5cm
C. √17cm
D. 13cm
E. 17cm
D. 13cm
300
How many minutes do you get to complete the math section of the ACT?
A. As long as you need
B. 50 mins
C. 45 mins
D. 120 mins
B. 50 mins
300
What is the Quadratic Formula?
x=((-b+-sqrt(b^2-4ac))/(2a))
400
What is ½% of 90?
.45
400
(D) $408.04
400
A company sells jeans and T-shirts. J represents jeans and T represents T-shirts in the equations below: 2J + T = $50 J + 2T = $40 Sarah buys one pair of jeans and one T-shirt. How much does she pay for her entire purchase?
F. $10. G. $20. H. $30. J. $70. K. $90
H. $30
400
If a circle with center (-6, 6) is tangent to the x axis in the standard (x, y) coordinate plane, what is the diameter of the circle?
A. -6. B. -12. C. 6. D. 12. E. 36
D. 12
400
A right triangle has a leg that is 4in long and the hypotenuse is 5in long. What is the area of the triangle?
F. 4. G. 5. H. 6. J. 12. K. 20
H. 6
400
Which pf the statements is FALSE
A. Figures are NOT drawn to scale.
B. The word line indicates a straight line.
C. The word average indicates mean
D. You should plan on spending about 5 minutes per problem.
D
400
What is the Midpoint Formula?
M=((x2+x1)/2),((y2+y1)/2)
500
In a shipment of 100 mp3 players, 1% are faulty. What is the ratio of non-faulty mp3 players to faulty mp3 players?
A. 1: 100. B. 99: 100. C. 1: 99
D. 99: 1. E. 1: 499
D. 99: 1
500
What is the largest possible product of 2 even integers whose sum is 22?
F. 11. G. 44. H. 100. J. 120. K. 144
J. 120
500
How many real solutions exist for the following equation:
x^2 + 8 = 0
A. 0. B. 1. C. 2. D. 4. E. 8
A. 0
500
Marta has just bought a new pair of tennis shoes. She wants to wear the new running shoes to run up and down a hill near her house. The measurements of the hill can be placed on a two-dimensional linear graph on which x = 5 and y = 165. If the line crosses the y axis at 15, what is the slope of this hill?
A. 10. B. 20. C. 30. D. 36. E. 75
C. 30
500
In an isosceles triangle, the vertex angle is 36°. What is the measure of one of its base angles?
72°
500
What is the perfect score on the Math Section of the ACT?
36
500
What is the equation for circle with center (h, k) and radius r?
(x-h)^2+(y-k)^2=r^2