ACT Math FREE Sample Practice Questions
ACT Math FREE Sample Practice Questions is a multiple-choice math challenge from Effortless Math. Read the problem, choose from the answer options below, then open the solution to see the full step-by-step working and check your reasoning against it.
B. (0.97)
C. (0.96)
D. (0.95)
E. (0.94)
4- What’s the ratio of the percentage of men in city A to the percentage of women in city C?
A. (frac{10}{9})
B. (frac{9}{10})
C. (1)
D. (frac{19}{20})
E. (frac{20}{19})
5- How many women should be added to city D to change the ratio of women to men to (1.2)?
A. (130)
B. (129)
C. (132)
D. (131)
E. (133)
6- In (1999), the average worker’s income increased by ($2,000) per year starting from ($24,000) annual salary. Which equation represents income greater than average? ((I =) income, (x = )number of years after (1999))
A. ( I > 2000 x + 24000)
B. ( I > – 2000 x + 24000)
C. ( I < -2000 x + 24000)
D. ( I < 2000 x – 24000)
E. ( I < 24,000 x + 24000)
7- What are the values of mode and median in the following set of numbers?
(1,2,2,5,4,4,3,3,3,1,1)
A. Mode: (1), (2) Median: (2)
B. Mode: (1), (3) Median: (3)
C. Mode: (2), (3) Median: (2)
D. Mode: (1), (3) Median: (2.5)
E. Mode: (3), Median: (3)
8- If (60%) of (x) equal to (30%) of 20, then what is the value of ((x+5)^2)?
A. (25.25)
B. (26)
C. (26.01)
D. (2025)
E. (225)
9- In the (xy)-plane, the point ((4,3)) and ((3,2)) are on line A. Which of the following equations of lines is parallel to line A?
A. (y=3x)
B. (y=10)
C. (y=frac{x}{2})
D. (y=2x)
E. (y=x)
10- When pointing A ((10, 3)) is reflected over the y-axis to get point B, what are the coordinates of point B?
A. ((10, 3))
B. ((-10, -3))
C. ((-10, 3))
D. ((10, -3))
E. ((0, 3))
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Answers:
1- D
The amplitude in the graph of the equation (y=a)(cos)(bx) is a. ((a) and (b) are constant)
In the equation (y=)(cos)(x), the amplitude is (2) and the period of the graph is (2π).
The only option that has two times the amplitude of graph (y = )cos (x) is (y=2+2) cos (x)
They both have an amplitude of (2) and a period of (2π).
2- B
(frac{2}{3}≅0.67,frac{8}{11}≅0.73,frac{5}{7}≅0.71,frac{3}{4}=0.75)
3- B
ratio of A: (frac{570}{600}=0.95)
ratio of B: (frac{291}{300}=0.97)
ratio of C: (frac{665}{0.95}=0.95)
ratio of D: (frac{528}{550} =0.96)
4- E
First, find the percentage of men in city A and the percentage of women in city C.
Percentage of men in city A =(frac{600}{1170}) and percentage of women in city C =(frac{665}{1365})
Find the ratio and simplify.
(frac{frac{600}{1170}}{frac{665}{1365}}=frac{20}{19})
5- C
(frac{528+x}{550}==1.2→528+x=660→x=132)
6- A
Let (x) be the number of years. Therefore, ($2,000) per year equals (2000)(x).
starting from($24,000) annual salary means you should add that amount to (2000)(x).
Income more than that is:
(I > 2000 x + 24000)
7- B
We write the numbers in the order: (1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5)
The mode of numbers is: (1) and (3), median is: (3).
8- E
(0.6x=(0.3)×20→x=10→(x+5)^2=(15)^2=225)
9- E
The slop of line A is: m(= frac{y_2-y_1}{x_2-x_1}=frac{3-2}{4-3}=1)
Parallel lines have the same slope and only choice E ((y=x)) has slope of (1).
10- C
When points are reflected over (y)-axis, the value of (y) in the coordinates doesn’t change and the sign of (x) changes. Therefore, the coordinates of point B is ((-10,3)).
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Official source: the structure of the ACT, the sections it covers and the time allowed for each are published by ACT, Inc., the organization that writes and administers the test, at act.org.
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