ACT Math FREE Sample Practice Questions

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10 Sample ACT Math Practice Questions

1- Which of the following has the same period and two times the amplitude of the graph
\(y =\) \(cos\) \(x?\)

A. \(y=\)\(cos\) \(2x\)

B. \(y=\)\(cos\)\( (x+2)\)

C. \(y=4 \)\(cos\)⁡\(2x\)

D. \(y=2+2\) \(cos\)\( x\)

E. \(y=4+\)\(cos\) \(x\)

2- Which of the following shows the numbers in increasing order?

A. \(\frac{2}{3},\frac{8}{11},\frac{5}{7},\frac{3}{4}\)

B. \(\frac{2}{3},\frac{5}{7},\frac{8}{11},\frac{3}{4}\)

C. \(\frac{5}{7},\frac{3}{4},\frac{8}{11},\frac{2}{3}\)

D. \(\frac{8}{11},\frac{3}{4},\frac{5}{7},\frac{2}{3}\)

E. None of the above

3- What’s the maximum ratio of the number of women to the number of men in each city?

A. \(0.98\)

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:

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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