10 Most Common ACT Math Questions

C
Employer’s revenue: \(0.2x+7000\)

B
The diagonal of the square is 8. Let \(x\) be the side.
Use Pythagorean Theorem: \(a^2 + b^2 = c^2\)
\(x^2 + x^2 = 82 ⇒ 2x^2 = 82 ⇒ 2x^2 = 64 ⇒x^2 = 32 ⇒x= √32\)
The area of the square is:
\(√32 × √32 = 32\)

B
\(x=20+125=145\)

B
By definition, the sine of an acute angle is equal to the cosine of its complement.
Since angle A and B are complementary angles, therefore:
sin A = cos B

E
Solve the system of equations by elimination method.
\(3x-4y= -20\)
\(-x+2y=10\)
Multiply the second equation by 3, then add it to the first equation.
\(3x-4y= -20\)
\(3(-x+2y=10)\)
\(\Downarrow\)
\(3x-4y= -20\)
\(-3x+6y=30)\)
⇒ add the equations
\(2y=10⇒y=5\)

C
Use distance formula:
\(Distance = Rate × time ⇒ 420 = 50 × T\), divide both sides by 50. \(420 / 50 = T ⇒ T = 8.4\) hours.
Change hours to minutes for the decimal part. 0.4 hours \(= 0.4 × 60 = 24\) minutes.

D
\(x\) and \(z\) are colinear. \(y\) and \(5x\) are colinear. Therefore,
\(x+z=y+5x\),subtract \(x\) from both sides,then,\(z=y+4x\)

D
Check each option.
A. \(\frac{3}{4} > 0.8\)
\(\frac{3}{4}\) =0.75 and it is less than 0.8. Not true!
B. \(10\% = \frac{2}{5}\)
\(10\% = 1/10<\frac{2}{5}\). Not True!
C. \(3 < \frac{5}{2}\)
\(\frac{5}{2} =2.5<3\). Not True!
D. \(\frac{5}{6} > 0.8\)
\(\frac{5}{6}\) =0.8333… and it is greater than 0.8. Bingo!
E. None of them above Not True!

C
\(40\%\) of 60 equals to: \(0.40×60=24\)
\(12\%\) of 600 equals to: \(0.12×600=72\)
\(40\%\) of 60 is added to \(12\%\) of \(600: 24+72=96\)

D
The relationship among all sides of special right triangle
30\(^\circ\)-60\(^\circ\)- 90\(^\circ\) is provided in this triangle:

In this triangle, the opposite side of 30\(^\circ\) angle is half of the hypotenuse.
Draw the shape of this question:
The latter is the hypotenuse. Therefore, the latter is 60 ft.