Top 10 8th Grade ACT Aspire Math Practice Questions

C.

D.

5- In the rectangle below if \(y>5\) \(cm\) and the area of a rectangle is \(50 cm^2\) and the perimeter of the rectangle is \(30 cm\), what is the value of \(x\) and \(y\) respectively?

A. \(4, 11\)

B. \(5, 11\)

C. \(5, 10\)

D. \(4, 10\)

6- A football team had \($40,000\) to spend on supplies. The team spent \($22,000\) on new balls. New sports shoes cost \($240\) each. Which of the following inequalities represent how many new shoes the team can purchase.

A. \(240x+22,000 ≤40,000 \)

B. \(240x+22,000 ≥40,000\)

C. \(22,000x+240 ≤40,000\)

D. \(22,000x+240 ≥40,000\)

7- Right triangle ABC has two legs of lengths \(6 cm\) (AB) and \(8 cm\) (AC). What is the length of the third side (BC)?

A. \(4 cm\)

B. \(6 cm\)

C. \(8 cm\)

D. \(10 cm\)

8- If \(3x-5=8.5\), What is the value of \(5x+3\)?

A. \(13\)

B. \(15.5\)

C. \(20.5\)

D. \(25.5\)

9- A bank is offering \(4.5\%\) simple interest on a savings account. If you deposit \($8,000\), how much interest will you earn in five years?

A. \($360\)

B. \($720\)

C. \($1800\)

D. \($3600\)

10- In a party, \(10\) soft drinks are required for every \(12\) guests. If there are \(252\) guests, how many soft drinks is required?

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A. \(21\)

B. \(105\)

C. \(210\)

D. \(2510\)

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Answers:

2- 600
The ratio of boys to girls is \(3:7\).
Therefore, there are \(3\) boys out of \(10\) students. To find the answer, first, divide the number of boys by \(3\), then multiply the result by \(10\).
\(180 ÷ 3 = 60 ⇒ 60 × 10 = 600\)

3- C
the population is increased by \(15\%\) and \(20\%\). \(15\%\) increase changes the population to \(115\%\) of the original population.
For the second increase, multiply the result by \(120\%\).
\((1.15) × (1.20) = 1.38 = 138\%\)
38 percent of the population is increased after two years.

4- B
A linear equation is a relationship between two variables, \(x\) and \(y\), that can be put in the form \(y = mx + b\).
A non-proportional linear relationship takes on the form \(y=mx + b\), where \(b ≠ 0\) and its graph is a line that does not cross through the origin.

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5- C
The perimeter of the rectangle is: \(2x+2y=30→x+y=15→x=15-y \)
The area of the rectangle is: \(x×y=50→(15-y)(y)=50→y^2-15y+50=0\)
Solve the quadratic equation by factoring method.
\((y-5)(y-10)=0→y=5 \)
(Unacceptable, because y must be greater than 5) or \(y=10\)
If \( y=10 →x×y=50→x×10=50→x=5\)

6- A
Let \(x\) be the number of new shoes the team can purchase. Therefore, the team can purchase \(240 x\).
The team had \($40,000\) and spent \($22,000\). Now the team can spend on new shoe \($18,000\) at most.
Now, write the inequality: \( 120x+22.000 ≤40.000\)

7- D
Use Pythagorean Theorem:
\(a^2 + b^2 = c^2\)
\(6^2 + 8^2 = c^2 ⇒ 100 = c^2 ⇒ c = 10\)

8- D
\(3x-5=8.5→3x=8.5 + 5=13.5→x = \frac{13.5}{3}= 4.5\)
Then;
\(5x+3=5 (4.5)+3=22.5+3=25.5\)

9- C
Use simple interest formula:
\(I=prt\)
\((I = interest, p = principal, r = rate, t = time)\)
\(I=(8000)(0.045)(5)=1800\)

10- C
Let \(x\) be the number of soft drinks for \(252\) guests. Write the proportion and solve for \(x\).
\(\frac{10 soft drinks}{12 guests}=\frac{x}{252 guests}\)
\(x = \frac{252×10}{12}⇒x=210\)

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