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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

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6 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : Solve Word Problems Leading To Equations: Ccss.Math.Content.7.Ee.B.4a

Gary is twice as old as his niece Candy. How old will Candy will be in five years when Gary is years old?

Possible Answers:

Not enough information is given to determine the answer.

Correct answer:

Explanation:

Since Gary will be 37 in five years, he is 37 - 5 = 32 years old now. He is twice as old as Cathy, so she is $32 \div 2 =16$ years old, and in five years, she will be 16 + 5 = 21 years old.

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Example Question #34 : Solve Word Problems Leading To Inequalities: Ccss.Math.Content.7.Ee.B.4b

A parking garage charges a minimum fee of $\$7$ to park in the garage. It also charges an additional fee of $\$2$ for every hour, or portion of an hour, in which a person parks in the garage. Cliff wants to pay a maximum of $\$20$ to park there. If he pulls into the garage at exactly $7\textup{:}00\textup { AM}$ , when must he leave at latest?

Possible Answers:

$2\textup{:}30\textup { PM}$

$1\textup{:}00\textup { PM}$

$1\textup{:}30\textup { PM}$

$12\textup{:}30\textup { PM}$

Correct answer:

$1\textup{:}00\textup { PM}$

Explanation:

Let be the number of hours that Cliff parks his car in the garage. Since he pays a flat fee of $\$7$ plus $\$2$ per hour or portion thereof, he pays 2X + 7 dollars. Since he does not want to spend more than $\$20$ ,

$2X + 7 \leq 20$

$2X + 7 - 7 \leq 20 - 7$

$2X \leq 13$

$2X \div 2 \leq 13 \div 2$

$X \leq 6.5$

Since a portion of an hour counts as much as an hour, must be a whole number.

$X \leq 6.5$

implies that

$X \leq 6$ .

Cliff can park in the garage for a maximum of 6 hours, and since he entered the garage at $7:00\textup { AM}$ , he must exit hours later:

7+ 6 - 12 = 1 ,

or $1:00\textup { PM}$ .

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Example Question #82 : How To Solve Two Step Equations

Solve the following:

$(12+13)\times2$

Possible Answers:

Correct answer:

Explanation:

$(12+13)\times2$

When solving this problem, remember order of operations PEMDAS. The parentheses come first followed by the multiplication.

12+13=25

$25\times2=50$

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Example Question #1145 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Solve:

$(34+17)\times2$

Possible Answers:

102

Correct answer:

102

Explanation:

$(34+17)\times2$

When solving this problem, remember order of operations PEMDAS. The parentheses come first followed by the multiplication.

34+17=51

$51\times2=102$

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Example Question #201 : Hspt Mathematics

What is the area of a circle with a radius of 10?

Possible Answers:

$\dpi{100} 100\pi$

$\dpi{100} 100$

$\dpi{100} 20\pi$

$\dpi{100} 10\pi$

Correct answer:

$\dpi{100} 100\pi$

Explanation:

The formula for the area of a circle is $\dpi{100} \pi r^{2}$

$\dpi{100} \pi r^{2}= \pi (10)^{2}=100\pi$

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Example Question #202 : Hspt Mathematics

What is the area of a circle with a radius of 7?

Possible Answers:

$49\pi$

$14\pi$

$7\pi$

Correct answer:

$49\pi$

Explanation:

To find the area of a circle you must plug the radius into in the following equation $A=\pi(r^{2})$

In this case the radius is 7 so we plug it into to get $7^{2}=49$

We then multiply it by pi to get our answer $A=49\pi$

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Example Question #203 : Hspt Mathematics

What is the area of a square with a side length of 8?

Possible Answers:

Correct answer:

Explanation:

To solve this question you must know the formula for the area of a rectangle.

The formula is A=B*H

In this case the rectangle is a square so we can plug in the side length for both base and height to yield A=8*8

Perform the multiplication to arrive at the answer of A=64

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Example Question #204 : Hspt Mathematics

Diagram_a

Refer to the above diagram, which shows an equilateral triangle with one vertex at the center of a circle and two vertices on the circle.

What percent of the circle (nearest whole number) is covered by the triangle?

Possible Answers:

18%

It is impossible to tell without knowing the radius.

12%

10%

14%

Correct answer:

14%

Explanation:

Let be the radius of the circle. The area of the circle is

$A_{1} = \pi r^{2}$

is also the sidelength of the equilateral triangle. The area of the triangle is

$A_{2} = \frac{\sqrt{3}}{4} \; r^{2}$

The percent of the circle covered by the triangle is:

$\frac{A_{2} }{A_{1}} \cdot 100= \frac{\frac{\sqrt{3}}{4}r^{2}}{\pi r^{2}}\cdot 100 = \frac{100 \sqrt{3}}{4 \pi } \approx 14$

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Example Question #205 : Hspt Mathematics

Julie wants to seed her rectangular lawn, which measures 265 feet by 215 feet. The grass seed she wants to use gets 400 square feet of coverage to the pound; a fifty-pound bag sells for $66.00, and a ten-pound bag sells for $20.00. What is the least amount of money Julie should expect to spend on grass seed?

Possible Answers:

$\$192$

$\$238$

$\$218$

$\$198$

$\$172$

Correct answer:

$\$198$

Explanation:

The area of Julie's lawn is $265 \cdot215 = 56,975$ square feet. The amount of grass seed she needs is $56,975 \div 400 \approx 142.4$ pounds. This requires three fifty-pound bags, the most economical option since it is cheaper to buy a fifty-pound bag for $66 than five ten-pound bags for $100.00. Julie will spend $\$66 \cdot3 = \$198$

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Example Question #314 : Ssat Middle Level Quantitative (Math)

Thingy

Above is a figure that comprises a red square and a white rectangle. The ratio of the length of the white rectangle to the sidelength of the square is 5:3 . What percent of the entire figure is red?

Possible Answers:

$40 \%$

$36 \%$

$60 \%$

$37.5 \%$

$62.5 \%$

Correct answer:

$37.5 \%$

Explanation:

To make this easier, we will assume that the rectangle has length 5 and the square has sidelength 3. Then the area of the entire figure is

$(3 + 5) \times 3 = 24$ ,

and the area of the square is

$3 \times 3 = 9$

The square, therefore, takes up

$\frac{9}{24} \times 100 = \frac{900}{24} = 37.5 \%$

of the entire figure.

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #2 : Solve Word Problems Leading To Equations: Ccss.Math.Content.7.Ee.B.4a

Example Question #34 : Solve Word Problems Leading To Inequalities: Ccss.Math.Content.7.Ee.B.4b

Example Question #82 : How To Solve Two Step Equations

Example Question #1145 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Example Question #201 : Hspt Mathematics

Example Question #202 : Hspt Mathematics

Example Question #203 : Hspt Mathematics

Example Question #204 : Hspt Mathematics

Example Question #205 : Hspt Mathematics

Example Question #314 : Ssat Middle Level Quantitative (Math)

All HSPT Math Resources

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