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HSPT Math : HSPT Mathematics

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

Example Questions

Example Question #1 : Rectangles

A rectangle has a width of 2x. If the length is five more than 150% of the width, what is the perimeter of the rectangle?

Possible Answers:

10(x + 1)

6x² + 5

5x + 10

6x² + 10x

5x + 5

Correct answer:

10(x + 1)

Explanation:

Given that w = 2x and l = 1.5w + 5, a substitution will show that l = 1.5(2x) + 5 = 3x + 5.

P = 2w + 2l = 2(2x) + 2(3x + 5) = 4x + 6x + 10 = 10x + 10 = 10(x + 1)

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Example Question #2 : Quadrilaterals

ABCD is a parallelogram. BD = 5. The angles of triangle ABD are all equal. What is the perimeter of the parallelogram?

Figure_1

Possible Answers:

$10\sqrt{3}$

$15\sqrt{3}$

$11\sqrt{2}$

Correct answer:

Explanation:

If all of the angles in triangle ABD are equal and line BD divides the parallelogram, then all angles in triangle BDC must be equal as well.

We now have two equilateral triangles, so all sides of the triangles will be equal.

All sides therefore equal 5.

5+5+5+5 = 20

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Example Question #1311 : Concepts

A square has a length of $19\textup{ feet}$ . What is the perimeter in inches?

Possible Answers:

$67\textup{ inches}$

$912\textup{ inches}$

$894\textup{ inches}$

$76\textup{ inches}$

$\frac{19}{3}\textup{ inches}$

Correct answer:

$912\textup{ inches}$

Explanation:

The square perimeter is $\textup{4 times}$ the side length.

P=4s

Substitute and multiply to find the perimeter.

$P=4(19\textup{ feet})= 76 \textup{ feet}$

There are $\textup{12 inches}$ in $\textup{1 foot}$

Multiply the perimeter with .

$76 \textup{ feet} (\frac{12 \textup{ inches}}{1 \textup{ foot}}) = 912 \textup{ inches}$

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Example Question #131 : Quadrilaterals

Rectangle

Give the perimeter of the above rectangle in centimeters, using the conversion factor 91.44 centimeters per yard.

Possible Answers:

$1,097.28 \textrm{ cm}$

$2,194.56 \textrm{ cm}$

$2,011.68 \textrm{ cm}$

$4,389.12 \textrm{ cm}$

$1,005.84 \textrm{ cm}$

Correct answer:

$2,011.68 \textrm{ cm}$

Explanation:

The perimeter of the rectangle is 8 + 3 + 8 + 3 = 22 yards. To convert this to centimeters, multiply by the given conversion factor:

$91.44 \times 22 = 2,011.68$ centimeters.

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Example Question #1321 : Concepts

Find the perimeter of a rectange with length 9 and width 4.

Possible Answers:

Correct answer:

Explanation:

To solve, simply use the formula for the perimeter of a rectangle.

Given the length of the rectangle is 9 and the width is 4; substitute these values into the perimeter equation.

Thus,

P=2(l+w)=2*(9+4)=2*13=26

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Example Question #1913 : Hspt Mathematics

A square has perimeter 20. Which of the following gives 75% of the length of one of its diagonals?

Possible Answers:

$\frac{15\sqrt{3}}{4}$

$\frac{15\sqrt{2}}{4}$

$\frac{15\sqrt{3}}{2}$

$\frac{15\sqrt{2}}{2}$

Correct answer:

$\frac{15\sqrt{2}}{4}$

Explanation:

The length of one side of a square is one-fourth of its perimeter, which here makes its length

$\frac{1}{4} \cdot 20 = 5$ .

The length of a diagonal of a square is $\sqrt{2}$ times this sidelength, so the square has diagonals of length $5 \sqrt{2}$ .

75% of this is

$5 \sqrt{2} \cdot \frac{75}{100} = \frac{5 \sqrt{2}}{1} \cdot \frac{3}{4} = \frac{15 \sqrt{2}}{4}$ .

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Example Question #1322 : Concepts

A circle has radius 8. Which of the following gives 60% of the circumference of this circle?

Possible Answers:

$\frac{192\pi }{5}$

$\frac{96 \pi }{5}$

$\frac{24 \pi }{5}$

$\frac{48 \pi }{5}$

Correct answer:

$\frac{48 \pi }{5}$

Explanation:

The circumference of a circle is its radius mulitplied by $2 \pi$ . The radius is 8, so the circumference is

$8 \cdot 2 \pi = 16 \pi$ .

60% of this is

$16 \pi \cdot \frac{60}{100}= 16 \pi \cdot \frac{3}{5} = \frac{48 \pi }{5}$

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Example Question #1323 : Concepts

Rectangle 2

Note: Figure NOT drawn to scale.

The above rectangle has area 18. Give its perimeter.

Possible Answers:

$47\frac{15}{16}$

$17\frac{15}{26}$

$8\frac{41}{52}$

$18\frac{11}{16}$

Correct answer:

$17\frac{15}{26}$

Explanation:

The product of the length and the width of a rectangle is its area, so to find the length, divide the area by the width:

$L = A \div W = 18 \div 3\frac{1}{4} = \frac{18}{1} \div \frac{13}{4} = \frac{18}{1} \cdot \frac{4} {13} = \frac{72}{13}$

We can use $L = \frac{72}{13}$ and $W = 3\frac{1}{4} = \frac{13}{4}$ to find the perimeter by adding each of these twice:

$P = \frac{72}{13} + \frac{13}{4} + \frac{72}{13} + \frac{13}{4}$

$P = \frac{288}{52} + \frac{169}{52} +\frac{288}{52} + \frac{169}{52}$

$P = \frac{914}{52} = \frac{457}{26} = 17\frac{15}{26}$

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Example Question #1324 : Concepts

A circle has area $\frac{16 }{25}\pi$ . Give its circumference.

Possible Answers:

$\frac{8}{5} \pi$

$\frac{64}{625} \pi$

$\frac{4}{5} \pi$

$\frac{256}{625} \pi$

Correct answer:

$\frac{8}{5} \pi$

Explanation:

The area of a circle, given its radius , is

$A = \pi r^{2}$

Set $A = \frac{16 }{25}\pi$ to find the radius.

$\frac{16 }{25}\pi = \pi r^{2}$

$\frac{16 }{25}\pi \div \pi = \pi r^{2} \div \pi$

$\frac{16 }{25} = r^{2}$

$r = \sqrt{\frac{16}{25}} = \frac{\sqrt{16}}{\sqrt{25}} = \frac{4}{5}$

Multiply this radius by $2 \pi$ to find the circumference:

$\frac{4}{5} \cdot 2 \pi = \frac{8}{5} \pi$

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Example Question #1325 : Concepts

Rectangle 2

The above rectangle has area 100. Give its perimeter in terms of .

Possible Answers:

$2N + \frac{200}{N}$

$100 N - N^{2}$

$50 N - N^{2}$

$N + \frac{100}{N}$

Correct answer:

$2N + \frac{200}{N}$

Explanation:

The width of a rectangle is the quotient of its area and its length, which are 100 and , respectively. Therefore, the width is $\frac{100}{N}$ . The four sides measure , , $\frac{100}{N}$ , and $\frac{100}{N}$ ; the perimeter is their sum, which is

$N + N + \frac{100}{N} + \frac{100}{N} = 2N + \frac{200}{N}$

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1 : Rectangles

Example Question #2 : Quadrilaterals

Example Question #1311 : Concepts

Example Question #131 : Quadrilaterals

Example Question #1321 : Concepts

Example Question #1913 : Hspt Mathematics

Example Question #1322 : Concepts

Example Question #1323 : Concepts

Example Question #1324 : Concepts

Example Question #1325 : Concepts

All HSPT Math Resources

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