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HSPT Math : Concepts

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Example Questions

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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Example Question #1326 : Concepts

Square a

The perimeter of the above square is 40% of what number?

Possible Answers:

57.6

120

19.2

360

Correct answer:

120

Explanation:

The perimeter of a square with sides of length 12 is 4 times this, or

$12 \times 4 = 48$ .

The number of which 48 is 40% can be found by dividing 48 by 40%, or $\frac{40}{100}$ :

$48 \div \frac{40}{100} = 48 \times \frac{100}{40}= 120$ ..

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Example Question #1327 : Concepts

What is the volume of a cube with a side of 9m?

Possible Answers:

81m^3

729m^3

27m^3

9m^3

Correct answer:

729m^3

Explanation:

Since volume is length times width times height, and every side on a cube is equal, multiply

$9\cdot 9\cdot 9=729$

The volume of this cube is 729 .

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Example Question #1328 : Concepts

A cube has six square faces, each with area 64 square inches. Using the conversion factor 1 inch = 2.5 centimeters, give the volume of this cube in cubic centimeters, rounding to the nearest whole number.

Possible Answers:

800 cubic centimeters

8,000 cubic centimeters

400 cubic centimeters

4,000 cubic centimeters

2,000 cubic centimeters

Correct answer:

8,000 cubic centimeters

Explanation:

The volume of a cube is the cube of its sidelength, which is also the sidelength of each square face. This sidelength is the square root of the area 64:

$\sqrt{64}=8$ inches.

Multiply this by 2.5 to get the sidelength in centimeters:

$\times 2.5$ = 20 centimeters.

The cube of this is

$20^{3}$ =8000 cubic centimeters

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Example Question #1329 : Concepts

A cube has a side length of 5 inches. Give the volume and surface area of the cube.

Possible Answers:

25 in^3 ,150 in^2

25 in^3 ,75 in^2

125 in^3 ,150 in^2

125 in^3 ,75 in^2

250in^3, 150 in^2

Correct answer:

125 in^3 ,150 in^2

Explanation:

A cube has all edges the same length. The volume of a cube is found by multiplying the length of any edge by itself twice. As a formula:

Volume=s^3 where is the length of any edge of the cube.

The Surface Area of a cube can be calculated as 6s^2 .

So we get:

Volume =s^3=5^3=125 in^3

Surface area $=6s^2=6\times 5^2=6\times 25=150 in^2$

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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

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

Example Question #1326 : Concepts

Example Question #1327 : Concepts

Example Question #1328 : Concepts

Example Question #1329 : Concepts

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