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ISEE Middle Level Math : ISEE Middle Level (grades 7-8) Mathematics Achievement

Study concepts, example questions & explanations for ISEE Middle Level Math

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All ISEE Middle Level Math Resources

6 Diagnostic Tests 303 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #13 : How To Find Length Of A Line

The point (2,-2) lies on a circle. What is the approximate length of the radius of the circle if the center is (3,-5) ?

Possible Answers:

$d=\sqrt{10}$

$d\approx 7$

$d=\sqrt{5}$

$d\approx5$

Correct answer:

$d=\sqrt{10}$

Explanation:

Because the radius is the distance from center to any point on a circle, the distance formula is used to find the measurement of the radius.

$d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2}- y_{1})^{2}$

$d = \sqrt{(3-2)^{2} + (-5--2)^{2}$

$1^{2} = 1\times1 = 1$

$-3^{2} = -3\times -3 = 9$

$d = \sqrt{1+9}$

$d =\sqrt{10}$

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Example Question #82 : Geometry

If the diameter of a circle is 12cm , then what is $\frac{1}{3}$ of the circle's radius?

Possible Answers:

2cm

4cm

10cm

8cm

Correct answer:

2cm

Explanation:

Radius is $\frac{1}{2}$ of the diameter.

If the diameter is 12cm , then the radius is 6m.

$\frac{1}{2}\cdot \frac{12}{1}=\frac{12}{2}=\frac{2\cdot6}{2}=6$

Therefore

$\frac{1}{3}$ of 6cm is,

$\frac{1}{3}\cdot \frac{6}{1}=\frac{6}{3}=\frac{3\cdot 2}{3}=2cm$ .

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Example Question #11 : Lines

Find the slope of a line that passes through A (-5,-1) and B (3,-1) .

Possible Answers:

The slope is undefined.

m = 0

m = 8

m = -1

Correct answer:

m = 0

Explanation:

Use the slope formula to solve:

$m = \frac{y_{2} -y_{1}}{x_{2} - x_{1}}$

Given the following points.

A (-5,-1)=(x_1,y_1)

B (3,-1)=(x_2,y_2)

The slope can be calculated as follows.

$m = \frac{-1 - (-1)}{3- (-5)}$

$m = \frac{0}{8}$

m = 0

Because the coordinates were the same for points A and B, this would form a horizontal line. The slope of any horizontal line is

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Example Question #12 : Lines

Find the length of a line from the point to the point .

Possible Answers:

30.4

Correct answer:

30.4

Explanation:

Find the length of a line from the point to the point .

To find this distance, we need to use distance formula (which is really similar to Pythagorean Theorem)

Distance formula is as follows

$d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

Where our x's and y's come from our ordered pairs.

So, let's plug and chug

$d=\sqrt{(9--12)^2+(14-36)^2}$

Simplify

$d=\sqrt{(21)^2+(-22)^2}$

$d=\sqrt{441+484}=\sqrt{925}\approx30.4$

So our answer is 30.4

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Example Question #21 : Lines

What is the length of a line segment with end points (3,5) and (6,1) ?

Possible Answers:

Correct answer:

Explanation:

The length of a line segment can be determined using the distance formula:

$D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$D=\sqrt{(3-6)^2+(5-1)^2}$

$D=\sqrt{-3^2+4^2}$

$D=\sqrt{9+16}=\sqrt{25}=5$

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Example Question #91 : Geometry

Prism

Give the volume of the above box in cubic centimeters.

Possible Answers:

$32,400 \textrm{ cm}^{3}$

$324,000 \textrm{ cm}^{3}$

$216,000 \textrm{ cm}^{3}$

$21,600\textrm{ cm}^{3}$

$28,800 \textrm{ cm}^{3}$

Correct answer:

$324,000 \textrm{ cm}^{3}$

Explanation:

100 centimeters make one meter, so convert each of the dimensions of the box by multiplying by 100.

$0.9 \times 100 = 90$ centimeters

$0.6 \times 100 = 60$ centimeters

Use the volume formula, substituting L = 90, W = H = 60 :

V = LWH

$V = 90 \cdot 60 \cdot 60 = 324,000$ cubic centimeters

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Example Question #92 : Geometry

A cube made of nickel has sidelength 20 centimeters, Nickel has a density of 8.9 grams per cubic centimeter. What is the mass of this cube?

Possible Answers:

$35.6 \textrm{ kg}$

$71.2 \textrm{ kg}$

$3.56 \textrm{ kg}$

$7.12 \textrm{ kg}$

Correct answer:

$71.2 \textrm{ kg}$

Explanation:

The volume of the cube is $20 ^{3} = 20 \times 20 \times 20 = 8,000$ cubic centimeters. Multiply by the number of grams per cubic centimeter to get $8,000 \times 8.9 = 71,200$ grams, or $71,200 \div 1,000 = 71.2$ kilograms.

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Example Question #1 : How To Find The Volume Of A Net

A rectangular prism has length 24 inches, width 18 inches, and height 15 inches. Give its volume in cubic feet.

Possible Answers:

$3 \frac{3}{4} \textrm{ ft}^{3}$

$4 \frac{1}{4} \textrm{ ft}^{3}$

$4 \frac{1}{2} \textrm{ ft}^{3}$

$4 \frac{3}{4} \textrm{ ft}^{3}$

Correct answer:

$3 \frac{3}{4} \textrm{ ft}^{3}$

Explanation:

Divide each dimension in inches by 12 to convert from inches to feet:

$L = 24 \div 12 = 2$ feet

$W = 18 \div 12 = 1 \frac{1}{2} = \frac{3}{2}$ feet

$H = 15 \div 12 = 1 \frac{1}{4} = \frac{5}{4}$ feet

Multiply the three to get the volume:

$V = LWH = 2 \cdot \frac{3}{2} \cdot \frac{5}{4} = \frac{15}{4} = 3 \frac{3}{4}$ cubic feet

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Example Question #93 : Geometry

Prism

Give the volume of the box in cubic inches.

Possible Answers:

$3,168 \textrm{ in}^{3}$

$1,056 \textrm{ in}^{3}$

$816 \textrm{ in}^{3}$

$1,344 \textrm{ in}^{3}$

$672 \textrm{ in}^{3}$

Correct answer:

$3,168 \textrm{ in}^{3}$

Explanation:

Use the volume formula, substituting L = 22, W = H = 12 :

V=LWH

$V=22 \cdot 12 \cdot 12 = 3168^{3}$

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Example Question #1 : How To Find The Volume Of A Net

Swimming_pool

One cubic foot is equal to (about) 7.5 gallons.

The above depicts a rectangular swimming pool for an apartment. The pool is seven feet deep everywhere. How many gallons of water does the pool hold?

Possible Answers:

$17,850 \textrm{ gal}$

$178,500 \textrm{ gal}$

$89,250 \textrm{ gal}$

$91,875 \textrm{ gal}$

$8,925 \textrm{ gal}$

Correct answer:

$91,875 \textrm{ gal}$

Explanation:

The pool can be seen as a rectangular prism with dimensions 50 feet by 35 feet by 7 feet; its volume in cubic feet the product of these dimensions, which is

$50 \times 35 \times 7 =12,250$ cubic feet.

One cubic foot is equal to about 7.5 gallons, so multiply:

$12,250 \times 7.5 = 91,875$ gallons.

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : ISEE Middle Level (grades 7-8) Mathematics Achievement

Study concepts, example questions & explanations for ISEE Middle Level Math

All ISEE Middle Level Math Resources

Example Questions

Example Question #13 : How To Find Length Of A Line

Example Question #82 : Geometry

Example Question #11 : Lines

Example Question #12 : Lines

Example Question #21 : Lines

Example Question #91 : Geometry

Example Question #92 : Geometry

Example Question #1 : How To Find The Volume Of A Net

Example Question #93 : Geometry

Example Question #1 : How To Find The Volume Of A Net

All ISEE Middle Level Math Resources

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