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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 #61 : Geometry

Find the area of a triangle with a base of 8in and a height of 12in.

Possible Answers:

$24\text{in}^2$

$56\text{in}^2$

$48\text{in}^2$

$36\text{in}^2$

$96\text{in}^2$

Correct answer:

$48\text{in}^2$

Explanation:

To find the area of a triangle, we will use the following formula:

$A = \frac{1}{2} \cdot b \cdot h$

where b is the base and h is the height of the triangle.

Now, we know the base of the triangle is 8in. We also know the height is 12in. So, we can substitute. We get

$A = \frac{1}{2} \cdot 8\text{in} \cdot 12\text{in}$

$A = 4\text{in} \cdot 12\text{in}$

$A = 48\text{in}^2$

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Example Question #67 : Geometry

Find the area of a triangle with a base of 10in and a height of 11in.

Possible Answers:

$58\text{in}^2$

$21\text{in}^2$

$42\text{in}^2$

$110\text{in}^2$

$55\text{in}^2$

Correct answer:

$55\text{in}^2$

Explanation:

To find the area of a triangle, we will use the following formula:

$A = \frac{1}{2} \cdot b \cdot h$

where b is the base and h is the height of the triangle.

Now, we know the base of the triangle is 10in. We also know the height of the triangle is 11in. So, we get

$A = \frac{1}{2} \cdot 10\text{in} \cdot 11\text{in}$

$A = 5\text{in} \cdot 11\text{in}$

$A = 55\text{in}^2$

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Example Question #33 : How To Find The Area Of A Triangle

Find the area of a triangle with a base of 8in and a height of 12in.

Possible Answers:

$72\text{in}^2$

$32\text{in}^2$

$54\text{in}^2$

$96\text{in}^2$

$48\text{in}^2$

Correct answer:

$48\text{in}^2$

Explanation:

To find the area of a triangle, we will use the following formula:

$A = \frac{1}{2} \cdot b \cdot h$

where b is the base and h is the height of the triangle.

Now, we know the base of the triangle is 8in. We also know the height of the triangle is 12in.

Knowing this, we can substitute into the formula. We get

$A = \frac{1}{2} \cdot 8\text{in} \cdot 12\text{in}$

$A = 4\text{in} \cdot 12\text{in}$

$A = 48\text{in}^2$

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Example Question #62 : Geometry

Find the area of a triangle with a base of $7\textup{ cm}$ and a height of $12\textup{ cm}$ .

Possible Answers:

$42\text{cm}$

$84\text{cm}^2$

$42\text{cm}^2$

$84\text{cm}$

$48\text{cm}^2$

Correct answer:

$42\text{cm}^2$

Explanation:

To find the area of a triangle, we will use the following formula:

$\text{area of triangle} = \frac{1}{2} \cdot b \cdot h$

where b is the base and h is the height of the triangle.

We know the base is 7cm and the height is 12cm. Knowing this, we will substitute into the formula. We get

$\text{area of triangle} = \frac{1}{2} \cdot 7\text{cm} \cdot 12\text{cm}$

$\text{area of triangle} = \frac{1}{2} \cdot 84\text{cm}^2$

$\text{area of triangle} = \frac{1}{2} \cdot \frac{84\text{cm}^2}{1}$

$\text{area of triangle} = \frac{1 \cdot 84\text{cm}^2}{2 \cdot 1}$

$\text{area of triangle} = \frac{84\text{cm}^2}{2}$

$\text{area of triangle} = 42\text{cm}^2$

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Example Question #1 : Lines

Lines

Figure NOT drawn to scale.

AE = 40, AB = x, BC = x + 3, CD = 2x, DE = x-6

Evaluate .

Possible Answers:

7.2

6.2

9.6

8.6

Correct answer:

8.6

Explanation:

By the Segment Addition Postulate,

AB + BC + CD + DE = AE

x +( x + 3) +( 2x) +( x-6) = 40

5x-3 = 40

5x-3 +3 = 40 + 3

5x = 43

$5x \div 5 = 43 \div 5$

x = 8.6

AB = x = 8.6

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Example Question #2 : 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 #2 : How To Find Length Of A Line

What is the length of a line with endpoints (1,1) and (10,1) .

Possible Answers:

Correct answer:

Explanation:

To find the length of this line, you can subtract 10-1 to get . Since the y-coordinates are the same, you don't have to take any vertical direction into account. Therefore, you only look at the x-coordinates!

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Example Question #405 : Ssat Middle Level Quantitative (Math)

Find the length of the line segment whose endpoints are (-3,5) and (5,4) .

Possible Answers:

8.06

Correct answer:

8.06

Explanation:

We can use the distance formula:

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

$=\sqrt{(-3-5)^2+(5-4)^2}$

$=\sqrt{64+1}$

$=\sqrt{65}\approx 8.06$

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Example Question #4 : How To Find Length Of A Line

The point (4,4) lies on a circle. What is the length of the radius of the circle if the center is located at (3,8) ?

Possible Answers:

4.12

3.12

4.4

Correct answer:

4.12

Explanation:

The radius is the distance from the center of the circle to anypoint on the circle. So we can use the distance formula in order to find the radius of the circle:

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

$=\sqrt{(4-3)^2+(4-8)^2}$

$=\sqrt{1+16}$

$=\sqrt{17}\approx 4.12$

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Example Question #11 : Lines

The coordinates of and are A(4,1) and D(7,-1) . Find the length of the diagonal of the following rectangle:

Possible Answers:

3.6

4.6

Correct answer:

3.6

Explanation:

A rectangle has two diagonals with the same length. So we should find the length of . We can use the distance formula:

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

$=\sqrt{(4-7)^2+(1+1)^2}$

$=\sqrt{9+4}$

$=\sqrt{13}\approx 3.6$

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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 #61 : Geometry

Example Question #67 : Geometry

Example Question #33 : How To Find The Area Of A Triangle

Example Question #62 : Geometry

Example Question #1 : Lines

Example Question #2 : Lines

Example Question #2 : How To Find Length Of A Line

Example Question #405 : Ssat Middle Level Quantitative (Math)

Example Question #4 : How To Find Length Of A Line

Example Question #11 : Lines

All ISEE Middle Level Math Resources

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