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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 #1 : How To Find Length Of A Line

If a circle has a radius of 12 inches, the biggest line that would be drawn within the circle is:

Possible Answers:

$24\ \textup{inches}$

$20\ \textup{inches}$

$26\ \textup{inches}$

$14\ \textup{inches}$

Correct answer:

$24\ \textup{inches}$

Explanation:

The largest line that can be drawn within a circle is the diamater. The diameter is equal to twice the radius. Given that the radius is equal to 12 inches, the largest line that could be drawn (the diameter) would be equal to 24 inches.

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

If you stand on a giant number line at point , what is your distance from point ?

Possible Answers:

Correct answer:

Explanation:

The distance on a number line is the number of whole number places between two numbers. When you are going from a negative value to a positive one or vice versa, you must find the distance from that both points are then add them together. is spaces away from and is spaces away. To find the distance you then add your two values of and to get .

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Example Question #71 : Geometry

One of the legs on a right triangle has a measurement of 30cm and the other leg has a measurement of 40cm. What is the length of the hypotenuse?

Possible Answers:

50cm

70cm

1200cm

10cm

Correct answer:

50cm

Explanation:

The Pythagorean Theorem states:

$a^{2 } +b^{2} =c ^{2}$ where represents the hypotenuse and and represent the measurements of the legs of the right triangle.

$30^{2} = 30 \times30 = 900$

$40^{2} = 40 \times 40 = 1600$

900 + 1600 = 2500

$\sqrt{c^{2}} = \sqrt{2500}$

c = 500 cm

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Example Question #6 : How To Find Length Of A Line

A right triangle has one leg with a length of and a hypotenuse of . What is the approximate measurement of the missing length?

Possible Answers:

$b\approx 11cm$

$b\approx 7.4cm$

$b \approx 9.5cm$

$b\approx 8.3cm$

Correct answer:

$b\approx 7.4cm$

Explanation:

The Pythagorean Theorem states that

$a^{2} +b^{2} = c^{2}$

Where and are the measurements of each leg and is the hypotenuse.

$3^{2} = 3 \times3 =9$

$8^{2} = 8\times 8 = 64.$

$9 + b^{2} = 64$

$(9-9) + b^{2} = 64-9$

$b^{2} = 55$

$\sqrt{b^{2}} = \sqrt{55}$

$b\approx 7.4cm$

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Example Question #71 : Plane Geometry

Rec

The coordinates of on the rectangle are D (5,2) and B (7,-3) . Find the length of the diagonal.

Possible Answers:

$d \approx 4.4$

$d\approx 6.4$

$d \approx 5.4$

$d\approx 7.4$

Correct answer:

$d \approx 5.4$

Explanation:

A rectangle has two diagonals with the same length. Therefore, use the distance formula to calculate the distance.

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

$(7-5)^{2} = 2^{2} = 4$

$(-3-2)^{2} = -5^{2} = 25$

$\sqrt{4+25}$

$\sqrt{29} \approx 5.4$

$d \approx 5.4$

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Example Question #81 : Geometry

If a circle has a radius of 8cm , what would be the length of the longest line drawn within that circle?

Possible Answers:

15cm

16cm

4cm

10cm

Correct answer:

16cm

Explanation:

The diameter of the circle would be the longest line that can be drawn within that circle.

Because radius is half of the diameter, the diameter is calculated by multiplying the radius of the circle by two.

If the radius is 8cm , then the diameter is $8m \times 2 = 16m$

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Example Question #12 : How To Find Length Of A Line

A ladder is leaning on a wall. It is 16ft ft long. The bottom of the ladder is 10ft from the base. How far up the wall is the top of the ladder?

Possible Answers:

$\approx 12.5ft$

$\approx11.5ft$

$\approx13.5ft$

$\approx 14ft$

Correct answer:

$\approx 12.5ft$

Explanation:

The Pythagorean Theorem states that:

$a^{2} +b^{2} = c^{2}$

With and representing the measurement of the legs and representing the hypotenuse.

$10^{2} +b^{2} = 16^{2}$

$100 + b^{2} = 256$

$(100-100) + b^{2} = 256-100$

$b^{2} = 156$

$\sqrt{b^{2}} = \sqrt{156}$

$b\approx 12.5ft$

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

What is the perimeter of a right triangle if the hypotenuse is 15cm and the measurement of one of its legs is 9cm?

Possible Answers:

36cm

39cm

12cm

33cm

Correct answer:

36cm

Explanation:

First, use the Pythagorean Theorem to get the measurement of the other leg.

$a^{2} +b^{2} =c^{2}$

$9^{2} + b^{2} =15^{2}$

$81 + b^{2} = 225$

$(81-81) + b^{2} = 225-81$

$b^{2} = 144$

b = 12cm

To get the perimeter of the triangle, add the measurements of each of the three sides.

9 + 15 + 12 = 36cm

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Example Question #14 : How To Find Length Of A Line

A line has endpoints (7,9) and (1,1). What is the distance of the line?

Possible Answers:

d = 12

d = 14

d = 10

d = 8

Correct answer:

d = 10

Explanation:

Use the distance formula

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

$d=\sqrt{(7-1)^{2} + (9-1)^{2}}$

$d=\sqrt{36+64}$

$d = \sqrt{100}$

d = 10

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Example Question #15 : How To Find Length Of A Line

Line has a length of 80cm. It is bisected at point , and the resulting segment is bisected again at point What is the length of line segment AD?

Possible Answers:

30cm

50cm

40cm

20cm

Correct answer:

20cm

Explanation:

First, write each portion of the statement in mathematical terms.

$AC =\frac{1}{2} AB$

Since AB=80 we will substitute that into the equation.

$AC =\frac{1}{2} (80)$

AC = 40

Now that we know AC we can calculate AD as follows.

$AD = \frac{1}{2} AC$

$AD = \frac{1}{2}(40)$

AD = 20cm

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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 #1 : How To Find Length Of A Line

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

Example Question #71 : Geometry

Example Question #6 : How To Find Length Of A Line

Example Question #71 : Plane Geometry

Example Question #81 : Geometry

Example Question #12 : How To Find Length Of A Line

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

Example Question #14 : How To Find Length Of A Line

Example Question #15 : How To Find Length Of A Line

All ISEE Middle Level Math Resources

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