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SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

Study concepts, example questions & explanations for SSAT Upper Level Math

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All SSAT Upper Level Math Resources

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Example Questions

Example Question #1 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

The base and height of a right triangle are each 1 inch. What is the hypotenuse?

Possible Answers:

0.5

$\sqrt{2}$

Correct answer:

$\sqrt{2}$

Explanation:

You need to use the Pythagorean Theorem, which is $a^{2}+b^{^{2}} = c^{^{2}}$ .

Add the first two values and you get . Take the square root of both sides and you get $\sqrt{2}$ .

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Example Question #131 : Geometry

Parallelogram2

Give the perimeter of the above parallelogram if BD = 24 .

Possible Answers:

$48\sqrt{3}$

$24+24 \sqrt{2}$

$32+16\sqrt{3}$

$24+24 \sqrt{3}$

$48\sqrt{2}$

Correct answer:

$48\sqrt{3}$

Explanation:

By the $30^{\circ}-60^{\circ}-90^{\circ}$ Theorem:

$AB = CD= BD\cdot \frac{\sqrt{3}}{3}= 24 \cdot \frac{\sqrt{3}}{3}= 8\sqrt{3}$ , and

$BC = AD = 2\cdot AB = 2 \cdot 8\sqrt{3} = 16 \sqrt{3}$

The perimeter of the parallelogram is

$AB + CD + BC + AD = 8\sqrt{3}+ 8\sqrt{3}+ 16\sqrt{3}+16\sqrt{3} = 48\sqrt{3}$

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Example Question #2 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

A right triangle has legs with lengths of units and units. What is the length of the hypotenuse?

Possible Answers:

4.64 units

5.38 units

units

5.20 units

Correct answer:

5.38 units

Explanation:

$\text{Hypotenuse}=\sqrt{\text{(leg 1)}^2+\text{(leg 2)}^2}$

Using the numbers given to us by the question,

$\text{Hypotenuse}=\sqrt{2^2+5^2}=\sqrt{29}=5.38$ units

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Example Question #2 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

A right triangle has legs with the lengths $4\:cm$ and $5\:cm$ . Find the length of the hypotenuse.

Possible Answers:

$41\:cm$

$\sqrt{35}\:cm$

$\sqrt{41}\:cm$

$3\:cm$

Correct answer:

$\sqrt{41}\:cm$

Explanation:

Use the Pythagorean Theorem to find the length of the hypotenuse.

$(\text{Hypotenuse})^2=(\text{leg 1})^2+(\text{leg 2})^2$

$\text{Hypotenuse}=\sqrt{4^2+5^2}=\sqrt{41}\:cm$

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Example Question #2 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Find the length of the hypotenuse in the right triangle below.

Possible Answers:

25.61

22.78

23.45

Correct answer:

25.61

Explanation:

Use the Pythagorean Theorem to find the hypotenuse.

$16^2+20^2=\text{Hypotenuse}^2$

$656=\text{Hypotenuse}^2$

$\sqrt{656}=25.61=\text{Hypotenuse}$

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Example Question #11 : Apply The Pythagorean Theorem To Find The Distance Between Two Points In A Coordinate System: Ccss.Math.Content.8.G.B.8

If James traveled north $30\textup { miles}$ and John traveled $40\textup { miles}$ west from the same town, how many miles away will they be from each other when they reach their destinations?

Possible Answers:

$40\textup { miles}$

$10\textup { miles}$

$60\textup { miles}$

$30\textup { miles}$

$50\textup { miles}$

Correct answer:

$50\textup { miles}$

Explanation:

The distances when put together create a right triangle.

The distance between them will be the hypotenuse or the diagonal side.

You use Pythagorean Theorem or $a^{2}+b^{2}=c^{2}$ to find the length.

So you plug and for and which gives you,

$900+1600=c^{2}$ or $2500=c^{2}$ .

Then you find the square root of each side and that gives you your answer of c=50 .

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Example Question #471 : Geometry

If the hypotenuse of a right triangle is 20, and one of the legs is 12, what is the value of the other leg?

Possible Answers:

Correct answer:

Explanation:

The triangle in this problem is a variation of the 3, 4, 5 right triangle. However, it is 4 times bigger. We know this because $5\cdot4=20$ (the length of the hypotenuse) and $3\cdot4=12$ (the length of one of the legs).

Therefore, the length of the other leg will be equal to:

$4\cdot4=16$

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Example Question #33 : Properties Of Triangles

A given right triangle has a base of length 9cm and a total area of $45cm^{2}$ . What is the height of the right triangle?

Possible Answers:

8cm

9cm

5cm

Not enough information provided

10cm

Correct answer:

10cm

Explanation:

For a given right triangle with base and height , the area can be defined by the formula $A=\frac{1}{2}bh$ . If one leg of the right triangle is taken as the base, then the other leg is the height.

Therefore, to find the height , we restructure the formula for the area as follows:

$A=\frac{1}{2}bh$

2A=bh

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

Plugging in our values for and :

$\frac{2(45cm^{2})}{9cm}=h$

$\frac{90cm^{2}}{9cm}=h$

10cm=h

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Example Question #34 : Properties Of Triangles

A given right triangle has a base length of 10cm and a total area of $100cm^{2}$ . What is the height of the triangle?

Possible Answers:

Not enough information provided

20cm

5cm

10cm

90cm

Correct answer:

20cm

Explanation:

For a given right triangle with base and height , the area can be defined by the formula $A=\frac{1}{2}bh$ . If one leg of the right triangle is taken as the base, then the other leg is the height.

Therefore, to find the height , we restructure the formula for the area as follows:

$A=\frac{1}{2}bh$

2A=bh

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

Plugging in our values for and :

$\frac{2(100cm^{2})}{10cm}=h$

$\frac{200cm^{2}}{10cm}=h$

20cm=h

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Example Question #31 : Properties Of Triangles

A given right triangle has a hypotenuse of 30cm and a total area of $200cm^{2}$ . What is the height of the triangle?

Possible Answers:

10cm

25cm

30.77cm

20cm

Not enough information provided

Correct answer:

Not enough information provided

Explanation:

For a given right triangle with base and height , the area can be defined by the formula $A=\frac{1}{2}bh$ . If one leg of the right triangle is taken as the base, then the other leg is the height.

However, we have not been given a base or leg length for the right triangle, only the length of the hypotenuse and the area. We therefore do not have enough information to solve for the height .

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SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #1 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Example Question #131 : Geometry

Example Question #2 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #2 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #2 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Example Question #11 : Apply The Pythagorean Theorem To Find The Distance Between Two Points In A Coordinate System: Ccss.Math.Content.8.G.B.8

Example Question #471 : Geometry

Example Question #33 : Properties Of Triangles

Example Question #34 : Properties Of Triangles

Example Question #31 : Properties Of Triangles

All SSAT Upper Level Math Resources

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