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

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

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Example Questions

Example Question #2 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

3

Possible Answers:

\(\displaystyle 4\)

\(\displaystyle 5\)

\(\displaystyle 8\)

\(\displaystyle 25\)

Correct answer:

\(\displaystyle 5\)

Explanation:

Use the Pythagorean Theorem to find the length of the missing side.

\(\displaystyle x^2+12^2=13^2\)

\(\displaystyle x^2+144=169\)

\(\displaystyle x^2=25\)

\(\displaystyle x=\sqrt{25}=5\)

Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

4

Possible Answers:

\(\displaystyle 100\)

\(\displaystyle 10\)

\(\displaystyle 14\)

\(\displaystyle 12\)

Correct answer:

\(\displaystyle 10\)

Explanation:

Use the Pythagorean Theorem to find the length of the missing side.

\(\displaystyle x^2+24^2=26^2\)

\(\displaystyle x^2+576=676\)

\(\displaystyle x^2=100\)

\(\displaystyle x=\sqrt{100}=10\)

Example Question #2 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

5

Possible Answers:

\(\displaystyle 64\)

\(\displaystyle 5\)

\(\displaystyle 8\)

\(\displaystyle 9\)

Correct answer:

\(\displaystyle 8\)

Explanation:

Use the Pythagorean Theorem to find the length of the missing side.

\(\displaystyle x^2+6^2=10^2\)

\(\displaystyle x^2+36=100\)

\(\displaystyle x^2=64\)

\(\displaystyle x=\sqrt{64}=8\)

Example Question #3 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

6

Possible Answers:

\(\displaystyle 10\sqrt5\)

\(\displaystyle 300\)

\(\displaystyle 20\)

\(\displaystyle 10\sqrt3\)

Correct answer:

\(\displaystyle 10\sqrt3\)

Explanation:

Use the Pythagorean Theorem to find the length of the missing side.

\(\displaystyle x^2+10^2=20^2\)

\(\displaystyle x^2+100=400\)

\(\displaystyle x^2=300\)

\(\displaystyle x=\sqrt{300}=10\sqrt{3}\)

Example Question #11 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

7

Possible Answers:

\(\displaystyle 400\)

\(\displaystyle 20\)

\(\displaystyle 15\)

\(\displaystyle 12\)

Correct answer:

\(\displaystyle 20\)

Explanation:

Use the Pythagorean Theorem to find the length of the missing side.

\(\displaystyle x^2+15^2=25^2\)

\(\displaystyle x^2+225=625\)

\(\displaystyle x^2=400\)

\(\displaystyle x=\sqrt{400}=20\)

Example Question #11 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

8

Possible Answers:

\(\displaystyle 34\)

\(\displaystyle 36\)

\(\displaystyle 18\)

\(\displaystyle 32\)

Correct answer:

\(\displaystyle 36\)

Explanation:

Use the Pythagorean Theorem to find the length of the missing side.

\(\displaystyle x^2+15^2=39^2\)

\(\displaystyle x^2+225=1521\)

\(\displaystyle x^2=1296\)

\(\displaystyle x=\sqrt{1296}=36\)

Example Question #12 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

9

Possible Answers:

\(\displaystyle 16\)

\(\displaystyle 15\)

\(\displaystyle 225\)

\(\displaystyle 17\)

Correct answer:

\(\displaystyle 15\)

Explanation:

Use the Pythagorean Theorem to find the length of the missing side.

\(\displaystyle x^2+8^2=17^2\)

\(\displaystyle x^2+64=289\)

\(\displaystyle x^2=225\)

\(\displaystyle x=\sqrt{225}=15\)

Example Question #13 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

10

Possible Answers:

\(\displaystyle 27\)

\(\displaystyle 900\)

\(\displaystyle 30\)

\(\displaystyle 35\)

Correct answer:

\(\displaystyle 30\)

Explanation:

Use the Pythagorean Theorem to find the length of the missing side.

\(\displaystyle x^2+16^2=34^2\)

\(\displaystyle x^2+256=1156\)

\(\displaystyle x^2=900\)

\(\displaystyle x=\sqrt{900}=30\)

Example Question #14 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

11

Possible Answers:

\(\displaystyle 16\)

\(\displaystyle 14\)

\(\displaystyle 15\)

\(\displaystyle 196\)

Correct answer:

\(\displaystyle 14\)

Explanation:

Use the Pythagorean Theorem to find the length of the missing side.

\(\displaystyle x^2+48^2=50^2\)

\(\displaystyle x^2+2304=2500\)

\(\displaystyle x^2=196\)

\(\displaystyle x=\sqrt{196}=14\)

Example Question #15 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

12

Possible Answers:

\(\displaystyle 56\)

\(\displaystyle 60\)

\(\displaystyle 26\)

\(\displaystyle 45\)

Correct answer:

\(\displaystyle 60\)

Explanation:

Use the Pythagorean Theorem to find the length of the missing side.

\(\displaystyle x^2+11^2=61^2\)

\(\displaystyle x^2+121=3721\)

\(\displaystyle x^2=3600\)

\(\displaystyle x=\sqrt{3600}=60\)

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