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SSAT Upper Level Math : Algebra

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All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #51 : Ssat Upper Level Quantitative (Math)

Micah is seeking new employment. The salary that he desires must be $4,000 per month with a tolerance of $600. Which absolute value inequality can be used to assess the salary which will be tolerable?

Possible Answers:

$\left | s-4000\right |\geq 600$

$\left | s-600\ \right | \leq 4,000$

$\left | s-600\right |\geq 4,000$

$\left | s-4000\right | \leq 600$

Correct answer:

$\left | s-4000\right | \leq 600$

Explanation:

$\left | s-4000\right | \leq 600$ is the correct solution.

This absolute value inequality states that the difference between the salary of $4,000 must be less than or equal to $600 to be tolerable.

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Example Question #27 : How To Find Absolute Value

In order to ride the roller coaster at the local amusement park, children must be 145cm tall with a tolerance of 5cm. Which of the following absolute value inequalities can be used to assess which heights will be tolerable?

Possible Answers:

$\left | h-5\right |\leq 145$

$\left |h-145 \right | \geq 5$

$\left | h-145\right | \leq 5$

$\left | h-5\right | \geq 145$

Correct answer:

$\left | h-145\right | \leq 5$

Explanation:

$\left | h-145\right | \leq 5$ is the correct solution.

This Absolute Value inequality states that the difference between the children's height and 145cm must be less than or equal to 5cm .

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Example Question #52 : Ssat Upper Level Quantitative (Math)

Using <, >, or = compare the following absolute value.

$\left | -9\right |$ __________ $\left | -7\right |$

Possible Answers:

$\left | -9\right |=\left | -7\right |$

$\left | -9\right |\leq \left | -7\right |$

$\left | -9\right |< \left | -7\right |$

$\left | -9\right |> \left | -7\right |$

Correct answer:

$\left | -9\right |> \left | -7\right |$

Explanation:

The absolute value of a number is its distance from zero. The absolute value of a negative integer is a positive integer. The distance from zero to on a number line is , so

$\left | -9\right | = 9$

The absolute value of a number is its distance from zero. The absolute value of a negative integer is a positive integer. The distance from 0 to on a number line is . Therefore:

$\left | -7\right | = 7$

Therefore

$\left | -9\right |> \left | -7\right |$

because

9>7

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Example Question #53 : Ssat Upper Level Quantitative (Math)

Evaluate the expression if x=5 and y=7 .

$\left | 4x+3y \right | - \left | 4x-3y \right |$

Possible Answers:

Correct answer:

Explanation:

$\left | 4x+3y \right | - \left | 4x-3y \right |$

To solve, we replace each variable with the given value.

$\left | 4 (5) +3 ( 7) \right | - \left | 4 (5) -3 ( 7) \right |\ .$

$\left | 20 +21 \right | - \left | 20 -21 \right |$

Simplify. Remember that terms inside of the absolute value are always positive.

$\left | 41 \right | - \left | -1 \right |=41-1 = 40$

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Example Question #54 : Ssat Upper Level Quantitative (Math)

Evaluate: $\begin{vmatrix}\; \; \left | 5- 3 \cdot 4\right |-8 \right \;\end{vmatrix}$

Possible Answers:

Correct answer:

Explanation:

$\begin{vmatrix}\; \; \left | 5- 3 \cdot 4\right |-8 \right \;\end{vmatrix}=\begin{vmatrix}\; \; \left | 5- 12\right |-8 \right \;\end{vmatrix}=\begin{vmatrix}\; \; \left | -7\right |-8 \right \;\end{vmatrix}=| 7 - 8| = | -1| = 1$

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Example Question #1 : Generate Equivalent Numerical Expressions: Ccss.Math.Content.8.Ee.A.1

Evaluate $\dpi{100} \frac{2^{10}}{2^{8}}$

Possible Answers:

$\dpi{100} 2$

$\dpi{100} \frac{8}{5}$

$\dpi{100} 200$

$\dpi{100} 4$

Correct answer:

$\dpi{100} 4$

Explanation:

If you divide two exponential expressions with the same base, you can simply subtract the exponents. Here, both the top and the bottom have a base of 2 raised to a power.

So $\dpi{100} \frac{2^{10}}{2^{8}}=2^{10-8}=2^{2}=4$

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Example Question #1 : Properties Of Exponents

$\dpi{100} 2^{3}\cdot 2^{2}$

Possible Answers:

$\dpi{100} 16$

$\dpi{100} 2^{6}$

$\dpi{100} 32$

Correct answer:

$\dpi{100} 32$

Explanation:

Since the two expressions have the same base, we just add the exponents.

$\dpi{100} 2^{3}\cdot 2^{2}=2^{3+2}=2^{5}=32$

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Example Question #2 : Properties Of Exponents

Evaluate: $\dpi{100} (3^{3})^{2}$

Possible Answers:

$\dpi{100} 243$

$\dpi{100} 3^{5}$

$\dpi{100} 3^{6}$

$\dpi{100} 729$

Correct answer:

$\dpi{100} 3^{6}$

Explanation:

A power raised to a power indicates that you multiply the two powers.

$\dpi{100} (3^{3})^{2}=3^{3\cdot 2}=3^{6}$

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Example Question #55 : Ssat Upper Level Quantitative (Math)

$\dpi{100} Evaluate: (0.50^{2})$

Possible Answers:

$\dpi{100} 2.5$

$\dpi{100} 1$

$\dpi{100} 0.25$

$\dpi{100} 25$

Correct answer:

$\dpi{100} 0.25$

Explanation:

We can either write $\dpi{100} 0.5\times 0.5$ , or we can convert this to a fraction and write

$\dpi{100} \frac{1}{2}\times \frac{1}{2}$

$\dpi{100} \frac{1}{2}\times \frac{1}{2}=\frac{1\times 1}{2\times 2}=\frac{1}{4}$

$\dpi{100} \frac{1}{4}$ in decimal form is 0.25.

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Example Question #4 : Properties Of Exponents

$\dpi{100} (0.75)^{2}=$

Possible Answers:

$\dpi{100} 49.5$

$\dpi{100} \frac{9}{16}$

$\dpi{100} 5.85$

$\dpi{100} 58.5$

Correct answer:

$\dpi{100} \frac{9}{16}$

Explanation:

Convert .75 to a fraction. $\dpi{100} \frac{75}{100}=\frac{3}{4}$ .

Now multiply $\dpi{100} \frac{3}{4}\times \frac{3}{4}=\frac{3\times 3}{4\times 4}=\frac{9}{16}$

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Algebra

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #51 : Ssat Upper Level Quantitative (Math)

Example Question #27 : How To Find Absolute Value

Example Question #52 : Ssat Upper Level Quantitative (Math)

Example Question #53 : Ssat Upper Level Quantitative (Math)

Example Question #54 : Ssat Upper Level Quantitative (Math)

Example Question #1 : Generate Equivalent Numerical Expressions: Ccss.Math.Content.8.Ee.A.1

Example Question #1 : Properties Of Exponents

Example Question #2 : Properties Of Exponents

Example Question #55 : Ssat Upper Level Quantitative (Math)

Example Question #4 : Properties Of Exponents

All SSAT Upper Level Math Resources

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