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SAT Math : SAT Mathematics

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Example Questions

Example Question #8 : Order Of Operations

Eight more than four is an unknown number less than a quarter of the same unknown number. What is the value of the unknown number?

Possible Answers:

–16

–9

Correct answer:

–16

Explanation:

Let x be the unknown number.

4 + 8 = 0.25x – x.

12 = –0.75x

x = 12/–0.75

x = –16

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Example Question #9 : Order Of Operations

Let a * b be defined as the following:

a * b = b²– a²+ ab

Find the value of 4 * (3 * (2 * 1)).

Possible Answers:

101

–237

–11

Correct answer:

Explanation:

We are told that a * b = b²– a²+ ab, and we need to calculate 4 * (3 * (2 * 1)).

We need to start at the innermost set of parantheses, which requires us to find 2 * 1.

2 * 1 = 1² – 2² + 2(1) = 1 – 4 + 2 = –1

We can replace 2 * 1 with negative one. Then our expression becomes.

4 * (3 * (–1))

Now, we must find 3 * (–1)

3 * (–1) = (–1)² – 3² + (3)(–1) = 1 – 9 – 3 = –11

So we can replace 3 * (–1) with –11.

Lastly, we must find 4 * (–11)

4 * (–11) = (–11)² –4² + 4(–11) = 121 – 16 – 44 = 61

The answer is 61.

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Example Question #11 : Arithmetic

Evaluate (√4 + √4)²

Possible Answers:

Correct answer:

Explanation:

The square root of 4 is 2. 2 + 2 = 4. Four squared is 16.

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Example Question #11 : Arithmetic

(11)(4 – 3)²– (2²+ 6) = ?

Possible Answers:

–53

111

Correct answer:

Explanation:

The answer is 1.

The correct order of operations is parenthesis, exponents, multiplication and division, then addition and subraction.

(11) * (4 – 3)²– (2²+ 6)

(11) * (1)²– (4 + 6)

(11) * (1) – (10)

(11) – (10) = 1

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Example Question #13 : Arithmetic

If (x – 7)²= 64, what is x?

Possible Answers:

–15

–1

Correct answer:

Explanation:

Solving for x yields 15.

√64 = 8, so we want x – 7 = 8; add 7 to both sides of the equation, so that x = 15

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Example Question #14 : Arithmetic

7 more than a number squared is 71. What is the number?

Possible Answers:

Correct answer:

Explanation:

Subtracting the 7 yields 64, and the square root of 64 is equal to 8.

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Example Question #11 : How To Find Order Of Operations

Evaluate $\dpi{100} \small 3x^{2}$ if $\dpi{100} \small x=2$ .

Possible Answers:

$\dpi{100} \small 2$

$\dpi{100} \small 0$

$\dpi{100} \small 6$

$\dpi{100} \small 12$

$\dpi{100} \small 36$

Correct answer:

$\dpi{100} \small 12$

Explanation:

$\dpi{100} \small 3(2)^{2} = 3(4)=12$

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Example Question #12 : How To Find Order Of Operations

Consider the function:

$f(x)=2x^3+4x^2+x-15$

What is the value of $f(-2)$ ?

Possible Answers:

–49

–33

It is impossible to square a negative number.

–17

Correct answer:

–17

Explanation:

$f(x)=2x^3+4x^2+x-15$

$f(-2)=2(-2)^3+4(-2)^2+(-2)-15$

$f(-2)=(2\times -8)+(4\times 4)-2-15$

$f(-2)=-16+16-2-15=-17$

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Example Question #13 : How To Find Order Of Operations

Solve:

$\left ( 14-2 \right )\times 6-4\div 2$

Possible Answers:

Correct answer:

Explanation:

To solve the above expression we must follow PEMDAS.

So the parentheses are first. $\dpi{100} \small 14-2 = 12 \times 6=72$ .

Then we need to divide 4 by 2 before subtracting because division comes before subtraction.

$\dpi{100} \small 72-2=70$

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Example Question #14 : How To Find Order Of Operations

$(3+4+5+6+7)\times \frac{(1+2-3-4-5)}{2}\times \frac{16+4+8+4}{4}=$

Possible Answers:

3600

900

Correct answer:

Explanation:

Order of operations: "PEMDAS”, or "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction".

$\dpi{100} \small (3+4+5+6+7)\times \frac{(1+2-3-4-5)}{2}\times \frac{(16+4+8+4)}{4}=$

$\dpi{100} \small (25)\times \frac{(-9)}{2}\times \frac{(32)}{4} =$

$\dpi{100} \small 25\times -4.5\times 8 = -900$

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #8 : Order Of Operations

Example Question #9 : Order Of Operations

Example Question #11 : Arithmetic

Example Question #11 : Arithmetic

Example Question #13 : Arithmetic

Example Question #14 : Arithmetic

Example Question #11 : How To Find Order Of Operations

Example Question #12 : How To Find Order Of Operations

Example Question #13 : How To Find Order Of Operations

Example Question #14 : How To Find Order Of Operations

All SAT Math Resources

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