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SAT Math : How to find order of operations

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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 : Order Of Operations

(11)(4 – 3)²– (2²+ 6) = ?

Possible Answers:

111

–53

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 #11 : Arithmetic

If (x – 7)²= 64, what is x?

Possible Answers:

–1

–15

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 : Order Of Operations

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 #12 : Order Of Operations

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

Possible Answers:

$\dpi{100} \small 0$

$\dpi{100} \small 2$

$\dpi{100} \small 12$

$\dpi{100} \small 36$

$\dpi{100} \small 6$

Correct answer:

$\dpi{100} \small 12$

Explanation:

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

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Example Question #13 : Order Of Operations

Consider the function:

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

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

Possible Answers:

It is impossible to square a negative number.

–17

–33

–49

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 #17 : 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 #11 : Arithmetic

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

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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Example Question #19 : Order Of Operations

Evaluate x^2+3x^3-y^2+y+7 when x=-3 and y=2 .

Possible Answers:

None of the other answer choices are correct.

Correct answer:

Explanation:

We can evaluate x^2+3x^3-y^2+y+7 when x=-3 and y=2 by plugging in and substituting:

(-3)^2+3(-3)^3-(2)^2+2+7

$9+(3\times -27)-4+2+7$

9-81-4+2+7=-67

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Example Question #14 : Order Of Operations

13+5-9

Possible Answers:

Correct answer:

Explanation:

When doing operations of subtraction and addition, there is no priority but we must work from left to right. The sum on the left is and we do the subtraction. The answer is .

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SAT Math : How to find order of operations

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #11 : Arithmetic

Example Question #11 : Order Of Operations

Example Question #11 : Arithmetic

Example Question #14 : Order Of Operations

Example Question #12 : Order Of Operations

Example Question #13 : Order Of Operations

Example Question #17 : Order Of Operations

Example Question #11 : Arithmetic

Example Question #19 : Order Of Operations

Example Question #14 : Order Of Operations

All SAT Math Resources

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