SAT Math : Arithmetic

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #11 : Arithmetic

Evaluate (√4 + √4)2

Possible Answers:

4

40

6

8

16

Correct answer:

16

Explanation:

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

Example Question #11 : Arithmetic

(11)(4 – 3)– (2+ 6) = ?

Possible Answers:

2

111

1

24

–53

Correct answer:

1

Explanation:

The answer is 1. 

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

(11) * (4 – 3)– (2+ 6)

(11) * (1)– (4 + 6)

(11) * (1) – (10)

(11) – (10) = 1

Example Question #12 : Arithmetic

If (x – 7)= 64, what is x?

Possible Answers:

15

–1

1

–15

Correct answer:

15

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

Example Question #13 : Arithmetic

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

Possible Answers:

64

8

9

7

Correct answer:

8

Explanation:

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

Example Question #11 : Order Of Operations

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

Possible Answers:

\dpi{100} \small 6

\dpi{100} \small 36

\dpi{100} \small 0

\dpi{100} \small 2

\dpi{100} \small 12

Correct answer:

\dpi{100} \small 12

Explanation:

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

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:

17

–33

–49

–17

It is impossible to square a negative number.

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

Example Question #11 : Arithmetic

Solve:

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

Example Question #14 : Order Of Operations

 

Possible Answers:

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

Example Question #11 : Order Of Operations

Evaluate when and .

Possible Answers:

None of the other answer choices are correct.

Correct answer:

Explanation:

We can evaluate when  and by plugging in and substituting:

Example Question #13 : Arithmetic

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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