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ACT Math : ACT Math

Study concepts, example questions & explanations for ACT Math

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14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Order Of Operations

Solve for :

$x = (3-2)^2 +3 - 3\cdot 2^2$

Possible Answers:

x = -4

x = 4

x =-8

x = 0

x = 8

Correct answer:

x =-8

Explanation:

We begin with

$x = (3-2)^2 +3 - 3\cdot 2^2$

We follow the order of P.E.M.D.A.S.

Parenthesis:

$x = 1^2 + 3 - 3\cdot 2^2$

Exponents:

$x = 1 + 3 - 3\cdot 4$

Multiplication:

x = 1 +3 -12

No division needed, so addition:

x = 4-12

Finally, subtraction:

x =-8

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Example Question #12 : Order Of Operations

Simplify the expression:

(7-5)^2+3*(-1-4)/5

Possible Answers:

Correct answer:

Explanation:

To evaluate an expression use PEMDAS to dictate the order of operations. Thus we simplify the parentheses first:

(7-5)=2 and (-1-4)=-5
next we move on to exponents so:

2^2 = 4
Next multiplication and division from left to right:
3*(-5)/5=(-15)/5=-3
and finally we add:
4+(-3) =1

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Example Question #12 : Arithmetic

Find the value of the following expression: 8(6-4)^2+10

Possible Answers:

240

266

170

Correct answer:

Explanation:

To correctly solve this expression, you must follow the correct order of operations: Parentheses- 8(6-4)^2+10=8(2)^2+10 ,

Exponents- 8(2)^2+10=8*4+10 ,

Multplication/ Division- 8*4+10=32+10 ,

and Addition/Subtraction- 32+10=42 .

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Example Question #13 : Arithmetic

Find the value of the following expression:

$\frac{(4*(8+2))^2}{10}-20$

Possible Answers:

120

180

140

Correct answer:

140

Explanation:

To correctly solve this expression, you must follow the correct order of operations:

Parentheses (starting with parenthesis inside other parenthesis)-

$\frac{(4*(8+2))^2}{10}-20=\frac{(4*(10))^2}{10}-20=\frac{(40)^2}{10}-20$ ,

Exponents-

$\frac{(40)^2}{10}-20=\frac{1600}{10}-20$ ,

Multplication/ Division-

$\frac{1600}{10}-20= 160-20$ ,

and Addition/Subtraction-

160-20=140 .

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Example Question #1081 : Act Math

Simplify the following expression:

(18/3)^2 - 3^2 + 11*1 - 12/2 + 15

Possible Answers:

Correct answer:

Explanation:

Use order of operations (PEMDAS) in order to simplify the expression:

(18/3)^2 - 3^2 + 11*1 - 12/2 + 15

PEMDAS means to do calculations in the following order.

P: Parentheses

(18/3)=6

E: Exponents

(18/3)^2=6^2=36

3^2=9

M: Multiplication

11*1=11

D: Division

12/2=6

Substituting in the above values we get our new equation to be:

36 - 9 + 11 - 6 + 15 .

A: Addition

S: Subtraction

From here we add and subtract from left to right

$\\27+ 11 - 6 + 15 \\=38-6+15\\=32+15 \\=47$

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Example Question #17 : How To Find Order Of Operations

Find the solution to the following: $\left ( 2+3\right )15-\frac{34}{2}$

Possible Answers:

Correct answer:

Explanation:

Order of operations is as follows: (P)arentheses, (E)xponenets, (M)ultiplication, (D)ivision, (A)ddition, (S)ubtraction, also known as PEMDAS.

In this particular scenario, we begin with the parentheses. 2+3=5 . The equation is now $\left ( 5\right )15-\frac{34}{2}$ .

From here, since there are no exponents, we proceed to the multiplication and division. 5(15)=75 , and $\frac{34}{2}=17$ . The equation is now 75-17 , which yields the answer .

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Example Question #12 : How To Find Order Of Operations

Given $f(x)=-x^{4}$ . What is the value of f(-3) ?

Possible Answers:

$(-3)^{-4}$

$(-3)^{4}$

$\frac{-1}{12}$

3^4

Correct answer:

Explanation:

When we evaluate the function $f(x)=-x^{4}$ at x=-3 , we can first plug in for to get

$f(-3)=-(-3)^{4}$ .

Since the power is even, we know that $(-3)^{4}=3^{4}$ , since any negative number to an even power is always a positive number.

Since the function is $-x^{4}$ , we first compute the exponent before mulitplying by .

So the final answer is $-3^{4}=-81$

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Example Question #12 : How To Find Order Of Operations

Distribute:

$(2+4)^2-10+2\cdot3$

Possible Answers:

Correct answer:

Explanation:

Order of operations means we start with parentheses, then move on to exponents, then multiplication, then division, then addition and subtraction.

Thus, $(2+4)^2-10+2\cdot 3=6^2-10+6=36-10+6=32$

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Example Question #1083 : Act Math

$-2 + 8/2 + (6 - 3) + 2^{0}=?$

Possible Answers:

Correct answer:

Explanation:

This is an order of operations, PEMDAS problem. PEMDAS stands for parentheses, exponents, multiplication, division, addition, and subtraction.

First we evaluate the parentheses. 6-3=3 .

Then, we evaluate the exponent. 2^0=1 , since everything raised to the zeroth power equals .

Then, we do the division. $\frac{8}{2}=4$

Lastly, we add the .

Putting it all together, we have 3+1+4-2=6 .

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Example Question #21 : How To Find Order Of Operations

Simplify: $2-5(7-3^2)^3 \div 2$

Possible Answers:

Correct answer:

Explanation:

Using PEMDAS helps us solve our equation step-by-step:

$2-5(7-3^2)^3 \div 2$ State the equation.

$2-5(7-9)^3 \div 2$ Solve inside the parenthesis first.

$2-5(-2)^3 \div 2$ Simplify inside the parenthesis.

$2-5(-8) \div 2$ Solve the exponent.

$2+ 40 \div 2$ Multiply.

2+ 20 Divide.

Add.

Thus, our answer is .

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ACT Math : ACT Math

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #11 : Order Of Operations

Example Question #12 : Order Of Operations

Example Question #12 : Arithmetic

Example Question #13 : Arithmetic

Example Question #1081 : Act Math

Example Question #17 : How To Find Order Of Operations

Example Question #12 : How To Find Order Of Operations

Example Question #12 : How To Find Order Of Operations

Example Question #1083 : Act Math

Example Question #21 : How To Find Order Of Operations

All ACT Math Resources

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