ACT Math : ACT Math
Study concepts, example questions & explanations for ACT Math
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Example Questions
Example Question #2 : Order Of Operations
Evaluate:
–1 + 2 * –3
5
–3
3
7
–7
–7
First you perform multiplication 2 * –3 = –6
Then you add –1 which gives you -7.
Example Question #3 : Order Of Operations
Evaluate:
–1
21
0
1
–21
–1
Evaluate the exponent, then distribute, then add.
Example Question #2 : Order Of Operations
Evaluate the expression:
(2 + 2)2 – 1
16
15
1
4
7
15
First you perform the operation in the parentheses and then you multiply the exponent; after that, subtract one.
Example Question #3 : Order Of Operations
Evaluate:
(–1) + (2)2 * (–3)
–13
–3
–9
9
13
–13
First you evaluate the exponent. Then you multiply it by (–3) which gives you –12. Add –1 makes it –13.
Example Question #1 : Order Of Operations
Solve the following equation:
(9 + 1) * (42 + 2) * (72 + 1) / 2 = ?
9000
39
4500
1500
1014.5
4500
Order of operations: "PEMDAS” or "Please Excuse My Dear Aunt Sally"
"Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction".
(9 + 1) * (42 + 2) * (72 + 1) / 2 =
(10) * (16 + 2) * (49 + 1) / 2 =
(10) * (18) * (50) / 2 =
9000/2 = 4500
Example Question #3 : Order Of Operations
Solve the following equation:
(4 * 12) / (5 + 6 + 1) + 72 + (2 * 1 + 2)3 = ?
126
86
98.6
90.6
140
140
Order of operations: "PEMDAS” or "Please Excuse My Dear Aunt Sally"
"Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction".
(4 * 12) / (5 + 6 + 1) + 72 + (2 * 1 + 2)3 =
(48)/(12) + 72 + (2 + 2)3 =
(48)/(12) + 72 + (4) 3 =
(48)/(12) + 72 + 64 =
4 + 72 + 64 = 140
Example Question #5 : Order Of Operations
Solve: 4 + 2 * 4 = ?
32
10
12
14
24
12
To solve you must use the order of operations PEMDAS.
Multiplication comes first 4 * 2 = 8. Then add 4 + 8 = 12.
Example Question #1 : Arithmetic
The operation ¤ is defined as “cube the number that is to the right of the ¤ and subtract the result from the number that is to the left of ¤.” What is the value of 100 ¤ (5 ¤ 1)?
64
36
–25
16
86
36
Starting inside the parentheses, cube the number to the right of the symbol, which is 1, and then subtract that from the number to the left of the symbol, 5, to get 4. Then we perform the same operation by cubing 4 to get 64, and then subtracting that from 100 to get 36.
Example Question #4 : Order Of Operations
The expression 
In order to find the equivalent expression, distribute 
Example Question #11 : Arithmetic
Four times the sum of a number and one is four greater than the square of the difference between the number and six. Which of the following equations could be used to find the number?
Because the "is" represents the equals sign, we must look at everything before "is" and set that equal to everything after.
The first part of the sentence requires us to represent four times the sum of a number and one. This means we must find the sum of the number and one, then multiply this entire quantity by four. The sum of a number and one can be represented as
If we were to then multiply 
The second part of the sentence asks us to find four greater than the square of the difference between the number and six. This means we must first find the difference between the number and six, and then we must square this quantity. After we do that, we must increase that quantity by four.
The difference between a number and six is represented by
If we were to find the square of this quantity, we could write this as
Because we want to write an expression that is four greater than this, we could write 
Thus, the final equation would be:
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