All ACT Math Resources
Example Questions
Example Question #6 : How To Evaluate Algebraic Expressions
Evaluate 4x2 + 6x – 17, when x = 3.
13
17
36
37
30
37
Plug in 3 for x, giving you 36 + 18 – 17, which equals 37.
Example Question #7 : How To Evaluate Algebraic Expressions
John has a motorcycle. He drives it to the store, which is 30 miles away. It takes him 30 minutes to drive there and 60 minutes to drive back, due to traffic. What was his average speed roundtrip in miles per hour?
30 mph
50 mph
60 mph
45 mph
40 mph
40 mph
The whole trip is 60 miles, and it takes 90 minutes, which is 1.5 hours.
Miles per hour is 60/1.5 = 40 mph
Example Question #8 : How To Evaluate Algebraic Expressions
If (xy/2) – 3w = –9, what is the value of w in terms of x and y?
3xy + 6
w = 3 + (xy/6)
(1/3)xy + 6
(1/2)xy – 3
3xy – 6
w = 3 + (xy/6)
–3w = –9 – (xy/2)
w = 3 + (xy/6)
Example Question #9 : How To Evaluate Algebraic Expressions
Evaluate 5x2 + 16x + 7 when x = 7
364
363
361
365
362
364
Plug in 7 for x and you get 5(49) + 16(7) + 7 = 364
Example Question #41 : Expressions
Let for all integers
and
. Which of the following is the value of
?
In order to solve the expression, replace with
and
with
in the definition given:
Example Question #11 : How To Evaluate Algebraic Expressions
What is the value of that satisfies the equation
?
Distributing the 5 on the left side of the equation gives you .
Subtracting from both sides of the equation gives you
.
Adding 5 to both sides of the equation gives you .
Dividing each side of the equation by 7 gives you .
Example Question #41 : Expressions
If and
, what is
?
Example Question #43 : Expressions
8 less than 4 times a number is 76. Find the number.
Example Question #14 : How To Evaluate Algebraic Expressions
Let ,
and
. Solve
Substitute the given values into the variables to get:
Example Question #44 : Expressions
Bob needs to order candy bars from a warehouse. The website he is ordering from shows that the candy bars come in cases of
boxes with
candy bars in each box. It is not possible to order partial cases. What is the fewest amount of cases that Bob should order?
The answer is .
Bob must order full cases, which contain boxes of candy bars with
bars per box. This comes out to a total of
candy bars per case. An order of
cases comes out to
candy bars which is not enough. However if he orders one more case, the total comes out to
candy bars which allows him to barely surpass his needed amount of
bars.
All ACT Math Resources
