Algebra I
Midterm Review
Name:___________________________
Date:_______________Block:________
This packet is intended to provide a review for the material we have covered. It may or may not have an
example of every type of problem you will have on the midterm. This packet is not the sole item for you to
use as review – you should use all materials from the beginning of the year until January exam week.
Chapter 1
1.
Write a variable expression for
“7 divided by the sum of x and 5”
2.
Simplify: 8 • 32 – 4
3.
Write an algebraic expression for
“three less than 5 times a number x”
4.
Write an algebraic expression for
“three times the difference of a number
x and 5”
5.
When the product of 4 and a number is
decreased by 5, the result is 12. Find
the number.
6.
Simplify:
7.
Simplify: –[–(4 + 3)]
8.
Evaluate: n3 when n is 5
2.
Simplify:
(–7) + 6 + [–(2 – 3)]
Chapter 2
1.
Between which two real numbers does
48 lie on the number line?
3
125
3.
Simplify:
5.
3 81 + 6 125
10
4.
Approximate and graph
Find the product: (–7)(3x)(–6)
6.
Find the product:
8
7.
Simplify: 720 ÷ (4 • 9 ÷ 3)
8.
Find the product:
(–8)
9.
Simplify:
4 • 0.5 + 22 – 4 + 3.1 • 3
10.
Simplify:
11.
Simplify:
3(2 – x) – 2(3 – x)
12.
Find the product: (3x)(–4y)(–5)
x ¸ y2 - 2x + y
where x = 24 and y= -2
Chapter 3
1.
Solve: 4x + 4 = 12
2.
Solve:
3n + 16 – n = 34
3.
Solve: 3 – 4z = –5 + 8z
4.
Solve:
5x – 9 = x – 3
5.
Solve: 5x + 14 – 2x = 9 – (4x + 2)
7.
Solve:
4x 6
1
1
x 3
(12 2 x)
3
2
(5x + s) - 3(x +1) = 2(x - 7)
6.
Solve:
8.
The trapezoid below has a perimeter of
30. Solve for x.
x+2
3x + 5
x
8
9.
11.
Write the equation as a function of s:
7 = t + 8s
Solve for v
10.
Write 9x – 4y = 5 as a function of y.
12.
Solve for x
2
x 4
pv nRT
5
x 2
Chapter 4
1.
Graph x = 3
2.
Graph 6y + 12 = 0
3. Which point lies on the graph of 2x –
= 3?
4.
or
Write the equation for the vertical line
passing through the point (–5, 2).
5.
State the x– and y–intercepts of
y = –7x + 7
6.
State the x– and y–intercepts of
7x + y = 3
7.
Find the slope of the line passing through
the points A(–5, –6) and B(2, –7).
8.
Find the slope of the line passing through
the points A(6, 5) and B(–4, –7).
9.
Find the slope of the line that is parallel to
the line that contains (9, 7) and (9, 9).
10.
Find the slope of the line perpendicular
to the line that goes through the (4, 7)
and (–6, 2).
11.
Write the variation and find the quantity indicated. 12.
x varies directly with y. If x is 144 when y is 160,
find x when y is 30.
The weight, W, of a plank varies directly
with its length, l. A 7.5 foot plank weighs
30 pounds. Write an equation relating
W and l.
13.
Rewrite the equation in slope–intercept form.
5x – 2y – 7 = 0
14.
Rewrite the equation in slope–intercept
form. 8x – 3y – 5 = 0
15.
Find the slope and y–intercept of the line:
6x – 3y = 36
16.
Find the slope and y–intercept of the
line: 4x + 2y = 24
17.
Solve for y and state the zero of the function:
18.
State the zero of the function:
2
f (x) = x - 6
3
Write in slope–intercept form and sketch
line: 4x +3y – 8 = 0
4x – 5y = 0
19.
Write in slope–intercept form and sketch
line: 3x – y – 2 = 0
20.
21.
Solve for y in 8x – 7y = –1. Determine if the
22.
line is parallel to y = x +
.
Find the slope and y–intercept of the line
y = 5x – 9. Is the line parallel to y = –5x – 9?
23.
Given f(x) = 2x + 4 and g(x) = f(x) - 4
Graph and label f(x) and g(x).
24.
Is the relation {(1, –2), (3, –2), (–6, –2)} a
function?
25.
Decide whether the information defines
a function. If it does, state the domain
of the function.
input 0 1 2 3 4
output 1 2 3 2 1
26. Given the function
what is f (1) ?
{(2, 3),(1,2),(-3, 4),(4,1)} ,
27.
Given the function, g ( x) 3x 2 5 ,
what is g ( 4) ?
Chapter 5
1.
Find an equation, in slope–intercept form,
of a line having slope 5 and y–intercept –8.
2.
Write an equation of the line with slope
equal to and y–intercept of –4.
3.
Write an equation of a line with slope 7
passing through the point (–7, 1).
4.
Find the y–intercept of a line that passes
through (3, 1) and has a slope of –3.
5.
Find an equation of the horizontal line that
passes through the point (7, –3).
6.
Write the equation of the vertical line
that passes through the origin.
7.
Which of the following lines are parallel to each other?
2x – 6y = 3
6x + 2y = 3
–2x + 6y = 3
8.
Which of the following lines are perpendicular to each other?
2x – 6y = 3
6x + 2y = 3
-2x + 6y = 3
Other
1. The cost per student of a band trip varies
inversely with the number of people going
on the trip, If 24 students go on the trip, each
student pays $500. What would each student
pay if 60 students go on the trip?
3. In which data set is the median value equal to the
mean value?
A. {2, 4, 7, 9, 11}
C. {6, 12, 18, 24, 27}
B. {7, 9, 10, 11, 16}
D. {33, 40, 46, 52, 59}
Chapter 6
4.
3.
2. The pressure in a tire varies inversely
with volume. The pressure in a tire is
32 psi for its 12 cubic inch volume. What is
the constant of variation for this tire?
4. Find the mean, range, variance, standard
deviation, and MAD for the following heights:
49 59 62 54 57 63 69 59 53 55
Translate the verbal phrase into an inequality and solve.
9.
Four less than double a number is at least 12.
10. Ten less a number is at most seven.
11.
y < 2x – 6
12.
y ≥ 4x + 8
13.
2x + 4y ≤ 14
14.
x – 3y > –6