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WorksheetsLOJ Algebra Final Review
Total questions: 86
Worksheet time: 4hrs 25mins
Evaluate the expression for p=5 and q=1
q+p
1
5
6
10
Solve for w
9 + w = -12
3
15
-3
-21
Solve for r
–4.6r = 9.2
-2
-4.6
13.8
42.32
Solve for a
4 + 3a - 6 = 43
11
15
14.3
22
Solve for a
S = n/2 (a + l)
a = 2S/n - l
a = l(2S) - n
a = (n + l )/2 - S
a = 2Sn - l
Solve the proportion for x
⅓= x/x-6
0
3
2
-3
0
3
2.5
1.6
A statement formed by combining two simple inequalities with the words AND or OR is a(n) _______________.
compound inequality
intersection
solution of an inequality
union
Write the inequality shown.
x < 2
x > 2
x ≤ 2
x ≥ 2
Solve the inequality.
-4(2 - 5) > (-3)2 - h
h < -3
h > -3
h ≤ -3
h ≥ -3
Solve the inequality.
4∣2x∣ < 24
x < 3
x > 3
-3 < x < 3
-3 > x > 3
A baseball coach is taking the team for ice cream. Four students can ride in each car. The mapping diagram shows the number of cars needed to transport 8, 10, 14, 16 students. Is the relation a function?
yes
no
Identify the graph for the function:
y = ∣x + 5∣ + 1
The graph shows the results of a 2003-2004 survey on class size at the given grade levels. Based on this relationship, predict the class size for the 9th grade.
40
28
33
30
Find the indicated term of the arithmetic sequence:
31st term: -15, -11, -7, -3, ...
97
105
-62
20
Write the equation in standard form:
4y = 7x
y = 7/4x
7x - 4y = 0
Find the x- and y-intercepts.
-x + 6y = 18
x-int: -18
x-int: 18
y-int: 3
y-int: -3
Find the slope
2
4
5
10
Find the slope of the line that contains the pair of points.
(-3,-6) and (4,1)
1
7
-1
-4
Identify the correct graph for the line described by the equation.
y - 1 = -1(x + 3)
Identify which lines are parallel:
I: y-2=-4(x-1)
II: y=4x-4
III: y=¼x
IV: y=-4x-2
I and III
II and III
I and IV
I and II
II and IV
Identify which lines are perpendicular:
I: y=2x
II: y-2=3(x+1)
III: y=⅔x-4
IV: y=-⅓x
I and III
II and III
I and IV
I and II
II and IV
Identify the set of equations that is g(x) translated 4 units up from f(x).
f(x)=x, g(x)=x+4
f(x)=4x, g(x)=-4x
f(x)=⅓x-2, g(x)=-⅓x-2
f(x)=½x, g(x)=4x+2
Which ordered pair is the solution of the given system?
x-2y=-2
y=½x+1
(0,-5)
(4,3)
(1¾,7¼)
(-1,-1)
Solve using substitution.
x+y=-1
y=-2x+3
(-9,-6)
(½,-2)
(-1,6)
(4,-5)
Solve using elimination.
x+y=12
2x+5y=27
(-1,3)
(5,-3)
(11,1)
(0,3)
Solve the system.
y=-x+4
x+y=4
no solution
infinite solutions
(-2,-4)
(-1,-3)
Classify the system. There may be more than one correct answer.
2x+y=2
y-2=-2x
consistent
inconsistent
dependent
independent
Identify the correct graph for the linear inequality.
x+y+4>0
Identify the ordered pairs that are possible solutions for the system of linear inequalities. Select all that apply.
x-y>7
x+3y≤15
(8,-8)
(0,0)
(0,-4)
(9,0)
Simplify.
s3/qr2
qr2s3
1/qr2s3
qr2/s3
Simplify.
∛125x6
25x3
5√5
5x2
5x3√5
Find the degree of the polynomial.
8st3
0
4
6
1
Add the polynomial.
4x5-6x6+2x5-7x5
-6x6-x5
-7x5
-13x6
x5+6x6
Multiply the polynomial.
(2q+6)(4q+5)
q2-6q-27
4q2-12q+20
8q2+34q+30
20q2-37q+8
Multiply the polynomial.
(c2-d)(c2+d)
c4-c2d+c2d-d2
c4-d2
c4+d2
(c2-d)2
Find the GCF of 29 and 30.
0
1
3
9
Select the correct factorization of the polynomial by using the GCF.
6b2-8b+15b-20
Select the correct factorization of the trinomial.
x2-2x-48
(x+3)(x-8)
(x-9)(x+4)
(x-12)(x+6)
(x-8)(x+6)
Select the correct factorization of the trinomial.
3x2-10x+8
(3x+4)(x+2)
(3x+7)(x+1)
(3x+2)(x+2)
(3x+1)(x-4)
Is the following trinomial a perfect square?
9x2+12x+4
yes
no
Is the following binomial a difference of squares?
121b2+9c8
yes
no
Is the following polynomial completely factored?
4x2+10x+6 = (4x+6)(x+1)
yes
no
Choose the correct factorization of:
10m3+4m2-90m-36
Select all quadratic functions
Select the graph that matches the following quadratic function:
3x2+6x=y-3
Select the transformations that apply to g(x)=3x2-1 compared to f(x)=x2
narrower
wider
translated down 1
translated up 1
same axis of symmetry
Use a graph to find the solutions of the function. Select all that apply.
-4x2=64-32x
4
-4
0
16
-16
Factor. Select all that apply.
x2+9x+14=0
2
7
-2
-7
Solve using square roots. Select all that apply.
2x2=50
√50
5
-√50
-5
Solve by completing the square. Select all that apply.
x2+4x=21
1
5
-1
-5
Solve using the quadratic formula . Select all that apply.
2x2-9x-5=0
½
5
-½
-5
Find the number of real solutions using the discriminant.
6x2-20=15x+1
0
1
2
Solve the system.
y=x2-4
y=-2x-1
(2,4) and (-1,1)
(-3,5) and (1,-3)
(1,-3) and (4,3)
(-2,-2) and (-5,4)
The first term of a geometric sequence is 4 and the common ratio is 5. What is the 10th term?
7,812,500
39,062,500
41
37
Which of the following sets of ordered pairs satisfies an exponential function?
{(0,1),(2,9),(4,81),(6,729)}
{(1,4),(2,16),(3,36),(4,64)}
{(-2,-8),(-1,-4),(0,0),(1,4)}
The population of a small town is decreasing at a rate of 4% per year. In 1970, the population was 24,500. What was the population in the year 2020.
174,113
3314
3182
167,417
What kind of model best describes the data?
{(-2,-¼),(-1,-½),(0,-1),(1,-2),(2,-4)}
linear
quadratic
exponential
none of the above
Michael is studying population changes in two types of birds living on an island. Compare the populations by finding and interpreting the average rates of change over the interval [0,18].
Select all true comparisons.
B is decreasing more rapidly
A is decreasing more rapidly
B starts at a smaller population
A starts at a smaller population
A(n) ____________ is one possible result of an experiment.
outcome
event
experiment
trial
How many more boys than girls participated during 2004?
0
6
14
20
A stem-and-leaf plot needs which of the following? Select all that apply.
Consecutive numbers in the stem
A key telling how to read the values
The last digit of values represented by leaves
Data divided into equal intervals
Data in numerical data in order
Find the mode of the data set.
5,14,25,7,8,10,12,33,12
14
12
no mode
28
A manufacturer inspects 800 batteries and finds that 796 have no defects.
There are 25,000 batteries in storage. How many batteries are likely to have no defects?
24,000
24,575
24,875
24,996
What is the theoretical probability of randomly selecting a month that starts with “J” from all month names?
1
½
¼
⅛
You roll two number cubes. One is a 6 and the other is a 1.
dependent
independent
Solve the proportion. Select all possible solutions.
48 = x
x 3
0
12
-2
-12
26 feet is 130% of what length?
20 feet
33.8 feet
104 feet
3380 feet
The direct variation equation y=⅚x matches which variables? Select all that apply.
x=12
x=24
y=18
y=20
The indirect variation equation y=26/x matches which variables? Select all that apply.
x=1.5
x=65
y=50
y=⅖
Simplify the expression if possible.
5x+4
15x2+12x
5x+4
5(3x2+4x)
1
3x
3x
For what values is the expression undefined? Select all that apply.
x+4
x2+9x+20
no values
0
-2
-4
Simplify
x-3
x-4
2x
4(x-3)
x-3
2x(x-4)
A.
B.
C.
D.
3√8 + 3√2
Multiply
(-2√7)(3√28)
-6√14
6√13
-84
-78
Simplify the following expression:
10√5 ⁄ 5
10√5 ⁄ √25
2√5
2√5 ⁄ 5
Simplify the expression:
2√6
√24
√8
3√24 / 3
Determine the value of x. Write your answer in simple radical form.
√15 in
9 in
√177 in
81 in
