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Algebra 1
Module 4 Inequalities Test Review
Name___________________
Date___________ Period____
A new game facility is opening for teens. You have to be older than twelve,
but nineteen or younger to enter.
1. Represent the ages x using algebraic symbols.
2. Represent the ages x using a number line.
A new ride at Disneyland allows children over 46 inches but less than 64
inches to ride.
3. Represent the heights h of children allowed to ride using algebraic
symbols.
4. Represent the heights h of children allowed to ride using a number line.
5. Express the following range of values shown using inequality symbols.
a.
-8
0
10
-4
0
5
0
12
0
17
b.
c.
-3
d.
-11
6. Graph the following inequalities on the number line.
a. x  4
b. 6  x  3
7. Represent the following using interval notation.
a. x  3
b. 0  x  15.7
c. x  8.2
d. 4  x  17
Solve.
8. 6  2r  8r
10.
9. 3  3 x  (5  7 x)
9.
4  2  4m  10m
11.
4( x  6)  2(3 x  7)
6 x  2 y  10
Solve each linear inequality for y.
12.
3x  5 y  1
13.
14.
4 x  3 y  5
15.
2 x  5 y  7
Sketch the graph of each linear inequality; be sure to state m, b, and your
test point.
16.
y
3
x2
4
17.
y  5 x  3
m = _______
m = _______
b = _______
b = _______
dotted or solid?
dotted or solid?
Test Point _______
Test Point _______
Sketch the graph of each linear inequality;
18.
y6
19. x  2
m = _______
m = _______
b = _______
b = _______
dotted or solid?
dotted or solid?
Test Point _______
Test Point _______
Sketch the graph of each linear inequality by putting in slope-intercept
form or using x and y intercepts. Show all work.
20.
4 x  4 y  12
21.
3x  2 y  8
m = _______
m = _______
b = _______
b = _______
dotted or solid?
dotted or solid?
Test Point _______
Test Point _______
22.
24.
6 x  2 y  10
23.
5x  3 y  9
m = _______
m = _______
b = _______
b = _______
dotted or solid?
dotted or solid?
Test Point _______
Test Point _______
3x  3 y  18
25.
6 x  4 y  16
m = _______
m = _______
b = _______
b = _______
dotted or solid?
dotted or solid?
Test Point _______
Test Point _______
Module 5 Investigation 1-7 Review
Name: _______________________
Date: ____________ Period: _____
1. Is (-2, 4) a solution to the following system? (show work)
2x - 2y = 8
x+y=4
2. Is (2,
1) a solution to the following system?(show work)
4x + y = 9
3x + 14y = 20
Name the point of intersection.
3.
4.
For #’s 5-8, solve each system by graphing.
5.
y  5x  1
y  5x  4
6.
y = -2
x=8
7.
8.
5
y  x 3
3
1
y  x 1
3
y  x6
y  4 x  9
Solve using substitution.
y  x6
9. ( _____, ______)
y  4 x  9
8x  y  2
10. ( _____, _____)
4x  4 y  8
Solve using elimination.
 x  5 y  13
11. ( _____, ______)
4 x  5 y  2
3x  5 y  23
12. ( ______, ______)
9 x  8 y  20
Solve using any method you choose.
13. ( ____, ______)
4 x  9 y  5
8 x  10 y  30
10 x  6 y  12
14. ( ____, _____)
5x  3 y  6
5 x  3 y  24
16 x  2 y  12
15. ( ____, _____)
8x  y  6
16. ( ______, _____)
8 x  y  21
17. Show algebraically and graphically what it means to have no solution & infinitely
many solutions.
No Solution
Infinitely Many Solutions
Algebraically (When you solve by elimination or substitution how do you know if it is no
solution or IMS)
18- 21 Graph this system of inequalities
18. y ≤ x
y≥3
19. y ≤ -x +1
x ≥ -1
20. y < ½ x + 1
y ≥ -1/2x - 4
21. y ≤ 0
x≥0
Application Practice:
22. Paul went to the baseball game with seven of his friends. Before the game started
Paul got everyone including himself, a soda and a hot dog and spent $48 (before tax)
After the 6th inning, 4 people wanted another soda and 2 people wanted another hot dog.
On this trip Paul spent $17.50 (before tax)
a. Define your variables
b. Write two equations representing the total cost of each trip to the concessions stand
based on the number of sodas and hot dogs purchased.
c. How much does the soda cost?
d. How much do the hot dogs cost?
Module 6 Investigation 1-3 Quiz Review
Name: ____________________________ Period: _______
Ann, Betty, Cassie, and Dawn discover a secret that no one else knows. On Day
1 each of them tells three other people. After that, everyone who learns the
secret on a given day tells the secret to three new people the next day. This
pattern continued for 4 days.
1. What quantities are varying in this situation?
2. How many new people learn the secret on day 1?
3. How many new people learn the secret on day 2?
4. Define a function f that determines the number of people f(n) who learned the
secret on day n.
5. Which of the following is represented exponentially correctly?
6 factors of 1.3
a. 61.3
c. 1.36
b. 1.3
d. 6(1.3)
6. Which of the following is represented exponentially correctly?
5 times as large as 3 factors of 8
a. 5(83)
b.158
c. 403
d. 245
7. Fill in the chart
Initial Amount
Growth or
Decay
Growth or
Decay Factor
Percent
Change
f(x) = 35(1.4)x
100
63
Decay
2%
1.35
f(x) =
27(0.65)x
8. Determine the growth factor, percent change initial value and exponential
function that models the data in the following table.
x
G(x)
Decay Factor: ___
Initial Value: ____
0
200
1
40
Percent change: _____
Exponential Function: _________
2
8
3
1.6
4
.32
9. An investment of $3500 increases by8.2% each year.
Growth Factor: ___
Initial Value: ____
Percent change: _____
Exponential Function: _________
Simplify:
10. (x y2)2
11. (36x10y2z4)2
12. ( 3x3)3 + x5
Name: ______________________________ Test Date: ___________ Period: _____
Module 7 Investigation 1-4 TEST Review
Given quadratic function f(x) = 3x2-1, Solve the equation f(x) = 47
Given quadratic function f(x) = 5x2+ 5, Solve the equation f(x) = 130
Given quadratic function f(x) = 3x2 -1, Solve the equation f(3)
Given quadratic function f(x) = 5x2+ 5, Solve the equation f(-1)
What is the type of equation is the table? Make sure you state why?
x
y
x
y
x
x
y
y
-1
-3
-1
10
-1
4.76
-1
-8
0
0
0
15
0
5
0
-9
1
5
1
20
1
5.25
1
-8
2
12
2
25
2
5.51
2
-5
3
21
3
30
3
5.79
3
0
Multiply the binomials
y = (x + 5)(2x – 3 ) f(y) = (3y + 4)(2y – 4)
f(x) = 2(x + 4)(x – 2)
y = 3x(x + 9)
Factor COMPLETELY
y = 2x2 – 98
f(x) = 225x2 – 196
State the roots or Zeros:
f(x) = x2 - 4
State The Vertex:
f(x) = x2 - 4
f(x) = 3x2 – 27
f(x) = 3x2 – 27
Put in standard form
f(x) = (x - 3)(x + 5) f(x) = 2(x + 2)(x - 2)
y = 175x2 – 252
y = (x + 3)(x – 5)
y = (x + 3)(x – 5)
f(x) = 3(x - 3)2
Identify if the function has a maximum or minimum?
f(x) = -x2 - 4
f(x) = 3x2 – 27
y = -(x + 3)(x – 5)
State the y-intercept:
f(x) = 2x2 + 3x + 1
f(x) = x2– 1
f(x) = 72x2 - 392
f(x) = x2 + 7x + 100
y = x(x – 6)
y = x(x – 6)
f(x) = -2x(x + 5)
y = x(x – 6)
f(x) = 2x2 + 3x
Write the correct equation for the graphs.
Determine the zeros (roots) of the function. Determine the coordinates of the vertex of
the function.State where the function is increasing, state where the function is
decreasing,Does g have a minimum or maximum value? & Graph, table must include 5
points (including vertex, zeros & 2 additional points)
x
y
f(x) = (x - 1)(x + 3)
Zeros/Roots:
Vertex:
Increasing Interval
Decreasing Interval
Maximum or Minimum?
Y-intercept:
x
y
f(x) = -x(x - 2)
Zeros/Roots:
Vertex:
Increasing Interval
Decreasing Interval
Maximum or Minimum?
Y-intercept:
f(x) = 2x2 - 8
Zeros/Roots:
Vertex:
Increasing Interval
Decreasing Interval
Maximum or Minimum?
Y-intercept:
x
y
Name: ________________________________________ Period: ____
Quadratic Functions and Factoring
Test Review
Factor Completely
f(x) = x2 – x – 90
f(x) = 4x2 – 4x - 8
f(x) = 2x2 +11x + 5
f(x) = 7x2 + 53x + 28
f(x) = 3x2 – 8x + 4
f(x) = 2x2 – 50
f(x) = x2 + 11x + 10
f(n) = 5n2 + 19n + 12
f(x) = 5x2 + 5
f(x) = x2 – 15x + 50
f(x) = 10x2 + 20x
f(x) = 9x2 +66x + 21
Use factoring and the zero-product property to find the roots/xintercepts/zeros.
x2 – 7x = -12
x2 – 10x = -16
x2 + x = 6
x2 + 6x + 3 = -2
x2 – 16 = 9
x2 – 8x + 20 = 5
Determine if the vertex for each quadratic function is a maximum or a
minimum.
f(x) = -x2-4
y= - (x+3)(x-5)
f(x)=3x2-27
y= x(x-6)
What is the vertex and axis of symmetry of the following quadratic
equations?
f(x) = (x-2)2 + 1
f(x) = (x-7)2 -5
Use the quadratic formula to find the roots/x-intercepts/zeros of each
quadratic function.
f(x) = 2x2 + 2x – 12
f(x) =x2 + 4x + 3
f(x) = 2x2 + 3x – 20
Use this function to find all three forms, the vertex, the vertical intercept, and the
zeros, line of symmetry, and Maximum or minimum. Then sketch the graph.
f(x) = x2 -8x -20
Standard form:
Vertex Form:
Factored Form:
Vertical intercept:
Line of Symmetry:
Zeros:
Vertex:
Maximum or Minimum:
Use this function to find all three forms, the vertex, the vertical intercept, and the
zeros, line of symmetry, and Maximum or minimum.
f(x) = 3(x-5)2
Standard form:
Vertex Form:
Factored Form:
Vertical intercept:
Zeros:
Line of Symmetry:
Vertex:
Maximum or Minimum:
Use this function to find all three forms, the vertex, the vertical intercept, the
zeros, line of symmetry, and Maximum or minimum.
f(x) = (x – 6)(x + 4)
Standard form:
Vertex Form:
Factored Form:
Vertical intercept:
Zeros:
Line of Symmetry:
Vertex:
Maximum or Minimum:
Use this function to find all three forms, the vertex, the vertical intercept, the
zeros, line of symmetry, and Maximum or minimum.
f(x) = x2 –8 x + 15
Standard form:
Vertex Form:
Factored Form:
Vertical intercept:
Zeros:
Line of Symmetry:
Vertex:
Maximum or Minimum: