The document is a review for an algebra test that covers topics including: - The coordinate plane (quadrants, axes, origin) - Ordered pairs and graphing points - Functions, domains, ranges - Solving equations - Graphing linear equations - Finding slopes and y-intercepts of lines - Systems of equations - Inequalities It contains 50 questions reviewing these essential algebra concepts in preparation for the test.

1. Name ________________________________ Date __________________
Algebra IB Review for Fall Semester Test Part B
____________________________________________________________________________________________________________
1) What is the vertical axis?
2) What is the horizontal axis?
3) What is the origin?
4) Label each of the quadrants with the appropriate names
5) The signs of the points in the third quadrant of the coordinate plane are ___________
6) The signs of the points in the fourth quadrant of the coordinate plane are ____________
Graph and label each of the ordered pairs on the graph provided.
7) A( 0, 4 )
8) B( -6, 1)
9) C( 2, 5 )
10) D( -3, -4)
11) E( -5, 0 )
12) F( 7, -5 )

2. List the coordinates of the points that are plotted on the graph to the right
13) A( , )
A
14) B( , ) B
15) C( , ) C
16) D( , ) D
17) E( , )
18) F( , )
E F
Define the following terms:
19) Domain
20) Range
21) Function
2
Given the relation { (5, -1), (-2, 3), (1.5, 7), (0, 4), ( , -6) } find
3
22) the domain ___________________________________
23) the range ____________________________________
Decide which of the relations below is a function and which is not ( answer YES or NO )
24) { (2, 4), (-4, 8), (5, 2), (-1, 3) } ______________
25) { (2, 1), (3, 1), (4, 1), (5, 1) } ______________
26) { (5, -2), (2, -6), (5, 1), (0, 4) } ______________
27) { (4, 1), (5, -6), (2, 3), (2, 3) } _______________

3. 28) Explain how the vertical line test works with graphs.
Decide whether not each graph represents a function. ( Answer YES or NO )
29) _____________ 30) _______________
31) ______________ 32) _______________
33) ______________ 34) ___________

4. Given the function f(x) = (x+1)2 - 2 find
35) f(2) ____________ 36) f(-1) _____________ 37) f(0) _____________
4
Given the function g(x) = + x find
x
38) g(-1) ____________ 39) g(2) ____________ 40) g(0) _____________
Given the domain D= { -1, 0, 2, 4 } find the range for each function
41) f(x) = 2x + 1 ___________________________
42) g(x) = x2 - 1 ___________________________
Solve for ‘y’ in each equation ( isolate the y variable )
43) y - 3x = 7 ______________ 44) 2y + x = 4 _________________
45) x - y = 3 ______________ 46) 4y - 8x = 12 _______________
Graph the following equations - Show the table you used to construct the graph in the space
to the left of the graph
1
47) y = -3x + 2 48) y = x-1
2
x y x y

5. 49) What is the slope of a line?
50) What is the y-intercept?
Find the slope and intercept of each line shown in the graphs
51) m = ______ b = _______ 52) m = _____ b = _______
53) m = ______ b = _______ 54) m = _____ b = _______

6. 55) Given the points (x1, y1) and (x2, y2) what is the formula we can use to
find the slope of the line through the points.
Find the slope of the line that passes through the two given points.
56) A(2, 6) B(4, 10) m = _______ 57) A(-3, 1) B(2, -1) m = _________
58) A(-2, 7) B(-2, -1) m = _______ 59) A(4, -3) B(1, -3) m = ________
Find the equation of the line with given slope and intercept
6
60) m = b = -4 ______________________
11
61) m = -5 b = 0 ______________________
5
62) m = 2 b = ______________________
4
Find the equation of the line passing through the given point with the listed slope.
63) m = 2 (-3, -1) ______________________
1
64) m = − (4, 3) ______________________
2
Find the equation of the line passing through the two given points
65) (3, 5) (5, 1) ______________________
66) (2, 0) (4, 1) ______________________

7. Find the equation of each line shown below
67) ____________________ 68) __________________
69) What does it mean for lines to be perpendicular?
70) What does it mean for lines to be parallel?
71) How do we know when lines are parallel?
72) How do we know when lines are perpendicular?
Decide if the listed pair of lines will be parallel, perpendicular, or neither.
73) y = 2x + 3 y = -2x + 3 ___________________
74) y = x + 4 y = -x - 2 ___________________
2 3
75) y = x+1 y= − x ___________________
3 2
76) y = -3x + 2 y = -3x - 5 ___________________
1 1
77) y = x-1 y= x+7 ___________________
3 3

8. Solve the systems of equations graphically
1
78) y = 3x - 2 79) y= − x+2
2
y = 2x + 1 y= x-3
Solve the following systems using substitution
80) y = x + 2 81) y = 3x - 4
y = -2x + 4 y = 2x - 3
Solve the following systems using elimination and multiplication where needed
82) 3x + 2y = 8 83) 4x + 3y = 13
x - 2y = 8 -2x + 3y = 7
84) 5x + y = 7 85) 2x - 6y = 3
x + 4y = 9 3x + 4y = -2

9. Graph the following inequalities
1
86) y > 3x - 5 87) y < - x+3
2
88) Solve the following system of inequalities by graphing
y < -2x + 4
1
y > X-3
3