Algebra Two/Trig Name_______________________ Fall Final Review
For help videos on selected problems, barcode scan the QR code with a smartphone. No smartphone? Visit: https://sites.google.com/a/hf233.org/dmcclain/ for all videos Chapter 1
1) Write the given numbers in increasing order, and then put them on the number line provided.
a)
3
,
4,
7.1, 12,
3, 1.7
4
b)
4
19
, 1.99,
4 ,
, 6.1
3
3
2) Evaluate the following expressions at the indicated variables.
a) b)
3) Simplifying the following expressions by performing basic operations.
a) b)
4) Solve the following equations for x.
a) b)
c) d)
2
17
12
3
x
5) Solve the following inequalities.
a) b)
6) A movie ticket costs $6.50. You have $35.00 to buy tickets and popcorn for four people. How much money is left to buy popcorn after the tickets are paid for? Set up a linear equation and solve.
7) The bill for your car repairs was $265.74. The cost for labor was $52 per hour. The cost for materials was $135.74. How many hours did the mechanic work on your car? Set up a linear equation and solve.
8) Solve for y in the following equations
a) b)
Chapter 2
9) Identify the domain and range of each relation. Then, determine if each relation represents a function.
a) b)
D : { } D : { }
R : { } R : { }
Function? Y / N Function? Y / N
10) Determine if the following equations are linear.
a) b)
Linear? Y / N. Why? Linear? Y / N. Why?
11) Find the slope between the given points. Then, indicate whether the line is increasing, decreasing, horizontal or vertical.
a) b)
c) d)
12) Solve for the variable given the slope
a) m = 2, points: (3, 4) and (x, 8) b) m =
2
13) Given two lines, determine if they are parallel, perpendicular or neither.
a) b)
14) Given the following functions, evaluate at the given value of x.
a) b)
15) Write the equation of each line in point slope (
y
y
1m x
(
x
1)
), slope intercept ( y = mx +b) and standard form (Ax +By = C).a) Given point and slope: b) Given:
Pt Slope _________________ Pt Slope _________________
Slope Int _________________ Slope Int _________________
Standard _________________ Standard _________________
c) Given two points: b) Given two points:
Pt Slope _________________ Pt Slope _________________
Slope Int _________________ Slope Int _________________
Standard _________________ Standard _________________
Chapter 3A
16) Determine the solution to the given system given the graph of the system
a) b)
17) Solve the following systems by any method.
a) b)
c) d)
18) A hair salon receives a shipment of 84 bottles of hair conditioner to use and sell to customers. The two types of conditioners received are type A, which is used for regular hair, and type B, which is used for dry hair. Type A costs $6.50 per bottle and type B costs $8.25 per bottle. The hair salon’s invoice for the conditioner is $588. How many of each type of conditioner are in the shipment?
19) Given the objective function C = 4x + 5y, find the maximum and minimum values over the given feasible region.
Chapter 3B
21) Determine the dimensions of the given matrices and whether the two can be multiplied. If yes, determine the product of the two matrices.
a) b)
Dim: ______ Dim: _______ Dim: ______ Dim: _______
Can Multiply? Y / N? Can Multiply? Y / N?
If Yes, the dimension is: ___________ If Yes, the dimension is: ___________
22) Determine the dimensions of each matrix and if the matrices can be added or subtracted. If yes, determine the sum or difference.
a) b)
Dim: ______ Dim: _______ Dim: ______ Dim: _______
Can Subtract? Y / N? Can Add? Y / N?
If Yes, the difference is: ___________ If Yes, the sum is: ___________
23) Find the determinant of the given matrices.
a) b)
24) Use matrices and rref( to solve the given systems.
a) b)
25) Solve the given equations for x
M at h Com poser 1. 1. 5 escaping in cubic meters per minute at atmospheric pressure, and p represents the pressure in kilopascals. How much pressure exists if the amount of escaping gas, e, is 8.75 kilopascals? Round your answer to the nearest whole number.
A.
5m
3B. 4m
3C. 2m
3D. 35m
3Chapter 4B
31) Which point is a solution to the graph shown here?
M at h Com poser 1. 1. 5
34) Write a quadratic equation in vertex form that has the given vertex and passes through the given point. Vertex: (-3, -4); point: (4, 94)
37) A quarterback throws a football to a receiver downfield. The distance (in feet) between the ball and the ground t seconds after it is thrown is given by . How long after the ball is thrown is it 18 feet from the
38) Determine the solutions to the following graph: A. No solutions
B. x = -2 C. x = -4
39) Solve for x: (4x +5)(2x – 3) = 0
Graphs
1) Graph the given lines
a) b)
2) Graph the given absolute value functions and identify the vertex of the graph.
a) b)
Vertex: ______________________ Vertex: ______________________
3) Graph the given square root functions
4) Graph the given quadratic and identify the vertex and axis of symmetry of the graph
a) b)
Vertex: ______________________ Vertex: ______________________
A.O.S ______________________ A.O.S ______________________
5) Graph the given inequalities and determine if the point (1, -2) is a solution to the inequality.
a) b)
Is (1, -2) a solution? Y / N ? Is (1, -2) a solution? Y / N ?
–10–9 –8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 9 10
–10 –5
5 10
x y
–10–9 –8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 9 10
–10 –5 5 10
x y
–10–9 –8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 9 10
–10 –5
5 10
x y
–10–9 –8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 9 10
–10 –5
5 10
x y
–10–9 –8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 9 10
–10 –5 5 10
x y
–10–9 –8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 9 10
–10 –5
5 10
x y
–10–9 –8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 9 10
–10 –5
5 10
x y
–10–9 –8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 9 10
–10 –5
5 10
x y
–10–9 –8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 9 10
–10 –5
5 10
x y
–10–9 –8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 9 10
–10 –5
5 10
