Download Algebra II/Trig: Semester 1 Review Chapter One: Foundations for

Algebra II/Trig: Semester 1 Review
Chapter One: Foundations for Functions
1.1
Sets of Numbers
1. Order the numbers 
3
, 1.74, 1.7 , 0,  3 from least to greatest and give the sets real numbers which it
2
belongs.
1.2
Properties of Real Numbers
2. Identify the property demonstrated by 3(6 + 7) = (6 + 7)3
1.3
Square Roots
3. Simplify
1.4
4 7
3
4.
4 5  45
Simplifying Algebraic Expressions
5. Simplify x(7x + 2y) + 3xy – 4x2 6. Evaluate (2g – 1)2 – 2g + g2 for g = 3
1.5
Properties of Exponents
 2xy 2 
7. Simplify  2 5 
x y 
3
8. Evaluate (-2)-3
3.0 X 1011
9. Evaluate: Write your answer in scientific notation
6 X 104
1.6
Relations and Functions
10. Is this relation a function? From city to zip code
11. Give the domain and range for this relation: {(10,5),(20,5),(30,5),(60,100), (90, 100)}
1.7
Function Notation
12. A carnival charges a $5 entrance fee and $2 per ride. A) write a function to represent the total cost after taking
a certain number of rides. B) What is the value of the function for an input of 12, and what does it represent?
Chapter Two: Linear Functions
2.1 Solving Linear Equations and Inequalities
13. Solve 7x + 9 = 9 + 10x + 3 – 3x
14. 8x – 6 ≤ -2x + 14
2.2 Proportional Reasoning
15. The right triangles ABC and DEF are similar. The hypotenuse of ABC measure 5 cm and the hypotenuse of
DEF measures 35 cm. If one of the legs of ABC measures 6 cm, what does the corresponding leg of DEF measure?
2.3 Graphing Linear Functions and 2.4 Writing Linear Functions
16. A line has slope 
5
and passes through (2,8). Is(-5,13) also on the line?
7
17. Write the equation of the line parallel to y = -3x – 6 and passing through (4, 11)
18. What is 5x – y – 25 = 0 in slope-intercept form?
2.5 Linear Inequalities in Two Variables
19. Graph -4y > 10x – 20
2.7 Curve Fitting with Linear Models
Lea keeps track of the number of hours she works in a week and her income for the week. Here are the results from
a randomly selected sample of weeks.
Hours
8
23
18
30
12
28
Income($)
152
465
315
530
240
525
20. A) find the line of best fit for this data. B) predict how much Lea would make in a 40 hour work week.
2.8 Solving Absolute-Value Equations and Inequalities
21.
x  3  15
22.
3x  1
1
5
2.9 Absolute-Value Functions
23. Graph
g ( x)  x  6
Chapter Three: Linear Systems
3.1 Using Graphs and Tables to Solve Linear Systems
24. Solve by graphing x + y = 5 and 3x – 2y = 20
3.2 Using Algebraic Methods to Solve Linear Systems
25. Solve with substitution 2x – y = 6 and 3x + 5y = 22
26. Solve with elimination x - 3y = -12 and 2x + 11y = -7
3.3 Solving Systems of Linear Inequalities
27. Classify the figure created b the solution region of the system of inequalities: y ≥ 2x – 3, y ≥
+ 4, y  
3
1
x + 2, y  x
4
4
1
x +2
2
3.4 Linear Programming
28. Ace Guitars produces acoustic and electric guitars. Each acoustic guitar yields a profit of $30, and requires 2
work hours in factory A and 4 work hours in factory B. Each electric guitar yields a profit of $50 and requires 4
work hours in factory A and 3 work hours in factory B. Each factory operates for at most 10 hours each day. Graph
the feasible region. Then, find the number of each type of guitar that should be produces each day to maximize the
company’s profits.
3.6 Solving Linea Systems in Three Variables
29. Solve. 3x + 4y – 2z = -19, -2x – 3y + z = 10, 6x + 5y – 3z = - 38
Chapter Four: Matrices
4.1 Matrices and Data
 1 5
4 2




30. If C  6 0 and D  1 4 evaluate 2C – D




 5 3
 3 2 
4.2 Multiplying Matrices
 3 2
 2 1 4


31. If P  
 and Q   1 1  Evaluate PQ

1
3
0


 2 0 
32. For S2X4, T4x2, and V2x4, what are the dimensions of VTS?
4.3 Using Matrices to Transform Geometric Figures
33. Dilate triangle PQR with vertices P(-1,-1), Q(3,1), and R(0,3) by a factor of 1.5. Write your answer as a matrix.
4.4 Determinants and Cramer’s Rule
34. Find the area of a triangle with vertices (1,-1), (4,3) and (0,5)
35. Solve using Cramer’s Rule: 6x + 7y = -9 and x – y = 5
4.5 Matrix Inverses and Solving Systems
36. Give the inverse of
 4 2
 1 4


4.6 Row Operations and Augmented Matrices
37. Solve using an augmented matrix. -2y + 4 = 3x and 6 = 7x + 5y
Chapter Five: Quadratic Functions
5.1 Using Transformations to Graph Quadratic Functions
38. Describe the transformations from the parent function f(x) = x 2 to g(x) = -2(x + 3)2 + 1
5.2 Properties of Quadratic Functions in Standard Form
39. Given the function f(x) = 2x2 + 6x – 7, give A)direction of opening B)vertex C)axis of symmetry D) y –
intercept E) stretch or compression
5.3 Solving Quadratic Equations by Graphing and Factoring
40. Solve by factoring 4x2 + 7x + 3 = 0
41. Solve by factoring n2 -81 = 0
42. Carmen is standing on the ground. She tries to throw a tennis ball over her house, but it hits the roof on the way
down at a height of 33 feet. The quadratic equation b(t) = -16t2 + 56t. How long did it take for the ball to hit the
roof after it left Carmen’s hand?
5.4 Completing the Square
43. Write the function f(x) = x2 + 6x – 11 in vertex form
44. Solve by completing the square x2 + x = -1
5.6 The Quadratic Formula
45. Solve using the quadratic formula g(x) = x2 + 7x + 15
46. Describe the type and number of solutions for f(x) = 8x 2 + 13x – 2.3
5.7 Solving Quadratic Inequalities
47. A boat operator wants to offer tours of San Francisco Bay. His profit P for a trip can be modeled by P(x) = -2x2
+ 120x – 788, where x is the cost per ticket. What range of ticket prices will generate a profit of at least $500?
5.8 Curve Fitting with Quadratic Models
48. Write a quadratic equation that fits the points (2,27), (4, 61) and (7, 142). You should know two ways to do
this.
5.9 Operations with Complex Numbers
49. Simplify. i49
50. (2 – 4i)(7 – 3i3)
51. (12 + 6i) – (-4 – 2i)
52.
6  2i
5  3i