Algebra 2 – Semester 1 Final Review (chapters 0-2)
Name___________________________
Date_____________ Period________
Show All Work for Full Credit!
Solve each equation:
1. -4x + 6 =22
2. 2x + 5 = x – 13
3. 9x + 3 = 10 – 2(3x + 5)
4.
1
(7𝑥
2
+ 40) = 80 − 10𝑥
5. Find the slope of the line through the points (3, 2) & (-4, 3).
6. List the slope and y-intercept for the line 2x + y = 14.
Graph each line:
7. 𝑦 = −𝑥 + 5
8. 2𝑥 + 𝑦 = 8
Graph each line:
9. 𝑥 + 2𝑦 = 8
10. 𝑥 = 4
11. Graph y =0.
12. Write the equation of the given line:
13. Write the equation of the line, in slope-intercept form, that passes through the point (4,-3) and has a
slope of 2.
14. Find the slope of the line passing through the points (8, 5) and (11, 14) and then WRITE THE
EQUATION OF THE LINE THROUGH THE TWO POINTS.
15. Write the equation of the line that passes through the points (-5, 9) & (-4, 7).
16. Graph the linear equation and estimate the solution:
2𝑥 − 𝑦 = 5
{
𝑦 = −𝑥 − 3
17. Graph the linear equation and estimate the solution:
𝑥 + 2𝑦 = 3
{
−7𝑥 + 3𝑦 = −21
18. Solve the linear system by the substitution method:
2𝑥 + 3𝑦 = 5
{
𝑥 = 9 + 5𝑦
19. Solve the linear system by the substitution method:
2𝑥 − 4𝑦 = 10
{
𝑥 + 4𝑦 = 5
20. Solve the linear system by the elimination method:
{
2𝑥 + 8𝑦 = 8
3𝑥 − 2𝑦 = −16
21. Solve the linear system by the elimination method:
{
−3𝑥 + 𝑦 = 2
8𝑥 − 15𝑦 = 7
22. (a) Write a system of equations to solve the problem. (b) Solve the system to answer the question.
Mark sold 497 tickets for the school play. Student tickets cost $4 and adult tickets cost $5. Mark’s sales
totaled $ 2283. How many student and adult tickets did Mark sell?
23. (a) Write a system of equations to solve the problem. (b) Solve the system to answer the question.
A sporting goods store receives a shipment of 124 golf bags. The shipment includes two types of bags,
full-size and collapsible. The full-size bags cost $38.50 each. The collapsible bags cost $22.50 each. The
bill for the shipment is $3430. How many of each type of golf bag are in the shipment?
Chapter 2 (or chapter 5 from the “old” book)
Graph each quadratic. Identify the vertex and axis of symmetry.
1. 𝑦 = 2𝑥 2 − 12𝑥 + 10
2. 𝑦 = −2(𝑥 + 3)2 − 4
Vertex ______
Vertex _______
Axis of symmetry ___________
Axis of symmetry ___________
3. Write the vertex form of the quadratic. _______________________________________
4. A technician is launching an aerial firework from the ground. The height of the firework in feet is
modeled by the function f(x) = -16(x – 3)2 + 256 where x is the time in seconds after the firework is
launched.
a) What is the maximum height that the firework reaches?
_______________________
b) How long does the firework stay in the air?
_________________________
For Problems 5-8 solve each quadratic by the square root method.
5. –x2 – 12 =-87
6. 2(x – 6)2 – 45 = 53
7. (2x – 5)2 = 81
8. 2x2 + 9 = -41
For Problems 9-12, solve each quadratic by the Factor Method.
9. x2 + 9x = -14
10. x2 = -3x + 10
11. 2x2 + 7x + 3 = 0
12. 5x2 = 7x – 2
For Problems 13 & 14, Graph each function by first writing in vertex form. List the Vertex.
13. f(x) = x2 + 6x + 4
Vertex: ___________
14. F(x) = -7x2 – 14x
Vertex: ___________
For problems 15-18, solve each quadratic by using the quadratic formula.
15. x2 + 3x – 2= 0
16. 2x2 + 3x = -1
17. x2 – 2x = 99
18. X2 = 8x – 35
x
 b  b 2  (4ac)
2a
For problems 19-22, simplify. Write your answers in standard form.
19.
(3 – 3i) – (4 + 7i)
21.
(4 + 5i)(2 + i)
20.
(-1 + 2i) + (6 – 9i)
22.
3i (2 – 3i)
23. Write the quadratic function in vertex form with a vertex of (-4, 6) and passing through (-1, 9).
24. Write the quadratic function in intercept form whose graph has x-intercepts of -2 and 2 and passes
through the point (-4, 8).
25. John made a rectangular pennant for the wrestling team. The area of the pennant is 70 ft2. The
length of the pennant is 3 feet longer than the width. What are the lengths of the length and width of
the pennant? (rem: area of rectangle is area=lw)