8th Grade Honors Math
Final Exam Review
Name:
Period:
Date:
1. Amiya is saving to buy a new car. She needs to save more than y dollars in order to purchase the car. She
currently has $2000 saved and is planning on saving $150 per month. Write an inequality that represents this
situation, where x is the number of months that she saves her money.
2. Write a linear inequality that represents each of the graphs shown below.
a.
b.
Shaded Region
Shaded Region
3. Graph the inequalities on the given coordinate plane.
3
a. y  x  5
5
c. 3x  2y  10
b. y   x  5
d. 2x  4y  8
4. You have a $150 gift card for Hollister. T-shirts are $25 each and sweaters are $50 each. Write and graph a
linear inequality that represents the possible combinations of t-shirts and sweaters that you can buy without
spending more than what’s on the gift card.
5. Is (-4, 8) a solution to the following system of inequalities? Explain why or why not.
10 x  7y  100
6 x  5y  40
6. Use the given graph to determine if the given points are solutions to the system of inequalities.
a) (2 , 3)
b) (-1, 2)
c) (-3,0)
7. Write and graph a system of inequalities that has no solution.
8. Graph each system of inequalities.
a.
y  4x  3
y  2 x  3
b.
2x  4y  4
3x  y  3
1
y  x 3
2
c. 2 x  y  3
x 3
9. Marsha is buying plants and soil for her garden. The soil cost $4 per bag, and the plants cost $10 each. She wants
to buy at least 5 plants and can spend no more than $100. Write and graph a system of linear inequalities to model
the situation.
10. Determine whether the functions in the tables are linear or quadratic. Explain your reasoning.
a.
x
y
0
b.
x
y
-4
0
8
1
1
1
6
2
6
2
0
3
11
3
-10
4
16
4
-24
11. The graph represents the function f(x) = -x2 + 2x + 8. Identify each of the properties listed.
Vertex:
Domain:
Range:
Y-intercept:
Zeros:
Interval of increase:
Interval of decrease:
12. Determine each of the following characteristics for the function f(x) = x2 – 4x – 5
Domain:
Range:
Zeros:
Interval of increase:
Interval of decrease:
13. Determine the x-intercepts of each function. Then, write each in factored form.
a. f(x) = x2 + 7x + 12
b. f(x) = -4x2 – 16x – 12
14. Determine the vertex of each function. Then write each in vertex form.
a. f(x) = x2 – 6x + 4
b. f(x) = 3x2 – 12x + 9
15. Determine the equation of the axis of symmetry given two symmetric points of the graph.
a. (3, 0) and (5, 0)
b. (-10, 5) and (-20, 5)
c. (-13, -2) and (7, -2)
16. Write a possible function for a quadratic function given the following characteristics.
a. opens up and has a y-intercept of (0, 9)
b. opens down and has x-intercepts (-2, 0) and (6, 0)
c. opens down and has a vertex at (-4, 2)
17. Write a function in vertex form given the following characteristics and sketch the graph of the function.
a. Is translated 7 units to the right and 4 units
down from the function f(x) = x2.
b. Is translated 2 units up
from the function f(x) = x2
18. Describe how the graph of each function compares to the graph of the given function f(x) = x 2.
a. f(x) = (x + 1)2 – 3
b. f(x) = -(x – 1)2
c. f(x) = -x2 + 3
#19-21: Rewrite each polynomial in standard form. Identify the degree and classify by the number of terms.
19. 3x2 – 4x3 + 2
20. -8x + 6x5 – x4 + 2
21. 7x + x2
#22-27: Perform the indicated operation and simplify.
22. 3x3( 2x – 7)
23. (3y 3  4y  2)  (2y2  4y  10)
24. (-5x2 + 7x – 3) – (x2 – 8x – 3)
25. ( x – 7 )( x + 4 )
26. (2x + 5)2
27. (x + 6)(3x2 – 4x + 1)
#28-33: Factor each expression completely.
28. x2 – 2x – 35
29. 2x2 + 22x + 36
30. 4x2 – 81
31. 9x3 – 3x
32. 2x2 + 13x + 15
33. 27x3 + 64
#34-39: Solve each quadratic equation using the method of your choice (factoring, quadratic formula , square
roots or completing the square). Determine the approximate and exact solutions.
34. 0 = 2x2 + 9x – 3
35. -12 = x2 + 7x
36. x2 = 7x – 10
37. 4x2 – 8x = 0
38. x2 – 14x + 19 = 0
39. 3x2 + 13 = -7x
#40-42: Determine both the approximate and the exact value of the radical (by extracting perfect squares).
40.
150
41.
42.
64
45
#43-44: Determine the approximate and exact solutions to the equations.
43.
(x + 3)2 = 60
44. (7 – x)2 = 24
45. A quarterback is throwing a football at an initial height of 6 feet. The football is traveling at a velocity of 25 feet
per second.
a. Write an equation that could be used to determine the time the ball traveled when it hit the ground.
b. How long will it take for the football to reach the ground after the quarterback threw it? Round to the nearest
hundredth.
#46-48: Determine the discriminant of each equation. Use the discriminant to determine the number of
solutions that the equation has.
46. 9x2 + 6x + 6 = 5
47. x2 + 5x + 2 = 0
48. -4x2 – 4x = 6
#49-50: Solve the following quadratic inequalities. Express solutions in interval notation.
49. x2 – 7x + 6 > -4
50. 2x2 – x + 3 ≤ 4
#51-52: Solve the following systems of linear and quadratic equations.
51.
y  x2  9x  7
y  5x  2
52.
y  3x 2  11x  15
y  2 x 2  3x