Download Part 1: Chapter 6- Analyzing Linear Equations

FINAL EXAM
REVIEW
TEST DATES:
____________________
____________________
NAME ________________________________________
PERIOD ________ DATE _______________________
Part 1: Algebra I: Part 1 Review
1. Solve 3x + 8 = -4
2. Solve
x
+8=5
2
3. Solve 2(a – 8) + 7 = 5(a + 2) – 4a – 19
4. Twelve minus two times a number is equal to three times the number plus 8. Find the number.
5. Find 3 consecutive even integers whose sum is 192.
6. Graph y =
3
x–3
4
7. What is the equation of the line whose graph passes through the origin and has a slope of 4?
8. What is the x-intercept of the graph of the equation 2x – 4y = 10?
9. If line m has a slope of
2
, then what is the slope of a line perpendicular to m?
3
Part 2: Systems of Linear Equations
10. Solve by graphing
y = 3x – 2
y=x+4
11. Solve the system x + 4y = 1 by substitution.
2x – 3y = -9
2x + 3y = 5
12. Use the elimination method to find the value of x in the system 5x + 4y = 16
13. What is the common expression for any 2 digit number, if t = the tens digit and u = the units digit?
14. The sum of the digits of a two-digit number is 14. If the digits are reversed, the new number
is 18 less than the original number. Find the original number.
Part 3: Polynomials
15. What is the simplest form of (2c3d4)(-5 c4d5)?
16. What is the simplest form of (x4)8?
25b5c 2
17. What is the simplest form of
, assuming denominator not equal to 0?
30b 1c 2
18. Any number, except for 0, raised to the zero power is __________.
19. What is the simplest form for 7(x2y2)0?
20. What is the degree of 3xy – 6x7y5 + x7y?
21. Write the following 17x3 – 4x + 3x5 + 3 with the powers of x in descending order.
22. What is the simplest form of (7m2 + 2m – 6) + (m2 – 4m + 7)?
23. What is the simplest form of (x – 8)(x + 7)?
24. What is the simplest form of (2y – 4)(5y2 +3y – 3)?
Part 4: Factoring
25. What is the prime factorization of 110?
26. Find the GCF of 16n6y4w and 24n5y.
27. Factor 12xy2 – 3xy.
28. Factor completely 6a3 – 21a2 + 9a
29. Factor 25x2 - 49
30. Factor the Perfect Square Trinomial 4a2 + 36a + 81
31. The length of a rectangle is twice the width. The area is 98 square cm. What is the length?
Part 5: Quadratic Equations
32. What are the equation of the axis of symmetry and the coordinates of the vertex of the graph of
y = 3x2 – 18x + 6?
33. Find the equation of the axis of symmetry for the graph of y = 4x2 + 8x + 1, and state whether this
axis contains the maximum point or the minimum point for the graph.
34. If a quadratic equation has exactly two real roots, then its graph intersects the x-axis at how many
points?
35. How many real roots does x2 – 3x + 5 = 0 have?
36. Solve 3x2 + 9x – 1 = 0.
37. Solve -2x2 + 5x + 8 = 0.
Part 6: Exponential Equations
38. Graph y =
1
∙ 2x?
4
39. Solve 8r 1  163r .
40. A certain fast growing bacteria can reproduce in 11 minutes. If you begin with 100 bacteria, how
many will there be 44 minutes later?
41. First City Bank’s “Perfect Ten” account pays 10% annual interest compounded monthly for a 10
month period. How much will a $30,000 investment be worth at the end of 10 months?
42. An $18,000 car depreciates in value at the rate of 11% per year. After how many years will the
car be worth less than $9,000?
Part 7: Rational Expressions and Equations
43. Simplify
y 2  3 y  40
.
y 2  25
44. Simplify
3n5 y 3 5nc

c5 18 y 5
45. What are the excluded values of x in the expression
46. Simplify
x7
3x  8

?
( x  4)( 2  x) 5 x  15
12m7 n mn
 4
p3
8p
47. In the long division x  2 2 x3  4 x 2  x  5 , the remainder is
48. Find
3x
7x

x2 x2
49. Find
7
5
 2
5n 4 n
50. Simplify
x
5
 2
x2 x 4
2 x  10
51. Simplify 3 x2  12
x  25
18
52. Solve
1 2
 5
3x 7
Part 8: Radical Expressions and Equations
53. Simplify 18n3 y 2
54. Simplify
7n7
3 y5
55. Simplify 9 13  13
56. Simplify 7 24  3 42  54
57. Solve
2 x 2 121  x
58. Solve.
2x  1  0
59. What is the process of removing a radical from the denominator of a fraction?
60. The number inside the radical symbol is called the ________________.
POSSIBLE PSSA PROMPTS/APPLICATION PROBLEMS… THERE WILL BE ONE
61. Tommy caught 6 redfish and 5 bluefish for a total of 27 pounds. Timmy caught 5 redfish and 6
bluefish for a total of 28 pounds. How much does each each redfish and bluefish weigh?
62. The area of a rectangular garden is 144 square feet. The length of the rectangle is 5 more than
some number and the width is 5 less than that same number.
a. Set up an equation representing the area of the garden.
b. Find the length and width of the garden.
63. An arch painted on the side of a buliding fits the equation y = -x2 + 16. Graph the arch.
a. If each block on the graph = 10 feet, what is the length of the segment along the floor?
b. What is the height of the arch?
c. The painter can use the formula A = ⅔bh to estimate the area under the parabola (b =
length of the base of the parabola at the x-axis, h = maximum height of the parabola).
What is the area under the arch?
d. How much would the paint cost to paint the walls under 8 arches if the paint is
$25/gallon, she applies 2 coats of paint, and the paint company says each gallon will
cover 180 ft2?
64. Joe Mama plans to eat at least 15 chicken wings and buffalo shrimp. Each chicken wing will cost
$0.25, and each buffalo shrimp will cost $0.40. She can spend no more than $4 on these 2 items.
Let x = number of chicken wings and y = number of buffalo shrimp.
A) Fill in the system for linear inequalities to represent the situation described above.
# of food items →
$ spent on food items →
x + y ≥ ______
______ x + ______ y ≤ ______
B) Graph the system of linear equations below using x- and y- intercepts. Then shade the appropriate
regions by testing the point (0,0) for each equation
# of chicken
wings
# of buffalo shrimp
C) Name 3 combinations of wings and shrimp that Joe Mama could buy
# of chicken wings
1.
2.
3.
# of shrimp