Algebra 1 Exam Review
Starting with Chapter 6
1. A television production company charges a basic fee of $4000 and then
$2000 per hour when filming a commercial.
a. Write an equation in slopeintercept form relating the
basic fee and per-hour charge.
b. Graph your equation.
c. Use your graph to find the
production costs if 4 hours of
filming were needed.
2. Find the x and y intercepts of -2x + 3y = 6
3. Write an equation in point-slope form for the line through the given point with
the given slope. (-2, 3); m = -1
(5, -3); m = -2
4. Is the relationship shown by the data linear? If it is, model the data with an
equation.
5. Write an equation for the line that is parallel to the given line, -7x - 3y = 3,
and that passes through the given point, (9, -7).
Tell whether the lines for the pair of equations are parallel, perpendicular, or
neither.
3x + 2y = -5
y= 2/3 x+6
6. Explain how the equation changed by translating the parent function y =
|x|.
y = |x|+ 4
y = |x – 2|
7. Solve each system of equations
by graphing:
2x + y = 6
3y = -6x + 9
8. Solve each system of equations
by graphing:
y=x
x = 2y + 2
9. Solve each system of equations by substitution:
2x + 4y = -6
x – 3y = 7
10.Graph each linear inequality.
6x - 4y < -16
-5x + 4y > -24
11. Solve each system of inequalities by graphing.
-5x + y > -2
-x + 3y >12
4x + y < 1
y > -x + 4
12. The length of a rectangle is 5 more than twice its width. If the perimeter is
34 inches, find the dimensions of the rectangle.
13. A grandmother wants to
spend at least $40 but no more
than $60 on school clothes for
her grandson. T-shirts sell for
$10 and pants sell for $20. How
many T-shirts and pants could
she buy?
a. Write a system of two
inequalities that
describes this situation.
b. Graph the system to
show all possible
solutions.
c. Write two possible
solutions to the problem.
14. Simplify the expression: 8a-3b2c-2
15. Simplify the expression: (3y)4
16. Explain the difference between –x4 and (-x)4
17. Write the following expression in standard notation: 4.155 x 107
18. Write the following expression in standard notation: 9.407 x 10-5
19. Write the following expression in scientific notation: 0.000005008
20. Write the following expression in scientific notation: 975,000,000,000
21. Simplify and write the following expression in scientific notation:
(4 x 109)(8 x 106)
22. Simplify:
23. Simplify:
24. Simplify: (2a3b-4)-2(a-3b-5)4
25. Mrs. McGrath just stocked her pond with 18 fish. If the number of fish
doubles every three months, how many fish will be in her pond after two
years?
26. Simplify the sum: (y3 + y2 – 2) + (y – 6y2)
27.Simplify the difference: (x2 – 8x – 3) – (x3 + 8x2 – 8)
28. Simplify the product: 4d2(d2 – 3d – 7)
29.Find the gcf of the terms of the polynomial: 4n4 + 6n3 + 8n2
30. Simplify the product: (3x + 1)(4x2 – 2x + 1)
31. Factor the expression: p2 – 10pq + 16q2
32. Factor the expression: d2 + 12d + 36
33. Factor the expression: f2 – 121
34. Factor the expression: 5x2 – 33x – 14
35. Factor the expression: 5y2 – 22y + 8
36. Factor by grouping: x2y – 3x2 – 2y + 6
37. Solve by factoring: x2 + 8x – 65 = 0
38. Graph the function:
y < x2 + x – 6
x
x2 + x – 6
y
39. Solve by graphing the
function:
F(x) = x2 + 3 = 12
x
y
40. Solve by using square roots: x2 – 45 = 19
41. Solve by using square roots: x2 + 30 = 5
42. Solve the equation by using the zero-product property:
5x(3x – 1)(x + 6) = 0
43. Write the functions in order from most narrow to the widest:
y = -x2
y = 7x2
y = ⅛x2
y = -⅚ x2
y = -3x2
44. Simplify:
45. Simplify:
46.Simplify:
47. Simplify:
48. Simplify:
49. Simplify: