Name: ________________________________ Date: ___________________ Period: ___
Algebra I CP Final Study Guide
Answer the following questions shown below!
y
x
1. The equation of the above graph is _________________________.
2. Write an equation to describe the graph below.
y
x
3. Which graph is a line with slope equal to
A.
1
?
2
B.
y
y
x
x
C.
D.
y
y
x
x
4. Which equation has a slope of -6?
A) y = -2x – 6
B) y = -6x + 3
C) y = 6x + 2
D) 2y = 12x
5. Which Equation describes the line with slope 2 and y intercept -4?
A) y = – 2x
D) y = – 4x + 2
Page 2
B) y = 4x – 2
C) y = – 2x – 4
E) y = 2x – 4
6. What is the slope of the line through the points (12, 15) and (14, 18)?
A)
3
2
B) -
3
2
C)
2
3
D) 3
E) - 1
7. What is the equation of the line passing through the point (1, 3) with a
slope of 5
A) y = 5x + 2
B) y = 5x - 2
C) y = 3x + 5
D) y = 2x - 5
E) y = - 5x - 2
8. What is the equation of the line through the points (1, -4) and (-2, -1)
and y intercept = -4?
A) y = x – 4
B) y = 3x – 4
E) y = - 5x – 4
D) y = 3x + 4
9.
C) y = -x - 4
Which equation describes a line parallel to the graph of y = 2x – 5 ?
A) y = x + 1
B) y = – x + 5
D) y = 2x + 1
C) y = 3x + 1
E) y = –3x – 5
10. Which equation has a y-intercept of 3?
A) y = 4x – 3
Page 3
B) y = 25x + 3
C) y = 3x + 4
D) 4y = 3x
11. Which ordered pair is a solution to the equation y = 8x + 2 ?
A) ( 1, 2 )
B) ( 0 , -2 )
C) ( 1 , 10)
D) ( 1, 7 )
E ) ( 1, -10 )
12. Which of the following graphs is the graph of 2y + 3x = -8?
A.
B.
y
y
x
x
C.
D.
y
y
x
Page 4
x
13. The solution to the graphed system of equations below is
A) (3,2)
B) ( -2,3)
C) no solution
D) infinite number of solutions
y
x
14. The solution to the graphed system of equations is
A) infinite number of solutions
B) (0 , 5)
C) no solution
y
x
Page 5
D) ( -1, 0 )
15. Two lines have the following equations
y = 2x – 9
and
y = 6x + 7
At what point do the lines intersect? ________________________
16. The graph of linear equations is two lines that intersect at one point.
How many solutions does the system have? ___________________
Solve each system using substitution
17. y = -2x + 4
-3x + y = 29
18. -y = -2x + 16
y = -3x + 4
Page 6
Solve each system using elimination
19. x – y = 12
x + y = 22
20. 2x – y = 6
-3x + y = 5
21. The equations y = 5x + 2 and y = 5x + 2 represent
_________________________ solutions.
22.
If y = 6x and
A) yes
3x – y = 6, does 6x – 3x = 4?
B) no
C) not enough information
23. Which point is not a solution of y < 4x + 2?
A) ( 4, 15 ) B) ( 0, 3 )
C) ( - 2, -7 )
D) ( 5, - 5 )
E ) ( 0 , -1 )
24. Is (5, -2) a solution for the following system of equations?
4x + 3y = 14 and 2x + 2y = 15 ___________
25. The function f(x) = x2 - 7x - 18 belongs to which family of functions?
A) direct variation B) absolute value C) linear
Page 7
D) quadratic
26. For the following equation name the values of a, b, and c. y = x2 + 2x +1
a = _____
b= _____
c= _____
27. What does the value of “a” tell you about the graph of the equation
-2x2 - 9x - 4 = 0
A) The graph opens upward
B) The graph is a line
C) The graph has a maximum
D) The graph is skewed
28. What is the y intercept for the following equation, x2 - 7x + 6 = 0
A) 6
B) -7
C) 1
D) 0
E) 7
29. Solve x2 = 81
A) x = 81
B) x = 9
C) x = -9
D) x = -9, 9 E) x = -81
C) x = -5
D) x = -5, 5
30. Solve 2x ² + 3 = 53
A) x = 53
B) x = 25
E) x = -25
31. Use the quadratic formula to find the solutions of 2x2 + 5x – 3 = 0
A) 1 and
3
2
B) -3and
1
2
C) -1 and -1
D) 1 and 1
32. Put the following equation into standard form. 3x2 = -2x + 8
_______________________
Page 8
33. Find the sum
( 2x² - 8x) + (-2x² + 14 )
________________________
34. Find the difference
(2x 5 - 4x³ + 9) – ( 3 x 5 + 2x² - 8 )
________________________________
35. Find the product x (x + 5)
________________________________
36. Find the product
A) 2x2 - 12
-2x (x + 6)
B) -2x2 – 12
C) -2x2 – 12x
37. Find the GCF 16x + 24
____________________
38. Factor using the GCF
6x2 – 18x
_______________________________
39. Factor
x2 – 5x + 6
40. Factor x2 + 6x - 40
Page 9
D) 2x2 + 12x
41. Factor x2 – 36
42. Factor 3x2 – 12
Solve
43. x2 + 11x + 28 = 0
44. x2 - 7x = 18
45. x2 - 81 = 0
46. 5x2 – 10x = 0
Page 10
Final Study Guide
ANSWER KEY
1. y = -3
2. y = -2x - 5
3. D
4. B
5. E
6. A
7. B
8. C
9. D
10. B
11.C
12.A
13.D
14.C
15.(-4,-17)
16.one
17. (-5,14)
18.(4,-8)
19.(17,5)
20.(-11,-28)
21.infinitely many
22.B
23.B
24.no
25.D
26.a = 1, b= 2, c= 1
27.C
28.A
29.D
30.D
Page 11
31. B
32. 3x2 +2x -8 =0
33. yes
Examples 34 - 37
34. 2x
35. x + 2
36. x2 + 2x + 2
37. 3x
38. x5 + 10x3 + 7x2 + x -10
39. -8x + 14
40. -x5 - 4x3 - 2x2 + 16
41. x(x + 5 )
42. – 2x2 – 12x
43. 7x4 – 14x3
44. 8
45. 6x( x – 3 )
46. ( x – 2 )( x – 3 )
47. ( x – 4 )(x + 10 )
48. ( x + 6 )( x – 6 )
49. 3( x + 2)(x – 2 )
50. -7, -4
51. 9 , - 2
52. 9, - 9
53. 0 , 2