PROGRESS CHECK – ALGEBRA I
VERSION 3
CALCULATORS ARE NOT TO BE USED ON THIS TEST
For each question, select the correct response. (Assume no variable will make the
numerator or denominator zero.)
1.
Simplify:
(x + 1) (x – 4)
x(3x + 3)
4.
a) x + 6
3x
b) x – 4
x
c) x – 4
3x
d) x – 3
3x
2
e) x – 3x – 4
3x2 + 3x
2.
Add:
x+5
x+3
+
x+2
x+3
5.
d) 2x + 7
x+3
e) 2x + 6
x(x + 5)
x+4
a) x2 (x + 5)
(x + 4)2
b) x + 4
x
c) x + 5
-
3
2x
Multiply:
x-2 • 7+x
x(x + 7) x + 2
a) x – 2
x2 + 2x
b) 2x + 5
x2 + 7x
c) x – 2
x+2
d) x + 6
x
e) x2 + 5x – 14
3x – 14
c) 2
Divide:
4x + 3
x
a) 12x + 7
3x
b) 8x + 3
2x
c) 2x + 3
x
d) 4x + 6
2x
2
e) x + 4x – 12
x – 2x
a) 2x + 3
x+3
b) 2x + 7
2x + 6
3.
Subtract:
÷
x
4+x
6.
Multiply:
a)
b)
c)
d)
e)
(x – 2) (4x + 2)
5x
4x2 – 4
4x2 – 6x + 4
4x2 – 6x – 4
4x2 + 6x – 4
d) 2x (x + 5)
x+4
e) x2 + 4x – 12
4x2 – 8x
Developed by the Milwaukee Mathematics Partnership with support by the National Science
Foundation under Grant No. 0314898.
Progress Check – Algebra 1 – Version 3
7.
Evaluate
a)
b)
c)
d)
e)
2–x
x+6
if x = –3
1
5
/3
-1
/9
5
/9
2
8.
Factor:
a2 + 5a - 6
a) (a + 6) (a – 1)
b) (a – 2) (a – 3)
c) (a – 5) (a – 6)
d) (a + 5) (a – 1)
e) (a – 6) (a + 1)
9.
Factor: 6x2 – x – 2
a) (6x – 2) (x + 1)
b) (3x – 2) (2x + 1)
c) (6x – 1) (x + 2)
d) (3x + 2) (2x – 1)
e) (3x + 2) (2x + 1)
10. Factor: 16x2 + 40xy + 25y2
a) (4x + 5) (4x – 5)
b) (4x + 5y) (4x – 5y)
c) (16x + 25y) (x + y)
d) (4x + 5y) 2
e) (4x – 5y) 2
11. Simplify:
4(x + 2) – (x – 5)
a) 3x + 13
b) 3x + 3
c) 3x – 13
d) 3x – 3
e) 3x + 7
12. Completely Factor: 4x2 – 36y2
a) (4x + 6y) (4x – 6y)
b) (4x – 36y) (4x + 36y)
c) (2x – 9y) (2x + 9y)
d) (4x – y) (x – 36y)
e) 4 (x – 3y) (x + 3y)
page 2
13. Divide:(x3 + 2x2 - 11x - 12) ÷ (x – 3)
a) x3 + 4x2 – 2x + 1
b) x3 – 4x2 + 2x + 1
c) x2 + 5x + 4
d) x2 – 5x – 5
e) x + 3
14. Find the slope of the line which
passes through (-1, 3) and (6, 0).
a) (7/3)
b) (3/7)
c) (11/1)
d) (10/8)
e) (-3/7)
15. Find an equation of the line which
passes through (2, 5) and (4, 4).
a) y = –2x – 6
b) y = 2x – 5
c) y = (1/2)x – 5
d) y = (-1/2)x + 6
e) y = –3x + 4
16. Find an equation of the line which
passes through (-1, -5) and has a
slope of 2.
a) y = –2x + 3
b) y = 2x – 3
c) y = –2x – 4
d) y = 2x + 3
e) y = –2x – 2
17. Write the slope-intercept form of
y – 3 = 5(x – 1).
a) y = 3x + 3
b) y = 5x + 1
c) y = 5x – 2
d) y = 3x –1
e) y = 3x – 6
Developed by the Milwaukee Mathematics Partnership with support by the National Science
Foundation under Grant No. 0314898.
Progress Check – Algebra 1 – Version 3
18. Find the y-intercept for the line
5x + 4y = -12.
a) (0, -3)
b) (0, 0)
c) (-3, 0)
d) (0, 3)
e) (3, 0)
19. Solve:
x2 – 3x – 4 = 0.
a) x = -1, 4
b) x = 1, -4
c) x = -1, 4
d) x = 1, 4
e) x = -3
20. Solve using the Quadratic formula:
5x2 + 3x – 1 = 0.
a) -3 + √29
5
b) 3 + √29
5
c) -3 + √29
10
d) 3 + √29
10
e)
-3 + √7
5
21. Solve P = 2(L + W) for W.
page 3
22. Rewrite with fractional exponents:
√ 64
(1
a) 8 /(12)
b) 64 (1/2)
c) 64 /4)
d) 8
e) 82
23. Evaluate:
a) 6
b) 8
c) 32
d) 24
e) 54
4
3
/2
24. Multiply and simplify:
√ 12xy
4
•
√4x4y8
a) 48x4y12
b) 48x4y12
c) 2x2y6 √ 12
d) 4x2y6 √ 3
e) None of the above
25. Simplify:
a) P – 2L
2
a)
x3
3y2
b) P + 2L
2
b)
y2
3x3
c) P – 2L
4
c)
3y2
x3
d) P + L
4
d)
x-3
3y-2
e) P + 2L
4
e) 3x3y2
3x3
y-2
Developed by the Milwaukee Mathematics Partnership with support by the National Science
Foundation under Grant No. 0314898.
Progress Check – Algebra 1 – Version 3
26. Evaluate | 3x – 7 | if x = -3
a) 16
b) -16
c) -1
d) 1
e) 2
27. Solve:
| 2y + 1 | = 5
a) y = 3
b) y = -2
c) y = -3, 2
d) y = 3, 2
e) y = -3, -2
28. Which is a solution for:
2x – 1 < 3x - 2
a)
b)
c)
d)
e)
-4 -3 -2 -1 0
1
2
3
4
-4 -3 -2 -1 0
1
2
3
4
-4 -3 -2 -1 0
1
2
3
4
-4 -3 -2 -1 0
1
2
3
4
-4 -3 -2 -1 0
1
2
3
4
29. Which is a solution for:
x>2
y > -1
{
a)
b)
c)
d)
e)
(-3, 2)
(-3, -2)
(3, 2)
(3, -2)
(2, -1)
30. Which is a solution for:
y < 2x – 1
y < (-1/3) x + 3
{
a)
b)
c)
d)
e)
(3, 2)
(-3, -2)
(-3, 2)
(-3, 3)
(6, 2)
page 4
31. Find the solution:
3x + 3y = 6
2x – 3y = 4
{
a)
b)
c)
d)
e)
(3, .667)
(2, -3)
(5, 10)
(2, 0)
(3, 10)
32. Find the equation of the line parallel
to y = 3x – 9 and going through the
point (-2,-1).
a) y – 1 = 3(x – 2)
b) y + 1 = 3(x + 2)
c) y – 1 = (-1/3)(x – 2)
d) y + 1 = (-1/3)(x + 2)
e) y – 9 = 3(x – 9)
33. Find the equation of the line that is
perpendicular to y =( -1/3) x + 2 and
goes through (3,-4).
a) y = (-1/3) x + 1
b) y = 3x – 4
c) y = 3x + 13
d) y = (-1/3) x – 4
e) y = 3x – 13
34. Solve:
2x + 44 = –2x – 8
a) 13
b) (52/5 )
c) (39/4)
d) -13
e) None of the above
35. Solve:(2/9) x + (1/7) = (1/3) x + (1/14)
a) (6/7)
b) (9/14)
c) 1(1/16)
d) (3/10)
e) 2 (9/10)
Developed by the Milwaukee Mathematics Partnership with support by the National Science
Foundation under Grant No. 0314898.
Progress Check – Algebra 1 – Version 3
36. Solve:
a) 4.7
b) -47
c) -7
d) 47
e) -24
3(x – 9) – 2x = 2(x + 10)
37. Factor: x2 + 10x + 9
a) (x – 3) (x + 3)
b) (x + 5) (x + 5)
c) (x + 9) (x + 1)
d) (x + 3) (x + 3)
e) (x + 4) (x + 5)
38. Multiply: 4ab3c5 • 3yac4
a) 12 ab3c9y
b) 12b2y
c) 12a2b2c6y
d) 12a2b2cy
e) 12a2b3c9y
39. Simplify: x3y2
x-2y6
5 4
a) x /y
b) x5/y12
c) xy4
d) xy-4
e) x5y4
page 5
41. Rewrite 3x + y = 4 in
slope-intercept form.
a) y = 3x – 4
b) y = –3x – 4
c) y = (3/2)x – 2
d) y = (-3/2)x + 2
e) y = –3x + 4
42. Which of the following is equivalent
to y = –3x + 7 ?
a) 3x – y = –7
b) 3x + y = 7
c) 3x + y = –7
d) –3x + y = 7
e) –3x – y = –7
43. Simplify: (x + 2) (x + 3)
2x
(x + 3)
4x + 8
2
a) (x + 2) (x + 3)
x
2
b) (x + 2) (x + 3)
x
c)
(x + 2) (x + 3)
2x
d)
2 (x + 2) 2
x
e) (x + 2) (x + 3)
4x
44. Rationalize the denominator:
40. Simplify: (x3y5)2
a) x6y10
(3
(3
b) x /5)y /5)
c) x(45y7
d) x /2) y
e) x32y52
a) 5x
b) 5√x
c) 5x2
d) 5x
√x
e) 5√x
x
Developed by the Milwaukee Mathematics Partnership with support by the National Science
Foundation under Grant No. 0314898.
5
√x