PROGRESS CHECK – ALGEBRA I
VERSION 4
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 + 6) (x + 2)
x(4x + 8)
4.
a) x + 6
3x
b) 2x + 4
3x2 – 6
c) –2
x
d) x + 6
4x
2
e) x + 4x – 12
3x2 – 6x
2.
Add:
x+1
x+3
+
x-3
x+3
5.
d) 2x – 2
x+3
e) 2x + 6
x(x + 6)
x+2
2
a) x (x + 3)
(x + 4)2
b) x + 3
c) 2x (x + 3)
x+4
-
x+2
3x
Multiply:
x–3
x+4
3(x + 4) • x – 2
a) x + 6
3x
b) x – 3
3x – 6
c)
1
x+4
d) x + 6
x
e) x2 + 4x – 12
3x2 – 6x
c) 2
Divide:
x+2
x
a) 4x + 8
3x
b) 5x + 18
2x
c) 2x + 4
3x
d) 4x + 12
3x
2
e) x + 4x – 12
x – 2x
a) 2x + 6
x+3
b) 2x + 6
2x + 6
3.
Subtract:
÷
x
2+x
6.
Multiply:
a)
b)
c)
d)
e)
(x – 3) (2x – 1)
3x – 4
2x2 – 3
2x2 – 7x + 3
2x2 + 7x + 3
2x2 + 7x – 3
d) x + 6
e) x2 + 4x – 12
3x2 – 6x
Developed by the Milwaukee Mathematics Partnership with support by the National Science
Foundation under Grant No. 0314898.
Progress Check – Algebra 1 – Version 4
7.
Evaluate
a)
b)
c)
d)
e)
8.
9.
(3/5)
(5/3)
(-3/5)
(-5/3)
1
1–x
x+5
if x = –2
Factor:
a2 + 5a + 6
a) (a + 2) (a + 3)
b) (a – 2) (a – 3)
c) (a – 5) (a – 6)
d) (a + 5) (a – 1)
e) (a – 6) (a + 1)
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: 4x2 + 20xy + 25y2
a) (2x + 5) (2x – 5)
b) (2x + 5y) (2x – 5y)
c) (2x + 5y) 2
d) (4x + 25y) (x + y)
e) (2x – 5y) 2
11. Simplify:
5(x + 3) – (x – 3)
a) 6x + 18
b) 4x + 18
c) 5x – 3
d) 5
e) 4x + 12
12. Completely factor: 16x2 – 4y2
a) 4 (2x – y) (2x + y)
b) (4x + 2y) (4x – 2y)
c) (16x – 4y) (16x + 4y)
d) (8x – 2y) (8x + 2y)
e) (16x – y) (x – 4y)
page 2
13. Divide:(x3 - 6x2 + 14x - 15) ÷ (x – 3)
a) x3 + 4x2 – 2x + 1
b) x2 – 3x + 5
c) x2 + 5x + 5
d) x2 – 5x – 5
e) x + 3
14. Find the slope of the line which
passes through (-3, -4) and (-1, 7).
a) (7/3)
b) (3/7)
c) (11/2)
d) (10/8)
e) (-3/7)
15. Find an equation of the line which
passes through (1, 1) and (4, -8).
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 (2, 7) 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 – 2
c) y = 5x – 1
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 4
18. Find the x-intercept for the line
4x + 5y = 20.
a) (0, 4)
b) (0, 0)
c) (-5, 0)
d) (0, -5)
e) (5, 0)
19. Solve:
x2 – 3x – 4 = 0.
a) x = 3, 4
b) x = 1, -4
c) x = -1, 4
d) x = 1, 4
e) x = -1, -4
20. Solve using the Quadratic formula:
3x2 + 5x – 4 = 0.
a) 5 + √73
6
b) 5 + √23
6
c) -5 + √-23
6
d) -5 + √73
6
e) -5 + √73
4
21. Solve P = 2(L + W) for L.
a) P + 2W
2
b) P – 2W
2
page 3
22. Rewrite with fractional exponents:
√ 25
1
/2
a) 5 1
b) 25 /4
c) 252
d) 5 1
e) 25 /2
23. Evaluate:
a) 64
b) 24
c) 96
d) 81.5
e) 6.35
3
/2
24. Multiply and simplify:
2
√ 81 x y
•
√ 3x2y3
a) √ 243x4y4
b)
9xy √ 3
c) 3x2y4 √ 3
d) 9x2y2√ 3
e) None of the Above
25. Simplify:
a)
x3
2y2
x-2
2y-3
2
b) x 3
2y
c) P + W
2
c)
d) P – 2W
4
d)
e) P + 2W
4
16
2y2
x3
y3
2x2
e) 2x2y3
Developed by the Milwaukee Mathematics Partnership with support by the National Science
Foundation under Grant No. 0314898.
Progress Check – Algebra 1 – Version 4
{
26. Evaluate | 3x - 5 | if x = 1
a) 8
b) -2
c) 2
d) -8
e) 5
a)
b)
c)
d)
e)
27. Solve:
| 2y + 3 | = 9
a) y = 3
b) y = -6
c) y = -3, 6
d) y = -3, -6
e) y = 3, -6
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 < -2
{
a)
b)
c)
d)
e)
(-3, 2)
(-3, -2)
(3, 2)
(3, -2)
(2, -1)
(-3, 2)
(-3, -2)
(0, 0)
(-3, 3)
(6, 2)
31. Find the solution:
2x – 3y = 9
-2x + 2y = -6
{
a)
b)
c)
d)
e)
28. Which is a solution for:
7 + x > 5x + 3
a)
page 4
30. Which is NOT a solution for:
y > 2x - 1
y < (-1/3) x + 3
(0, -3)
(0, 3)
(1, .8)
(5, 0)
(3, 0)
32. Find the equation of the line parallel
to y = 3x – 4 and going through the
point (-3, -2).
a) y – 2 = (-1/3)(x – 3)
b) y – 2 = 3(x - 3)
c) y + 2 = 3(x + 3)
d) y + 2 = (-1/3)(x + 3)
e) y – 4 = 3(x – 4)
33. Find the equation of the line that is
perpendicular to y = (-1/3) x + 2 and
goes through (-1,-1).
a) y = (-1/3) x + 1
b) y = 3x + 10
c) y = 3x – 10
d) y = (-1/3) x – 2
e) y = 3x + 2
34. Solve:
6x – 23 = -2x + 1
a) 7
b) 3
c) -3
d) -7
e) (-49/3)
Developed by the Milwaukee Mathematics Partnership with support by the National Science
Foundation under Grant No. 0314898.
Progress Check – Algebra 1 – Version 4
35. Solve: (1/3) x + (1/7) = (5/6 ) x + (2/7)
a) (6/7)
b) 1(1/6 )
c) (3/10 )
d) (-2/7)
e) 2 (2/7)
36. Solve:
a) 4.7
b) -29
c) -6
d) -87
e) 24
2(x – 7) – x = 5(x + 2)
37. Factor: x2 + 4x + 3
a) (x + 2) (x + 3)
b) (x + 3) (x + 3)
c) (x + 9) (x + 1)
d) (x + 1) (x + 3)
e) (x + 4) (x + 5)
38. Multiply: 6ab2c • 2yc3
a) 12 ab2c4y
b) 12a2b2c9y
c) 12b2y
d) 12a2b2c6y
e) 12a2b2cy
39. Simplify: x3y-4
x-2y8
a) x/y4
b) x5/y12
c) xy4
d) xy-4
e) x5y-4
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 = –2x – 4 ?
a) 2x + y = -4
b) 2x – y = 4
c) 2x + y = 4
d) –2x + y = 4
e) –2x – y = -4
43. Simplify: (x + 2) (x + 3)
2x + 4
(x + 3)
4x + 8
a) 2x + 4
2
b) (x + 2) (x + 3)
x
c)
(x + 2) (x + 3)
2x
d) (x + 2) (x + 3)
x
e)
(x + 2) (x + 3) 2
4x
44. Rationalize the denominator:
a) 5√y
7 3 5
40. Simplify: (x y )
a) x75y35
b) x35y15
c) x(535y3 (5
d) x /7) y /3)
e) x12y8
b) 5√y
y
c) 5y2
d) 5y
√y
e) 5y
Developed by the Milwaukee Mathematics Partnership with support by the National Science
Foundation under Grant No. 0314898.
5
√y