Compass Practice B
Algebra Test
B1. Which of these is the product of
(a + 2b) and (c - d)?
 A.
 B.
 C.
 D.
 E.
ac + ad + bc - 2bd
ac - ad + bc - 2bd
ac - ad + bc - 2bd
ac - ad + 2bc + 2bd
ac - ad + 2bc - 2bd
B1. Which of these is the product of
(a + 2b) and (c - d)?
ac  2bd
(a  2b)(c  d )
2bc
Answer
E
 ad
ac  ad  2bc  2bd
B2. If a = -2 and b = 3, what is the value
of the expression 3(a + b)(a - b).
 A.
 B.
 C.
 D.
 E.
-5
3(a  b)( a  b) 
5
3(( 2)  (3))(( 2)  (3))
15

3
(
1
)(

5
)
-15
 15
75
Answer
D
B3. This is a graph of which equation?
 A. y   3 x  6
2
3
 B. y  x  6
2
2
 C. y  x  6
3
2
 D. y   x  6
3
 E. y   2 x  6
3
B3. This is a graph of which equation?
 A. y0   33 x(9) 6 6
Answer
D
22
3
 B. y  x  6
2
2
 C. y  x  6
3

The x-intercept
is (9, 0). Try this
point in both
equations.
Notice first that the slope
2
D.(0y)   (x9) 6 6 is going down (negative).
This eliminates B and C.
3
 E. y   2 x  6
3
Notice that the y-intercept
is positive 6.
This eliminates E.
B4. What is the solution to the
equation 2(x + 3) - 3(x + 5) = 13 ?
2( x  3)  3( x  5)  13
2x  6  3x 15  13
 x  9  13
 x  22
Answer
A
x  22
 A. -22
 B. -12
 C. -4
 D. 5
 E. 15
B5. Peggy gets paid a weekly salary of D
dollars a week plus a commission of 8% on
her total sales S. Which expression below
best describes Peggy’s weekly pay?
 A.
 B.
 C.
 D.
 E.
D+S
8D + S
D + 8S
D + .08S
.08(D + S)
Answer
D
Convert 8% to decimal .08
and eliminate choices
A, B, and C.
Choice E would mean Peggy
would only get 8% of her
salary D. And Peggy will not
stand for that!
B6. Which of these is the product of
(D3 + 2D2 - 2D + 3) and (D - 5) ?
 A.
 B.
 C.
 D.
 E.
D4 + 2D3 - 2D2 + 3D
D4 - 3D3 - 8D2 + 13D - 15
D4 - 3D3 - 12D2 - 7D - 15
D4 + 7D3 + 12D2 + 13D + 15
D4 - 3D3 - 12D2 + 13D - 15
B6.
Which of these is the product of (D3 + 2D2 - 2D + 3)
and (D - 5) ?
This problem is asking you to multiply
(D - 5) (D3 + 2D2 - 2D + 3)
First distribute the D through the polynomial.
(D) (D3 + 2D2 - 2D + 3) = D4 + 2D3 - 2D2 + 3D
Now distribute the -5
(-5) (D3 + 2D2 - 2D + 3) = -5D3 - 10D2 + 10D - 15
Combine like terms
D4 + 2D3 - 2D2 + 3D - 5D3 - 10D2 + 10D - 15 =
D4 - 3D3 - 12D2 + 13D - 15 =
Answer
E
B7. What is the distance from point
A to point B?
 A. 13
 B. 85
 C.
A
5
 D. 13
 E. 85
B
B7. What is the distance from point
A to point B?
Answer
E
You can use the Pythagorean
theorem to find the distance.
a2 + b 2 = c 2
First determine the
length of the legs.
6 7  c
2
36  49  c
2
85  c
85  c
2
2
A
c85  c
6
2
B
7
B8. For all a  0 and b  0,
2
 A.
a
2
b
 B.
 C.
6
b
2
a
a b
5 4
ab
6
b
 D.
8
a
3
b
4
a
3 2
 E.
1
2 2
ab
B8. For all a  0 and b  0,
3 2
4 2
3 2
a b
5 4
ab
6
a b
bb
b
 5 3  8
5 4
ab
aa
a
First make all of the
exponents positive.
Multiply by adding
the exponents.
Answer
D
B9. For all a, b, and c,
 A.
 B.
 C.
 D.
 E.
a5b4c2
a6b4c2
a9b4c2
a5b4c3
2a3b2c
3
2
2
(a b c)
When raising a power
to a power, multiply
exponents.
(a3 b 2c)2 =
3(2)
2(2)
1(2)
a b c =
a6 b 4c2 Answer
B
B10. For all x, 3(2x + 5) - 4(x - 2) = 3(2x + 2) + 1
 A.
 B.
 C.
 D.
 E.
x=9
x = -5
x=4
x=3
x=0
B10. For all x, 3(2x + 5) - 4(x - 2) = 3(2x + 2) + 1
3(2x + 5) - 4(x - 2) = 3(2x + 2) + 1
6x + 15 - 4x + 8 = 6x + 6 + 1
2x + 23 = 6x + 7
16 = 4x
Answer
4=x
C