This study guide is for students trying to test into
College Algebra . There are three levels of math study
guides.
1.If x=2 and y=-1,what is the value of
the expression If 
2. Which of the fol lowing expressions represents the
product of four less than three times x
and two more than x?
3. A student earned scores of 92, 89, and 79 on three of
four exams. What must the student
score on the fourth exam to have an average (arithmetic mean) of exactly 85?
4. What is the equation of the line that contains the
points (3, 5) and (6, –2)?
5. For all 
6. A board 79 inches long is cut into 3 pieces. The second
piece is 5 inches longer than the
first. The third piece is twice as long as the second. If x represents the
length of the first
piece, then which equation can be used to de termine the length of the first
piece?
7. The product of 
is
8. The statement “any integer evenly divisible by two is
even ” is
A. always true
B. never true
C. true for positive integers only
D. true for negative integers only
E. true only if the integer is a perfect square
9. If x =-2 what is the value of ,
?
10. Which of the following is the complete factorization
of 
11. Which of these is the product of (x – y) and (2x + y)?
12. If x = -3 and y = 5, what is the value of
?
13. Which of the following equations is graphed above?
14. Solve this equation:
15. A car salesman receives a weekly salary of W dollars
plus a 6% commission on his total
sales S. Which expression best describes his weekly pay?
16. Which of these expressions is the product of
17. On the graph shown above, what is the distance from
point A to point B?
18. For all 
and
,simplify:
19. For all a, b, and c, simplify:
20. Solve this equation:
Answers for Test 1:
1. B
2. D
3. A
4. B
5. E
6. D
7. E
8. A
9. D
10. C
11. B
12. B
13. A
14. C
15. D
16. E
17. C
18. B
19. E
20. C
SOLUTIONS TO PRACTICE TEST
1. If x=2 and y=-1 what is the value of the
expression, and 
Answer: B
Explanation:
2. Which of the following expressions represents the
product of four less than three times x
and two more than x?
Answer: D
Explanation:
“Four less than three times x” 3x – 4
and “two more than x” x + 2
You are asked to multiply the two expressions.
3. A student earned scores of 92, 89, and 79 on three of
four exams. What must the student
score on the fourth exam to have an average (arithmetic mean) of exactly 85?
Answer: A
Explanation:
4. What is the equation of the line that contains the
points (3, 5) and (6, –2)?
Answer: B
Explanation:
All of the answers are in slope – intercept form, y = mx + b.
You xould find the slope first and then eliminate some answers.
The slope
Use the point (3,5) and the y = mx +b form to find the
value of b.
Therefore, the equation of the line is
If you do not remember the slope formula and the slope –
intercept form for a line, you
could plug both points into the five equations and eliminate the distractors.
5. For all 
Answer: E
Explanation:
This problem involves simplifying a rational expression and factoring.
Factor the numerator as (x – 7)(x + 6).
Factor the denominator as (x + 6)(x – 6).
Divide out the common factor of (x + 6), and the resulting
expression is 
6. A board 79 inches long is cut into 3 pieces. The second
piece is 5 inches longer than the
first. The third piece is twice as long as the second. If x represents the
length of the first
piece, then which equation can be used to determine the length of the first
piece?
Answer: D
Explanation:
Let x represent the length of the first piece. Then x + 5 represents the length
of the second
piece, and 2(x + 5) represents the length of the third.
Therefore, equation D, shown above, can be used to
determine the length of the first
piece.
7. The product of 
is
Answer: E
Explanation:
This is the product of two binomials, so you can use the FOIL method.
8. The statement “any integer evenly divisible by two is
even” is
Answer: A
Explanation:
The statement represents the definition of an even integer, and therefore it is
always
true.
9. If x=-2 what is the value of ,
Answer: D
Explanation:
10. Which of the following is the complete factorization
of ? 
Answer: C
Explanation:
If you do not know how to factor this expression, you could FOIL each of the
choices
11. Which of these is the product of (x – y) and (2x + y)?
Answer: B
Explanation:
FOIL the two binomials:
. Then combine the
like
terms to obtain 
.
12. If x=-3 and y=5 , what is the value of
?
Answer: B
Explanation:
Be careful to keep the negative sign on the –3. Also,
remember that
multiplication comes before addition on the –3 +3(5) expression, giving 12 not
0.
13. Which of the following equations is graphed above?
Answer: A
Explanation:
These equations are all written in slope-intercept form, y = mx + b.
Look at the graph and note the y-intercept is at (0, 1), so b = 1. therefore E
is not the
solution. From point (0, 1), you can go to the point (2, –4) by moving down 5
units (–5)
and to the right two units (+2). Slope is the ration,
so the slope is
, making the equation of this line
14. Solve this equation:
Answer: C
Explanation:
Make certain that you distribute correctly. The most
common mistake in this kind of
problem occurs when the –2 is distributed incorrectly over (x + 1).
15. A car salesman receives a weekly salary of W dollars
plus a 6% commission on his total
sales S. Which expression best describes his weekly pay?
Answer: D
Explanation:
This can be d one by the process of elimination.
Answer A is not correct because the 6% is not involved.
Answer B is not correct because the 6% should me multiplied by the sales only.
Answer C is not correct because the 6% is multiplied by the weekly salary
instead of
by the sales
Answer E is not correct because the 6% is not correctly converted to decimal
form .
.06.%6=
Answer D is correct
16. Which of these expressions is the product of
Answer: E
Explanation:
Each term in the binomial must be multiplied by each term in the second
polynomial .
Multiplying by y:
Multiplying by –5:
Combining the like terms :
17. On the graph shown above, what is the distance from
point A to point B?
Answer: C
Explanation:
This question can be answered with the Distance Formula or the Pythagorean
Theorem.
Using the Distance Formula, first determine the coordinates of the two points on
the
graph and plug those values into the distance formula.
Point A is (–5, 2) and Point B is (4, –3).
Using the Phythagorean Theorem, you could note that
segment AB is the hypotenuse
of a right triangle with vertex at (–5, –3). You can see that the lengths of the
legs of
this triangle are 9 and 5 units. Plug those values into the Phythagorean
Theorem.
18. For all
and
simplify:
Answer: B
Explanation:
Using the definition of negative exponents
or
,make all exponents
positivel Then using the rule for multiplying with exponents
,add the
exponents of like bases .
19. For all a, b, and c, simplify:
Answer: E
Explanation:
To find the power of a product, raise each factor to the power:
, and to find
the power of a power, multiply the exponents:
20.Solve this equation: 2(3x+1) – 3(x – 3) = 4(2x + 1) + 2
Answer: C
Explanation:
 |
|
 |
Use the distributive property. |
 |
Combine like terms. |
 |
Add –3x to both sides |
 |
Add –6 to both sides |
 |
Divide both sides by 5. |
This study guide has been created to give students the
opportunity to review concepts covered
on the assessment test. This has been prepared as a general study guide an in no
way
represents every question you will have on the assessment.
