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ALGEBRA – STUDY GUIDE
TRIMESTER 1 (Holt Chapters 1-4)
CHAPTER 1
1. If n is a real number, then 2n would
never be part of which number set?
(A) a real number
(B) an irrational number
(C) a rational number (D) an imaginary number
(E) an integer
2. If 3n – 1 is an odd integer, what is true
about 3n + 1?
(A) It is an odd integer.
(B) It is an even integer.
(C) It can be an odd or even integer.
(D) It is a prime number.
(E) It is a perfect square.
3. If 3x  4  4 x  y and x = 3, what is x  y ?
(A) -5
(B) -4
(C) 2
(D) 4
(E) 5
4. Which one of the following is false?
(A) If m and n are odd, then m + n is even.
(B) If m and n are even, then mn is even.
(C) If m and n are odd, then mn is odd.
(D) If m and n are even, then m - n is even.
(E) If m and n are odd, then (m – 1)(n + 1) is odd.
5. Which property is shown by the equation?
3
2
3
2
(9  15)   6  9  (15   6 )
5
9
5
9
A. Associative Property of Addition
B. Distributive Property
C. Commutative Property of Addition
D. Identity Property of Addition
E. Inverse Property
6. Which set of numbers contains the fewest
number of elements?
(A) whole numbers
(B) natural numbers
(C) integers
(D) real numbers
(E) rational numbers
7. If y  x 2  x  4  2 x  1 and x  3 , then
1

y
(A) 
(D)
1
9
1
11
1
21
1
(E)
7
(B)
(C)
1
11
8. If m is a positive odd integer and n is a
negative even integer, what MUST be
true about the sum of m and n?
(A) The sum is a negative even integer.
(B) The sum is a positive even integer.
(C) The sum is a negative odd integer.
(D) The sum is a positive odd integer.
(E) The sum cannot be equal to zero.
9. If 2n 2 is an even integer, what is true
about n + 1?
(A) It is an even integer.
(B) It is an odd integer.
(C) It can be an odd or even integer.
(D) It is a prime number.
(E) It is a perfect square.
10. The equation 3(4a  5b)  (4a  5b)3
demonstrates which property?
(A) Distributive Property
(B) Associative Property of Addition
(C) Associative Property of Multiplication
(D) Commutative Property of Addition
(E) Commutative Property of Multiplication
11. If the lengths of the sides of a square are
integers, which of the following could be the
area of the square in square units?
(A) 1
(B) 2
(C) 6
(D) 8
(E) All of the above
12. Which expression is equivalent to  3(2 x  y 2 ) ?
A.  3xy2
B.  9xy 2
C.  6 x  3 y 2
D.  5 x  6 y E.  6 x  3 y 2
13. Evaluate x 3  2 x 2  5 x  10 for x = -3.
(A) -80
(B) -75
(C) -70
(D) -69
(E) -65
14. Which operation is NOT CLOSED under the
set of integers?
A. addition
B. subtraction C. multiplication
D. division
E. none of these
15. Which of these sets of numbers is a subset of
rational numbers?
A. imaginary B. whole
C. irrational
D. real
E. none of these
16. Simplify 2(6x + 7) - 5(x + 3).
A. 7x – 1
B. 7x + 1
C. 7x + 19
D. 17x – 1
E. 17x + 19
21. Which property is used in this equation:
(5 x  7 y )1  5 x  7 y ?
A. Associative Property of Addition
B. Associative Property of Multiplication
C. Identity Property of Addition
D. Identity Property of Multiplication
E. Inverse Property of Multiplication
22. If x =-3 and y  2 x  4  6  3x ,
then what does y equal?
A. -13
B. -5
C. 5
D. 13
E. 17
17. What is the first step in simplifying
 2  3(2 x  1) ?
A. add -2 and -3
B. add 2x and -1
C. multiply -2 by -3 D. multiply -3 by 2x
E. add 2 to both sides
23. Which of these values is not an integer?
A. -2
B. 0
C. 36
16
1
D.
E. 
4
2
18.
24. 
-1
T
0
Which of the following values could NOT be
the value of T on the number line above?
3
A. 
5
D.  
B.  0.6
2
3
19. If x =
A. -18
D. 6
5
C.   
7
3
3
and form a pair of
4
4
A. multiplicative inverses
B. identities
C. reciprocals
D. additive inverses
E. none of these
2
E. NONE OF THESE
1
and y = -6, then xy2 
2
B. -12
C. -6
E. 18
20. Martin changed the expression  a  a   b into
0  b by using which property?
A. Inverse Property of Addition
B. Distributive Property
C. Associative Property of Multiplication
D. Identity Property of Addition
E. Identity Property of Multiplication
CHAPTER 2
1. When a number n is subtracted from 18
and the difference is divided by n, the
result is 2. What is the value of n?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 14
2. Christoph has 9 more baseball trading cards than
Miguel. The number of cards that they have
combined is 45. If c represents the number of
cards Miguel has, which equation correctly
represents the situation?
(A) 2c + 9 = 45 (B) c + 9 = 45 (C) c = 45
(D) 3c + 9 = 45
(E) 2c + 9 = 45 - c
3. Bill and Ross are twins. Their brother Mark was
born on the same day as the twins, but is three
years older. If Mark was born in 1990, in what year
did the three boys’ ages total 21?
(A) 1995
(B) 1996
(C) 1997
(D) 1998
(E) 1999
4. Solve the equation for x: y = mx + b.
y
b
(A) x = y - m – b
(B) x =
m
(C) x = my + b
(D) x = y + m + b
y b
(E) x =
m
5. The perimeter of a rectangle is 54 in. The length
is 3 in. more than the width. What is the length of
the rectangle?
(A) 13 in.
(B) 15 in.
(C) 25.5 in.
(D) 28.5 in. (E) 31 in.
6. Mr. Lawrence stops at a gas station. He has
enough cash in his pocket to buy nine gallons of
gas. If the cost of each gallon of gas was 20 cents
less, Mr. Lawrence could buy one more gallon.
How much cash does Mr. Lawrence have?
(A) $18.00
(B) $19.00
(C) $20.00
(D) $22.00
(E) $25.00
7. Leroy travels often for his job. He has figured
that he must pay $650 per month for rent, $2 per
day for water for every day he is in his apartment,
and $4 per day for electricity for every day he is in
his apartment. If x represents the number of days
Leroy is in his apartment, which of the following
represents the amount Leroy pays each month for
rent, water, and electricity?
(A) x + 656 (B) x + 830 (C) 6x + 650
(D) 650x
(E) 830x
8. Kelly’s class is collecting box tops. Kelly has
collected 75 and plans to collect an additional 4 box
tops each week. The equation y = 75 + 4x can be
used to represent this situation. How many weeks
will it take her to collect 119 box tops?
(A) 8
(B) 11
(C) 15
(D) 44
(E) 48
9. If x = -3 and x 2  xy  15 , what is the value of y
?
(A) -2
(B) -1
(C) 2
(D) 3
(E) 5
10.
(0,y)
y
x
(5,0)
If the area of the triangle shown is 30 square units,
what is the value of y ?
(A) 5
(B) 6
(C) 8
(D) 10
(E) 12
11. The equation y = 3x + 7 is equivalent to which
of the following?
 3x  y
 7
A.  3x  y  7
B.
3
 3x  7
C. 3x  y  7
D. y 
1
E. x  y  7  3
12. If 3x - 2 = y, which of the following is equal to y
- 2?
(A) 3x
(B) 3x – 4
(C) 3x + 2
(D) 3x + 4
(E) 3x + 8
13. If 5x  8  a  2 , which of the following
is equal to a?
(A) 5x
(B) 5x – 6
(C) 5x - 2
(D) 5x + 2
(E) 5x + 6
14. The lengths of the sides of a rectangle are
consecutive even integers. If the perimeter
of the rectangle is 28 units, what is the area
of the rectangle in square units?
(A) 14
(B) 24
(C) 28
(D) 32
(E) 48
15. If 4y = 3x - 1, then 3x =
4
A. 4y + 1
B. y  1
3
4y 1
4y 1
D.
E.
3
3
C.
4
y 1
3
16. Solve for y:
2a  z
x
2a  z
C. y 
x
E. y  2ax  zx
xy  z
a ?
2
A. y 
B. y 
24. Twice the sum of two consecutive integers is
10 fewer than 5 times the smaller integer. Find the
greater integer?
A. 12 B. 14 C. 13 D. -6 E. -8
2( a  z )
x
25. Which expression represents the verbal phrase
“the sum of three times a number and five”?
A. 3(n + 5)
B. 3 + n (5) C. 3(5) + n
D. 3 + (n +5) E. 3n + 5
D. y  2ax  zx
17. Find x -5 if 2( x  1)  16 ?
A. 9 B. 14 C. 7 D. 4 E. 28
18. If x represents an odd integer, which would
represent the previous consecutive odd integer ?
A. x
B. x  1
C. x  2
D. x  1
E. x  2
19. If 4x + 3 = 2x + y, then 2x =
A. y – 6
B. y – 3
C. y + 3
D. 2y – 3
E. 2y + 3
20. The value of Mrs. Jones’ car decreases by $1000
each year. If she paid $18,000 for her car in 2000,
which expression tells how much the car was worth
in 2003?
A. 18000-1000
B. 1800 0+2000
C. 18000+3000
D. 18000-2000
E. 18000-3000
21. Which of the following is an identity?
A. x + 0 = 3x
B. 1  2( x  1)   x  1
C. 5 x  6 y
D.  ( x  2)   x  2
E. 3 x  6  3( x  2)
22. Solve for p in the equation q  1 
A. p  100q  1
100
q
E. p  100(q  1)
C. p  1
q 1
B. p 
100
q
D. p  1 
100
23. Solve for x: 2  x 
p
.
100
B. x = -26
D. x = 26
E. x = 54
C. x =
27. Which value of h makes the equation true?
3
(24  8h)  2(5h  1)
4
11
A. h = 1
B. h =
C. h = 3
4
17
D. h =
E. h = 4
4
28. Which operation is used on both sides of the
equation to solve it:
A. Add
3
4
D. Multiply by
3
x  24
4
B. Subtract
3
3
C. Multiply by
4
4
4
3
B. w  3  2 C. w  5
D. w  7  2 E. w  1  5
18
5
E. Divide by 3.
29. The number line below represents the
solution to which equation?
A. w  1
8 x  40
7
A. x = -54
26. Hector has 6 times as many coins as Wilma. If
Hector has 126 coins, which equation would you
use to find out how many coins Wilma has?
A. c + 6 = 126 B. 6c = 126 C. 6(126) = c
126  6
D. c 
E. 126c = 6
6
CHAPTER 3
1. Maxine graphed an absolute value inequality and
found that the solution set was all the numbers
between -4 and 6. This solution is an example of
which?
(A) injunction (B) identity
(C) contradiction
(D) disjunction (E) conjunction
2. Your soccer team averages between 1 and 5
goals per game. Which absolute value inequality
describes the average number x of goals per game?
(A) x  2  5 (B) x  3  5 (C) x  3  2
(D) x  2  5 (E) x  2  5
4. For what values of x is 2 x  1  3  8 ?
(A) x < 2
(B) -2 < x < 3 (C) -3 < x < 2
(D) x < -2 or x >3
(E) x <-3 or x > 2
5. Which of the following is equivalent to
3 x  (2  6 x)  28 ?
A. x  10
B.  3x  30 C.  3x  2  32
D.  3x  2  6x  28 E. 6 x  (4  12 x)  14
6. Which of the following is the graph of the
solution set of -2x - 2  x + 10?
B.
C.
D.
A.
B.
C.
D.
E.
9. Which statement is false?
3. What is the smallest integer that satisfies
the inequality 4x + 5 > 2x - 3?
(A) -5
(B) -4
(C) -3
(D) 4
(E) 5
A.
8. Which of the following is the graph of the
solution set of x  3  3x  5 ?
6
 3
2
A.  3.02  3.2
B. 
C. 2 4  4 2
D. 13 2  13  13  13 2
E.  53  (5) 3
10. Solve: x 
1 x
 2
2 4
1
2
D. x > 3
B. x < 2
A. x <
C. x > 2
E. x < 3
11. Which graph represents the solution of
 6  x  3  1 ?
A.
B.
C.
-4
4
-4
4
-4
4
-4
4
-4
4
E.
7. If x 2  5 x  14  0 , then which of the following
can NOT equal x?
A. -21
B. -19
C. 1
D. 3
E. 19
D.
E.
CHAPTER 4
1. What is the equation of the function that
matches the table?
2
2
A. y   x B. y  2 x  9 C. y   x  2
5
5
3
D. y   x  2
E. y  3x  11
4
2. What is the range of the function graphed?
A. all real numbers
B. all real number less than or equal to -3
C. all real numbers less than or equal to 2
D. all real numbers greater than or equal to 2
E. all real numbers greater than or equal to -3
3. A technology consultant charges her clients a $50
estimation fee plus $65 per hour. Which function
best represents how she figures her total bill?
A. f (x ) = 65x
B. f (x ) = -65x + 50
C. f (x ) = 65x – 50 D. f (x ) = 50x + 65
E. f (x ) = 65x + 50
4. The sum of three consecutive odd numbers is
327. This can be represented by the equation, n +
(n - 2) + (n - 4) = 327. What does n represent?
A. The least integer
B. The greatest integer
C. The sum of the integers
D. The integer in the middle
E. The number of integers
5. If f (x ) =  x 2  2 x  3 then f (-3) =
(A) -18 (B) -12
(C) -6
(D) 6 (E) 18
6. If f (a) = 11, then use the table tofind f (a - 2).
(A) 4
(B) 7
(C) 9
8. The graph of f (x) is shown. What is the value of
f ( 0) ?
(A) -3 (B) -2 (C) 0
(D) 2 (E) 3
9. Which of the following best describes the
correlation between the variables x and y in the
scatter plot?
A.
B.
C.
D.
E.
strong positive correlation
weak positive correlation
strong negative correlation
weak negative correlation
no correlation
10. What is the difference between the price for a
300-page novel on the trend line and the actual
price of a 300-page novel?
(D) 16 (E) 21
7. The table of values given can be derived from
which one of the following functions?
A. f (x) = 2x + 10
C. f (x) = 2x  2
E. f (x) = x – 6
B. f (x) = x + 2
D. f (x)= 4 - x
A. $0
B. $1
C. $3
D. $6
E. $8
11. Which is the most reasonable predicted annual
average dial-up modem sales for a store in Year 6?
15. Which pair of variables could be supported by
this scatter plot?
12. The graph below shows the horsepower needed
as the revolutions per minute of an agitator
increases. What is the most valid statement about
this function?
A. x = the price per gallon of gasoline
y = number of miles driven
B. x = hours worked
y = amount of free time
C. x = capacity of gas tanks in cars
y = amount of miles driven on one tank of gas
D. x= monthly rainfall amount for a community
y = amount of watering done by a resident in
the community
E. x = amount of time a person spends at baseball
games
y =amount of time a person spends on his
woodworking hobby
A. The domain includes both positive and negative
values.
B. The range includes both positive and negative
values.
C. For at least one x-value there is more than one
y-value.
D. For at least one y-value there is more than one
x-value.
E. The domain includes the set of all real numbers.
16. Which situation would require the use of a
piecewise function?
A. The Lions Club earns 15% of total sales if they
sell 100 or fewer candy bars and 20% if they sell
more than 100.
B. Sarah charges $6 per hour to babysit on
weekdays and $8 per hour on Friday and Saturday.
C. Al’s Plumbing charges a service call of $25 plus
$40 per hour for plumbing issues.
D. Roberto has taken three quizzes so far and
wants to have an average of at least 90 percent.
E. The population of a particular city increased for
two years and then decreased for the next three.
A. 500 B. 100
C. 50
D. 5
E. 1
13. The bus company in town sells a bus pass each
year for $8.50, and then charges $0.25 a ride. Using
the function f (b ) = 0.25b + 8.5, how much will it
cost someone to ride the bus 38 times?
A. $9.50
B. $18.00
C. $20.00
D. $9.50
E. $118.00
14. Let f (x) = 0.4 + .85x be the equation of the
line-of-best-fit used to approximate the data on a
scatter plot. What would be the approximate value
of f (5)?
A. 4.65 B. 5.41 C. 6.25 D. 8.25 E. 24.25
17. When you graph the function y  x  1 for
x=-3, -2, -1, 0, 1, what type of shape is made?
A. line
B. C-shape
C. U-shape
D. V-shape E. none of these
Answer Key—Trimester 1 Final Exam Study Guide
CHAPTER 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
D
A
C
E
A
B
E
E
C
E
A
E
C
D
B
A
D
E
E
A
D
A
E
D
CHAPTER 2
1
B
2
A
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
E
E
B
A
C
B
A
E
A
B
E
E
A
A
D
C
B
E
E
E
E
C
E
B
A
D
B
CHAPTER 3
1
E
2
3
4
5
6
7
8
9
10
11
C
C
C
B
B
C
C
D
B
A
CHAPTER 4
1
C
2
D
3
E
4
B
5
B
6
B
7
D
8
B
9
C
10
C
11
C
12
D
13
B
14
A
15
C
16
A
17
D