Benchmark Review / Study Guide
Evaluate each expression given that x = 4 , a = -2 and k = 5
1) x + 3
2) 18 – k
3) 3a
4) 25
k
5) 12 – (3k – 10) + 8
6) x + a + 14
7) k(x) -3
8) 4k + a
9) 6x – k
10) x(k)
Write the algebraic expression or equation for each of the following. Use the variable x for unknown numbers.
11) 12 increased by a number
12) the sum of a number and 8
13) the product of twice a number and 7
14) 5 subtracted from a number
15) the difference between 4 times a number and 6
16) 8 less than 25
17) The sum of 14 and 3 is 17.
18) The difference between 20 and 13 is 7.
19) 17 is the sum of twice a number and 5.
20) The quotient of 24 and 6 is 4.
Solve for the value of the variable. Show each step on a separate line
21) n + 9 = 24 22) c – 9 = -25
23) -10 + x = 14 24) 6y = 90
25) z = 216 26) 4x = 96
12
27) x + 17 = 6 28) 19 – k = 7
29) What is the solution to the number sentence?
x + 14 = -62
A -76 B -48
C 76 D 48
30) What value of m makes the following true?
48 =m
3
F 16 G -144
H -16 J 144
31)
A 8 B 6
C 2 D 4
32)
Which is the solution to the equation represented in the model?
A -8 B -6
C -2 D -10
33) Todd makes $550 a week at his job. The company gave Todd a raise and he will receive $634 a week. How much was Todd's raise?
F $16 G $1,184
H $588 J $84
34) There are 24 students in Mrs. Black's class. If the students need to be put into 4 equal groups, how many students will be in each group?
A 96 B 20
C 4 D 6
35) Nicholas is 7 years older than Travis. If Nicholas is 10 years old, what is Travis' age?
A 4 B 20
C 17 D 3
36) Ryan wants to buy a computer. He has saved $350. The computer costs $1479. Which equation shows how you can solve this problem to find out how much more Ryan needs?
F x – 350 = 1479 G 1479 + x = 350
H 350 + x = 1479 J 1479 + 350 = x
37) What is the first step when solving the equation
b - 4 = 10?
A Multiply 10 by 4 and multiply -4 by 4
B Divide 10 by -4 and divide -4 by 4
C Subtract 4 from -4 and subtract 4 from 10
D Add 4 to -4 and add 4 to 10
38) Which could be used to find the number y ?
Six more than a number, y , is equal to eight.
F 6 + 8 = y G 6y = 8
H y + 6 = 8 J 6 - y = 8
39) John called a plumber to fix a leak in his bathroom. The plumber charged $30 to come to the house and $25 an hour while fixing the leak. If the final bill was $105, how many hours was the plumber at John's house?
A 7 B 3
C 5 D 4
40) What value of d makes the following true?
48 = 12d
A 4 B .4
C 6 D 1
4
41) Which value of t makes the following true?
-16 + t < -32
A -15 B -17
C -16 D 17
42)
A. x 2 B. x -2
C. x 8 D. x -8
43) What is a value of d that makes the following true?
-15 + d > -12
A 2 B -2
C 4 D -4
Solve each inequality and graph its solution.
44) n + 7 3
45) 6 + b < -2
46) -1 > p + 5
47) 8x 168
48)
Which sequence has a common difference of -9?
A Sequence 3 B Sequence 1
C Sequence 4 D Sequence 2
49) Look at the following variable expression.
x - 9
Which sequence is described by the given variable expression?
A 4, 13, 22, 31, 40, ... B 22, 13, 5, -4, -13, ...
C 27, 18, -9, 0, 9, ... D 18, 9, 0, -9, -18, ...
50) Which sequence has a common ratio of 6?
F 23, 29, 35, 41, ... G 3, -18, 108, -648, ...
H 2, 12, 72, 432, ... J 432, 72, 12, 2, ...
51) Look at the following sequence.
80, 40, 20, 10, 5, ...
Which variable expression describes the relationship between the terms in the sequence?
A 2n B n - 5
C n + 10 D n
2
52) Ginni wrote the following geometric sequence in her notebook.
3, 9, 27, 81, 243, 729, . . .
What would be the 8th term in Ginni’s sequence?
A 5,832 B 6,561
C 1,458 D 2,187
53) Tracy is going to create a sequence with a common difference of 4. She wants to ensure that the number 23 is included in her sequence. Which number could she choose to begin her sequence with?
F 10 G 9
H 11 J 12
54) A submarine moves 60 feet below the surface of the ocean. It rises 43 feet and dives further into the water 20 feet. It finally rises 15 feet. The final location of the submarine is —
56) Which number sentence illustrates the associative property of addition?
F 7(5 + 3) = 35 + 21
G 7 + (-7) = 0
H (7 + 5) + 3 = 7 + (5 + 3)
J 7 + 5 = 5 + 7
57) Kayla shows her work when simplifying an expression.
6 + (4 • 3) • 1 + 0
Step 1: 6 + 12 • 1 + 0
Step 2: 6 + 12 + 0
Step 3: 18 + 0
Step 4: 18
Which property was applied to result in step 2?
F Multiplicative identity property
G Additive inverse property
H Multiplicative inverse property
J Additive identity property
58) Enrique researched the planet Mars and found that Mars orbits at 426,000,000 miles from our sun. How can Enrique rewrite this distance (scientific notation) for his research paper?
59) Katie, Hannah and Chris were measured in gym class. Katie was 65 ¾ inches. Hannah was 65 7/8 inches. Chris was 65 1/2 inches. Who was the tallest?
F Katie
G Hannah
H Chris
J All were the same height
60) Which is a true statement?
61) Which of the following shows the numbers listed from least to greatest?
62) Which is a square root of 256?
F 90.25 G 722
H 180.5 J 16
63) What is the value of: 232 ?