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Cumulative Exam — Cumulative exam Answers

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1
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What is the solution to –2(8x – 4) < 2x + 5?

A
x >
Option A
B
x <
Option B
C
x > 6
D
x < 6
2
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The table shows the total cost of purchasing x same-priced items and a catalog.

Question illustration
A
$4, the cost per item
B
$4, the cost of the catalog
C
$6, the cost per item
D
$6, the cost of the catalog
3

Which table represents a direct variation function?

A
A table with 6 columns and 2 rows. The first row, x, has the entries, negative 3, negative 1, 2, 5, 10. The second row, y, has the entries, negative 4.5, negative 3.0, negative 1.5, 0.0, 1.5.
Option A
B
A table with 6 columns and 2 rows. The first row, x, has the entries, negative 5.5, negative 4.5, negative 3.5, negative 2.5, negative 1.5. The second row, y, has the entries, 10, 8, 6, 4, 2.
Option B
C
A table with 6 columns and 2 rows. The first row, x, has the entries, negative 5.5, negative 5.5, negative 5.5, negative 5.5, negative 5.5. The second row, y, has the entries, negative 3, negative 1, 2, 5, 10.
Option C
D
A table with 6 columns and 2 rows. The first row, x, has the entries, negative 3, negative 1, 2, 5, 10. The second row, y, has the entries, negative 7.5, negative 2.5, 5.0, 12.5, 25.0.
Option D
4

Which graph shows the solution to the system of linear inequalities?2x – 3y <12y < –3

A
Option
B
Option
C
Option
D
Option
5

Which sequences are arithmetic? Select three options.–8.6, –5.0, –1.4, 2.2, 5.8, …2, –2.2, 2.42, –2.662, 2.9282, …5, 1, –3, –7, –11, …–3, 3, 9, 15, 21, …–6.2, –3.1, –1.55, –0.775, –0.3875, …

A
–8.6, –5.0, –1.4, 2.2, 5.8, …
B
2, –2.2, 2.42, –2.662, 2.9282, …
C
5, 1, –3, –7, –11, …
D
–3, 3, 9, 15, 21, …
E
–6.2, –3.1, –1.55, –0.775, –0.3875, …
6

Which graph represents the function y = 2x – 4?

A
Option
B
Option
C
Option
D
Option
7

Two solutions of different concentrations of acid are mixed creating 40 mL of a solution that is 32% acid. One-quarter of the solution is made up of a 20% acid solution. The remaining three-quarters is made up of a solution of unknown concentration, c.Which equation can be used to determine c, the unknown concentration?

A
30c + 10(0.2) = 40(0.32)
B
(c) + (0.2) = 40(0.32)
C
(c)( (0.2)) = 40(0.32)
D
30(c)(10(0.2)) = 40(0.32)
8

Which system of linear inequalities has the point (2, 1) in its solution set?

A
y less-than negative x + 3. y less-than-or-equal-to one-half x + 3
Option A
B
y less-than negative one-half x + 3. y less-than one-half x.
Option B
C
Option
Option C
D
y less-than one-half x. y less-than-or-equal-to negative one-half x + 2
Option D
9

A mapping diagram shows a relation, using arrows, between input and output for the following ordered pairs: (negative 3, negative 4), (0, negative 4), (negative 2, 2), (negative 2, negative 1), (1, negative 3), (3, 7).

Question illustration
A
(–3, –4)
B
(–2, –1)
C
(1, –3)
D
(3, 7)
10

The weight of Jacob’s backpack is made up of the weight of the contents of the backpack as well as the weight of the backpack itself. Seventy percent of the total weight is textbooks. His notebooks weigh a total of 4 pounds, and the backpack itself weighs 2 pounds. If the backpack contains only textbooks and notebooks, which equation can be used to determine t, the weight of the textbooks?

A
0.7(t) = t – 4 – 2
B
0.7(t) = t + 4 + 2
C
0.7t(4 + 2) = t
D
0.7(t + 4 + 2) = t
11

How many solutions does this linear system have?y = x+ 2 6x – 4y = –10

Question illustration
A
one solution: (–0.6, –1.6)
B
one solution: (–0.6, 1.6)
C
no solution
D
infinite number of solutions
12

Which equation is equivalent to –k + 0.03 + 1.01k = –2.45 – 1.81k?

A
–100k + 3 + 101k = –245 – 181k
B
–100k + 300 + 101k = –245 – 181k
C
–k + 3 + 101k = –245 – 181k
D
–k + 300 + 101k = –245 – 181k
13

Sun, a kayaker, paddles 8 miles upstream (against the current) in 2 hours. Returning to her original location, she paddles downstream (with the current) the same distance in 1 hour. The equations represent x, the paddling speed, and y, the speed of the current.2(x – y) = a b(x + y) = 8Which are true? Select two options.a = 8b = 8a = 1b = 1a = b

A
a = 8
B
b = 8
C
a = 1
D
b = 1
E
a = b
14

Manny has 48 feet of wood. He wants to use all of it to create a border around a garden. The equation can be used to find the length and width of the garden, where l is the length and w is the width of the garden. If Manny makes the garden 15 feet long, how wide should the garden be?

Question illustration
A
9 feet
B
18 feet
C
30 feet
D
33 feet
15

What is the value of x in the equation (x + 12) = (x + 14) – 3?

Question illustration
A
–24
B
–6
C
negative StartFraction 2 Over 3 EndFraction.
Option C
D
0
16

At a carnival, food tickets cost $2 each and ride tickets cost $3 each. A total of $1,240 was collected at the carnival. The number of food tickets sold was 10 less than twice the number of ride tickets sold.The system of equations represents x, the number of food tickets sold, and y, the number of ride tickets sold.2x + 3y = 1240 x = 2y – 10How many of each type of ticket were sold?

A
180 food tickets and 293 ride tickets
B
180 food tickets and 350 ride tickets
C
293 food tickets and 180 ride tickets
D
350 food tickets and 180 ride tickets
17

Which exponential function has a growth factor of 5?

A
f(x) = 2(5x)
B
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It goes through (negative 1, 2) and crosses the y-axis at (0, 0.5).
Option B
C
f(x) = 0.5(2x)
D
A 2-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries one-eighth, one-fourth, one-half, 1, 2.
Option D
18

What is the solution to the linear equation?–12 + 3b – 1 = –5 – b

A
b = –2
B
b = –1.5
C
b = 1.5
D
b = 2
19

What is the missing step in solving the inequality 4(x – 3) + 4 < 10 + 6x?1. The distributive property: 4x – 12 + 4 < 10 + 6x2. Combine like terms: 4x – 8 < 10 + 6x3. The addition property of inequality: 4x < 18 + 6x4. The subtraction property of inequality: –2x < 18 5. The division property of inequality: ________

A
x < –9
B
x > –9
C
x <
Option C
D
x > –
Option D
20

How many intersections are there of the graphs of the equations below?x + 5y = 63x + 30y = 36

Question illustration
A
none
B
one
C
two
D
infinitely many

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