AnswersMathematics IIIN/A

Practice Exam Answers

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21
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Which of the following shows the graph of y is equal to negative 2 to the x th power minus 1 ?

A
Image with description On a coordinate plane, the curve approaches x axis for negative values of x in the third quadrant. It passes through (negative 1 comma negative 1), (0 comma negative 2), (1 comma negative 4), and decreases rapidly in the fourth quadrant.
B
Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis, both labeled from negative 10 to 10 in increments of 2. A curve extends horizontally to the left along the horizontal line y = 1 with an arrowhead pointing left. From left to right, the curve passes through 0 comma 0, 1 comma negative 1, 2 comma negative 3, 3 comma negative 7, and curves steeply downward into the fourth quadrant with an arrowhead pointing down.
C
Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis, both labeled from negative 10 to 10 in increments of 2. A curve extends horizontally to the left just below the x-axis with an arrowhead pointing left. From left to right, the curve passes through 0 comma negative 0.5, 1 comma negative 1, 2 comma negative 2, 3 comma negative 4, and curves steeply downward into the fourth quadrant with an arrowhead pointing down.
D
Image with description On a coordinate plane, the curve approaches the line y equals negative 1 for negative values of x in the third quadrant. It passes through (0 comma negative 2), (1 comma negative 3), (2 comma negative 5), and decreases rapidly in the fourth quadrant.
22
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What is the minimum value of cap c is equal to 7 x plus 8 y , given the constraints on x and y listed? 2 x plus y is greater than or equal to 8 x plus y is greater than or equal to 6 x is greater than or equal to 0 y is greater than or equal to 0

A
32
B
42
C
64
D
46
23

An equation for the depreciation of a car is given by y is equal to cap A times open paren 1 minus r close paren to the t th power , where y is equal to current value of the car, cap A is equal to original cost, r is equal to rate of depreciation, and t is equal to time, in years. The current value of a car is 12 dollars comma 282 point 5 0 The car originally cost 20 dollars comma 000 and depreciates at a rate of 15 percent per year. How old is the car?

A
4 years
B
1 third years
C
3 years
D
1 fourth years
24

Angle cap b has a measure between 0 degrees and 360 degrees and is coterminal with a negative 865 degrees angle. What is the measure of angle cap b ?

A
110 degrees
B
210 degrees
C
115 degrees
D
215 degrees
25

The formula for the volume of a pyramid is cap v is equal to 1 third cap b h Which of the following equations is equivalent to the given formula?

A
cap b is equal to 3 h over cap v
B
cap b is equal to the fraction with numerator cap v plus 1 third and denominator h
C
cap b is equal to 3 cap v over h
D
cap b is equal to the fraction with numerator cap v minus 1 third and denominator h
26

Which of the following shows the extraneous solution to the logarithmic equation 2 log sub 5 open paren x plus 1 close paren is equal to 2 ?

A
x is equal to negative 6
B
x is equal to negative 4
C
x is equal to negative 2
D
x is equal to negative 1
27

Which of the following gives a single solution of the inequality start absolute value x plus 3 end absolute value minus 2 is less than or equal to 0 and shows a graph that can be used to determine the entire solution set of the inequality?

A
x is equal to negative 1 Image with description A coordinate plane with a horizontal x-axis labeled from negative 6 to 4 in increments of 1 and a vertical y-axis labeled from negative 5 to 5 in increments of 1. A V-shaped graph opens upward with its vertex at negative 3 comma 0. A horizontal line passes through 2 on the y-axis, intersecting the V-shaped graph at negative 5 comma 2 and negative 1 comma 2.
B
x is equal to 5 Image with description A coordinate plane with a horizontal x-axis labeled from negative 4 to 6 in increments of 1 and a vertical y-axis labeled from negative 5 to 5 in increments of 1. A V-shaped graph opens upward with its vertex at 3 comma 0. A horizontal line passes through 2 on the y-axis, intersecting the V-shaped graph at 1 comma 2 and 5 comma 2.
C
x is equal to 0 Image with description A coordinate plane with a horizontal x-axis labeled from negative 6 to 4 in increments of 1 and a vertical y-axis labeled from negative 5 to 5 in increments of 1. A V-shaped graph opens upward with its vertex at negative 3 comma 0. A horizontal line passes through 2 on the y-axis, intersecting the V-shaped graph at negative 5 comma 2 and negative 1 comma 2.
D
x is equal to 2 Image with description A coordinate plane with a horizontal x-axis labeled from negative 4 to 6 in increments of 1 and a vertical y-axis labeled from negative 5 to 5 in increments of 1. A V-shaped graph opens upward with its vertex at 3 comma 0. A horizontal line passes through 2 on the y-axis, intersecting the V-shaped graph at 1 comma 2 and 5 comma 2.
28

The ideal gas law states that the volume, v , of a gas in liters varies directly with the amount of the gas in moles, n , and the absolute temperature, cap t , in kelvins and varies inversely with the pressure, cap p , in atmospheres. Two moles of a gas have a volume of 35 point 4 2 4 L at 270 kelvins when cap p is equal to 1 point 2 5 atmospheres. What is the volume of 3 moles of a gas at 280 kelvins when cap p is equal to 1 point 5 atmospheres?

A
27 point 3 3 L
B
103 point 3 2 L
C
45 point 9 2 L
D
11 point 4 8 L
29

Triangle RST has sides measuring 22 inches and 13 inches and a perimeter of 50 inches. What is the area of triangle RST ? Round to the nearest square inch. Heron’s formula: Area is equal to square root of s open paren s minus A close paren open paren s minus b close paren open paren s minus c close paren end root

A
60 square inches
B
95 square inches
C
19 square inches
D
37 square inches
30

The table shows the different times it takes Paula to drive to her grandmother’s house depending on the rate at which she drives. Rate vs. Time Rate (mph) 30 40 50 60 Time (h) 2 point 5 1 point 8 7 5 1 point 5 1 point 2 5 If one day Paula rides a scooter to her grandmother’s house at a constant rate of 24 miles per hour, how long should it take her?

A
3 point 1 2 5 hours
B
2 point 7 5 hours
C
3 point 7 5 hours
D
2 point 6 2 5 hours
31

If you are given the graph of g of x is equal to the log base 2 of x , how could you graph f of x is equal to the log base 2 of x plus 5 ?

A
Translate each point of the graph of g x 5 units up.
B
Translate each point of the graph of g x 5 units right.
C
Translate each point of the graph of g x 5 units left.
D
Translate each point of the graph of g x 5 units down.
32

The number of bacteria in a sample after x days is represented using the equation b is equal to 50 comma 000 times 1 point 0 5 raised to the negative x power By what approximate percent does the population change per day?

A
4 point 8 percent decrease
B
95 point 2 percent decrease
C
105 point 0 percent increase
D
5 point 0 percent increase
33

A circle has a central angle measuring 7 pi over 6 radians that intersects an arc of length 18 cm. What is the length of the radius of the circle? Round your answer to the nearest tenth. Use 3 point 1 4 for pi

A
4 point 9 cm
B
15 point 4 cm
C
3 point 7 cm
D
14 point 3 cm
34

Mr. Lee asks a student to solve the following system of linear equations. negative 28 is equal to negative 40 q minus 14 p 10 q plus 4 is equal to 2 p Which ordered pair open paren p comma q close paren is the solution to the system?

A
open paren 0 comma 2 close paren
B
open paren 2 comma 0 close paren
C
open paren negative 2 comma negative 7 fifths close paren
D
open paren negative 7 fifths comma negative 2 close paren
35

Cheryl has 56 dollars and wants to buy as many notebooks as she can to donate to her school. If each notebook costs 1 point 6 0 dollars , which inequality shows n , the maximum number of notebooks she can buy with her money?

A
1 point 6 n is less than or equal to 56
B
56 n is less than or equal to 1 point 6
C
56 n is greater than or equal to 1 point 6
D
1 point 6 n is greater than or equal to 56
36

What is 4 log sub 1 half w plus open paren 2 log sub 1 half u minus 3 log sub 1 half v close paren written as a single logarithm?

A
log sub 1 half w to the 4th power open paren the fraction with numerator u squared and denominator v cubed close paren
B
log sub 1 half times open paren w times open paren the fraction with numerator u squared and denominator v cubed close paren close paren to the 4th power
C
log sub 1 half of open paren the fraction with numerator w to the 4th power and denominator u squared v cubed close paren
D
log sub 1 half w to the 4th power u squared minus v cubed
37

What values are excluded from the domain and range of the function f of x is equal to the fraction with numerator x plus 3 and denominator 2 x plus 5 ?

A
domain: x is not equal to 1 half range: y is not equal to negative 5 halves
B
domain: x is not equal to negative 3 range: y is not equal to 2
C
domain: x is not equal to negative 5 halves range: y is not equal to 2
D
domain: x is not equal to negative 5 halves range: y is not equal to 1 half
38

Which equation has x is equal to 4 as the solution?

A
log sub 3 of open paren 2 x minus 5 close paren is equal to 2
B
log sub 4 of open paren 3 x plus 4 close paren is equal to 2
C
the log base x of 64 is equal to 4
D
the log base x of 16 is equal to 4
39

An initial investment of 200 dollars is now valued at 350 dollars The annual interest rate is 8 percent compounded continuously. The equation 200 e raised to the 0 point 0 8 t power is equal to 350 represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use a calculator and round your answer to the nearest whole number.

A
22 years
B
5 years
C
7 years
D
19 years
40

Which system of equations is consistent and dependent?

A
5 x plus 4 y is equal to negative 30 3 x minus 9 y is equal to negative 18
B
2 x plus 3 y is equal to negative 6 2 x plus 3 y is equal to negative 12
C
3 x plus 2 y is equal to 3 6 x plus 4 y is equal to 6
D
4 x plus 6 y is equal to 2 4 x plus 6 y is equal to 1

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