AnswersHigh School Math 2 AGeometric Sequences

Geometric Sequences — Cumulative exam Answers

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An equation for the depreciation of a car is given by y = A(1 – r)t, where y = current value of the car, A = original cost, r = rate of depreciation, and t = time, in years. The current value of a car is $12,282.50. The car originally cost $20,000 and depreciates at a rate of 15% per year. How old is the car?

A
years
Option A
B
years
Option B
C
3 years
D
4 years
2
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What is the range of the function graphed below?

Question illustration
A
y greater-than 0
Option A
B
y less-than 0
Option B
C
y less-than 0
Option C
D
y greater-than 0
Option D
3

Which is the graph of ?

Question illustration
A
On a coordinate plane, a curve starts at (2, 0) and curves up and goes through (3, 3) and (9, 5).
Option A
B
Option
Option B
C
Option
Option C
D
On a coordinate plane, a curve starts at (2, 6) and curves down and goes through (3, 3) and (10, 2).
Option D
4

Two different radioactive isotopes decay to 10% of their respective original amounts. Isotope A does this in 33 days, while isotope B does this in 43 days. What is the approximate difference in the half-lives of the isotopes?

A
3 days
B
10 days
C
13 days
D
33 days
5

What are the solutions of the equation (x + 2)2 – 2(x + 2) – 15 = 0? Use u substitution to solve.

A
x = –7 and x = 1
B
x = –5 and x = 3
C
x = –3 and x = 5
D
x = –1 and x = 7
6

For what values of x does ?

Question illustration
A
x = –3, x = 1
B
x = –1, x = 3
C
x = negative three-halves, x = 2
Option C
D
x = negative 2, x = three-halves
Option D
7

A polynomial function has a root of –7 with multiplicity 2, a root of –1 with multiplicity 1, a root of 2 with multiplicity 4, and a root of 4 with multiplicity 1. If the function has a positive leading coefficient and is of even degree, which statement about the graph is true?

A
The graph of the function is positive on (2, 4).
B
The graph of the function is negative on (4, ).
Option B
C
The graph of the function is positive on (, –7).
Option C
D
The graph of the function is negative on (–7, –1).
8

Jerome solved the equation below by graphing.Which of the following shows the correct system of equations and solution?

Question illustration
A
; x = 3
Option A
B
; x = 4
Option B
C
; x = 33
Option C
D
; x = 44
Option D
9

A student showed the steps below while solving the equation by graphing.Step 1:Write a system of equations: Step 2: Use the change of base formula to rewrite the equations:Step 3:Graph the two equations:Step 4:Identify the x-value at the point of intersection:In which step did the student make the first error?

Question illustration
A
step 1
B
step 2
C
step 3
D
step 4
10

Which of the following shows the graph of

Question illustration
A
On a coordinate plane, a curve approaches the y-axis in quadrant 3. It increases into quadrant 2 and crosses the x-axis at (negative 0.5, 0).
Option A
B
On a coordinate plane, a curve approaches the y-axis in quadrant 3. It increases into quadrant 2 and crosses the x-axis at (negative 4, 0).
Option B
C
On a coordinate plane, a curve approaches the y-axis in quadrant 4. It increases into quadrant 1 and crosses the x-axis at (0.5, 0).
Option C
D
On a coordinate plane, a curve approaches the y-axis in quadrant 4. It increases into quadrant 1 and crosses the x-axis at (4, 0).
Option D
11

If , what is the value of x?

Question illustration
A
Five-eighths
Option A
B
Eight-fifths
Option B
C
2
D
8
12

The graph below is an example of which type of function?

Question illustration
A
quadratic
B
linear
C
cubic
D
square root
13

Which graph shows the solution to the equation below?

Question illustration
A
On a coordinate plane, a curve starts in quadrant 3 and curves up into quadrant 1 and approaches y = 3. It crosses the x-axis at (1, 0). A horizontal straight line is at y = 1.
Option A
B
On a coordinate plane, a curves starts in quadrant 4 and curves up into quadrant 1 and approaches y = 3. It crosses the x-axis at (1, 0). A horizontal straight line is at y = negative 1.
Option B
C
On a coordinate plane, a curve starts in quadrant 3 and curves up into quadrant 1 and approaches y = 1. It crosses the x-axis at (negative 1, 0). A horizontal straight line is at y = 1.
Option C
D
On a coordinate plane, a curves starts in quadrant 3 and curves up into quadrant 1 and approaches y = 2. It crosses the x-axis at (negative 1, 0). A horizontal straight line is at y = negative 1.
Option D
14

Which function has a domain of and a range of ?

Question illustration
A
y = StartRoot x minus 5 EndRoot + 3
Option A
B
y = StartRoot x + 5 EndRoot minus 3
Option B
C
y = negative StartRoot x minus 5 EndRoot + 3
Option C
D
y = negative StartRoot x + 5 EndRoot minus 3
Option D
15

The two expressions below have the same value when rounded to the nearest hundredth.What is the approximate value of to the nearest hundredth?

Question illustration
A
0.93
B
1.23
C
9.16
D
65.53
16

What are the solutions of the equation x4 – 5x2 – 36 = 0? Use factoring to solve.

A
x = ±2 and x = ±3
B
x = ±2i and x = ±3
C
x = ±2 and x = ±3i
D
x = ±2i and x = ±3i
17

Over which interval does the exponential show a more rapid rate of change?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
18

Which of the following is the graph of ?

Question illustration
A
On a coordinate plane, an absolute value curve curves up and to the right in quadrant 4 and starts at y = negative 1.
Option A
B
On a coordinate plane, an absolute value curve curves up and to the right in quadrant 4 and starts at y = 1.
Option B
C
On a coordinate plane, an absolute value curve opens down and to the left in quadrant 2 and starts at y = 1.
Option C
D
On a coordinate plane, an absolute value curve opens down and to the left in quadrant 2 and starts at y = negative 1.
Option D
19

What is the end behavior of the graph of the polynomial function f(x) = –x5 + 9x4 – 18x3?

A
As , and as , .
Option A
B
As , and as , .
Option B
C
As , and as , .
Option C
D
As , and as , .
Option D
20

A function is graphed on a coordinate grid. As the domain values approach infinity, the range values approach infinity. As the domain values approach negative infinity, the range values approach negative infinity. To which family of functions might the described function belong?

A
absolute value
B
exponential
C
cube root
D
square root

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