N/A — Exam Answers — Algebraic Reasoning

1

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Which table shows input and output values that represent a quadratic function?

A

Table cap d

B

Table cap b

C

Table cap c

D

Table cap A

2

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Which is the diagonal matrix containing these elements?

A

the 5 by 5 matrix, row 1, column 1, 16 column 2, 0 column 3, 0 column 4, 0 column 5, 0 row 2, column 1, 0 column 2, negative 8 point 7 column 3, 0 column 4, 0 column 5, 0 row 3, column 1, 0 column 2, 0 column 3, 5 point 4 column 4, 0 column 5, 0 row 4, column 1, 0 column 2, 0 column 3, 0 column 4, 1 point 3 column 5, 0 row 5, column 1, 0 column 2, 0 column 3, 0 column 4, 0 column 5, negative 6 point 9

B

the 5 by 5 matrix, row 1, column 1, 16 column 2, negative 3 point 7 column 3, 6 column 4, 1 point 7 column 5, negative 8 point 8 row 2, column 1, 0 column 2, negative 8 point 7 column 3, negative 4 point 1 4 column 4, 1 column 5, 7 row 3, column 1, 0 column 2, 0 column 3, 5 point 4 column 4, negative 9 column 5, negative 3 row 4, column 1, 0 column 2, 0 column 3, 0 column 4, 1 point 3 column 5, 5 row 5, column 1, 0 column 2, 0 column 3, 0 column 4, 0 column 5, negative 6 point 9

C

the 5 by 5 matrix, row 1, column 1, 16 column 2, 0 column 3, 0 column 4, 6 column 5, 0 row 2, column 1, 0 column 2, negative 8 point 7 column 3, 0 column 4, 0 column 5, 5 row 3, column 1, 0 column 2, 0 column 3, 5 point 4 column 4, 0 column 5, 0 row 4, column 1, 2 column 2, 0 column 3, 0 column 4, 1 point 3 column 5, 0 row 5, column 1, 0 column 2, 1 column 3, 0 column 4, 0 column 5, negative 6 point 9

D

the 5 by 5 matrix, row 1, column 1, 16 column 2, 0 column 3, 0 column 4, 0 column 5, 0 row 2, column 1, negative 6 column 2, negative 8 point 7 column 3, 0 column 4, 0 column 5, 0 row 3, column 1, 5 column 2, 43 column 3, 5 point 4 column 4, 0 column 5, 0 row 4, column 1, 3 column 2, 2 column 3, 1 point 2 column 4, 1 point 3 column 5, 0 row 5, column 1, negative 9 point 9 column 2, 7 column 3, negative 6 point 8 column 4, negative point 0 5 column 5, negative 6 point 9

3

Find the missing values for the exponential function represented by the table and complete the table.

A

negative 23 point 6 2 5 35 point 4 3 7 5

B

23 point 6 2 5 35 point 4 3 7 5

C

10 point 5 7

D

negative 23 point 6 2 5 negative 35 point 4 3 7 5

4

Which model best represents the data?

A

exponential, because the height of the object increases or decreases with a multiplicative rate of change

B

quadratic, because the height of the object increases or decreases with a multiplicative rate of change

C

quadratic, because the height increases and then decreases

D

exponential, because the height increases and then decreases

5

Which statements accurately compare the functions in the graph? Choose two correct answers.

A

The functions share a y -intercept of negative 1 .

B

Both functions have a domain of all real numbers.

C

Neither function has a maximum value.

D

The functions share an x -intercept of 1 .

E

Both functions have a range of all real numbers.

6

Which function can be used to compute the approximate area, in square inches, of a stop sign if it has a side length of x inches?

A

f of x is equal to 4 point 8 to the x th power

B

f of x is equal to 4 point 8 x squared

C

f of x is equal to 4 to the x th power

D

f of x is equal to 4 x squared

7

Find the missing value for the exponential function represented by the table. Then select the graph that best fits the equation.

A

negative 9 point 9 4 7 , Graph A

B

9 point 2 1 3 , Graph B

C

8 point 7 5 6 , Graph B

D

9 point 9 4 7 , Graph A

8

What is the vertex of the graph of f of x is equal to start absolute value x minus 13 end absolute value plus 11 ?

A

13 comma 11

B

negative 13 comma 11

C

negative 11 comma 13

D

11 comma 13

9

Which graph includes a function, its inverse, and a dashed line that verifies the relationship?

A

Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has two curves and a dashed line. The first curve goes through (negative 5 comma negative 1) and (negative 2 comma 0). It then intersects the y-axis at (0 comma 1). The second curve goes through (negative 1 comma negative 4), goes up, and crosses the y-axis at (0 comma negative 2). It then goes up, intersects the x-axis at (1 comma 0), and moves further up. Both the curves intersect at (1 comma 1). A horizontal dashed line at y equals 1.

B

Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has two curves and a dashed line. The first curve goes through (negative 5 comma negative 1) and (negative 2 comma 0). It then intersects the y-axis at (0 comma 1). The second curve goes through (negative 1 comma negative 4), goes up, and crosses the y-axis at (0 comma negative 2). It then goes up, intersects the x-axis at (1 comma 0), and moves further up. Both the curves intersect at (1 comma 1). A dashed vertical line at x equals 1.

C

Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has two curves and a dashed line. The first curve goes through (negative 5 comma negative 1) and (negative 2 comma 0). It then intersects the y-axis at (0 comma 1). The second curve goes through (negative 1 comma negative 4), goes up, and crosses the y-axis at (0 comma negative 2). It then goes up, intersects the x-axis at (1 comma 0), and moves further up. Both the curves intersect at (1 comma 1). A dashed line with a negative slope passes through (5 comma negative 5), the origin, and (negative 5 comma 5).

D

Image with description On a coordinate plane, the x and y axes range from negative 7 to 7 in increments of 1. The graph has two curves and a dashed line. The first curve goes through (negative 5 comma negative 1) and (negative 2 comma 0). It then intersects the y-axis at (0 comma 1). The second curve goes through (negative 1 comma negative 4), goes up, and crosses the y-axis at (0 comma negative 2). It then goes up, intersects the x-axis at (1 comma 0), and moves further up. Both the curves intersect at (1 comma 1). A dashed line with a positive slope passes through (negative 5 comma negative 5), the origin, and (5 comma 5).

10

By what approximate factor is the intensity of an earthquake with magnitude 5 point 4 greater than an earthquake with magnitude 5 point 3 ? cap m is equal to the log of open paren the fraction with numerator l and denominator l sub 0 close paren cap m is equal to the magnitude of an earthquake cap i is equal to the intensity of an earthquake cap i sub 0 is equal to the smallest seismic activity that can be measured, which is 1

A

1 point 2 1

B

1 point 0 1

C

10 point 4 4

D

1 point 2 6

11

Myra uses an inverse variation function to model the data for the ordered pairs. open paren 2 comma 30 close paren , open paren 3 comma 20 close paren , open paren 4 comma 15 close paren , open paren 5 comma 12 close paren , open paren 6 comma 10 close paren Which statement best explains whether an inverse variation function is the best model for the data?

A

An inverse variation function is not the best model because data points approximate a straight line.

B

An inverse function is the best model because the products of corresponding x - and y -values are equal.

C

An inverse function is the best model because as x increases, y decreases.

D

An inverse variation function is not the best model because the data points show an exponential decay.

12

In one day, Joe consumes 530 calories by drinking 1 serving of juice, 2 servings of milk, and 1 soda. Darius consumes 370 calories by drinking 2 servings of juice and 1 serving of milk. Marian consumes 510 calories by drinking 3 servings of milk and 1 soda. Using matrices to solve, how many calories are in 1 serving of milk?

A

180

B

130

C

110

D

90

13

The quadratic model f of x is equal to negative 5 x squared plus 200 represents the approximate height, in meters, of a ball x seconds after being dropped. The ball is 50 meters from the ground after about how many seconds?

A

5 point 4 8

B

2 point 4 5

C

7 point 0 7

D

3 point 1 6

14

Consider the system of linear equations and the matrix equations. negative x plus 3 y is equal to 2 4 x minus 2 y is equal to 22 the 2 by 2 matrix, row 1, column 1, negative 1 column 2, 3 row 2, column 1, 4 column 2, negative 2 the 2 by 1 column matrix x y is equal to the 2 by 1 column matrix 2 22 What is the value of x in the equation?

A

64

B

7

C

3

D

negative 36

15

What is the remainder when open paren x cubed plus 1 close paren is divided by open paren x squared minus x plus 1 close paren ?

A

x plus 1

B

0

C

2

D

x

16

What is the value of cap A in the matrix equation? cap A plus the 2 by 4 matrix, row 1, column 1, 3 column 2, 9 column 3, negative 1 column 4, negative 8 row 2, column 1, 16 column 2, negative 2 column 3, 3 column 4, 13 is equal to the 2 by 4 matrix, row 1, column 1, 0 column 2, negative 5 column 3, 6 column 4, 10 row 2, column 1, 3 column 2, 0 column 3, negative 2 column 4, 7

A

the 2 by 4 matrix, row 1, column 1, negative 3 column 2, negative 14 column 3, 7 column 4, 2 row 2, column 1, negative 13 column 2, 2 column 3, negative 5 column 4, negative 6

B

the 2 by 4 matrix, row 1, column 1, negative 3 column 2, negative 14 column 3, 7 column 4, 2 row 2, column 1, 19 column 2, 2 column 3, negative 5 column 4, negative 6

C

the 2 by 4 matrix, row 1, column 1, negative 3 column 2, negative 14 column 3, 7 column 4, 18 row 2, column 1, negative 13 column 2, 2 column 3, negative 5 column 4, negative 6

D

the 2 by 4 matrix, row 1, column 1, negative 3 column 2, negative 14 column 3, 7 column 4, 18 row 2, column 1, 19 column 2, 2 column 3, negative 5 column 4, negative 6

17

Phan fills the tank of her car with gasoline before starting her road trip. The table shows the amount of gas left in her tank as she drives. Number of Hours vs. Amount Left in Tank Number of Hours Spent Driving h 3 5 7 9 Amount of Gas Left in Tank, in gallons g 12 8 4 0 Which equation models the amount of gas left in the car as Phan drives, and how many gallons of gasoline does it take to fill her tank?

A

g is equal to 18 minus 2 h ; 18 gallons

B

g is equal to 3 h plus 3 ; 12 gallons

C

g is equal to 3 h plus 3 ; 30 gallons

D

g is equal to 18 minus 2 h ; 16 gallons

18

If 7500 dollars is invested at an interest rate of 5 percent each year, what is the value of the investment in 4 years? Write an exponential function and solve.

A

y is equal to 7500 times 1 point 0 5 to the 4th power ; 9116 point 3 0 dollars

B

y is equal to 7500 times 4 raised to the 1 point 0 5 power ; 32 dollars comma 153 point 2 0

C

y is equal to 7500 times 1 point 0 5 to the negative 5 power ; 6170 point 2 7 dollars

D

y is equal to 4 times 1 point 0 5 to the 7500th power ; 7859 point 9 1 dollars

19

If cap k is equal to the 2 by 2 matrix, row 1, column 1, negative 4 column 2, 6 row 2, column 1, 2 column 2, negative 3 and cap m is equal to the 2 by 2 matrix, row 1, column 1, 2 column 2, negative 2 row 2, column 1, 8 column 2, 5 , what is cap x when 2 cap x minus cap k is equal to cap m ?

A

the 2 by 2 matrix, row 1, column 1, negative 4 column 2, 8 row 2, column 1, 20 column 2, 4

B

the 2 by 2 matrix, row 1, column 1, 12 column 2, negative 16 row 2, column 1, 12 column 2, 16

C

the 2 by 2 matrix, row 1, column 1, negative 1 column 2, 2 row 2, column 1, 5 column 2, 1

D

the 2 by 2 matrix, row 1, column 1, 3 column 2, negative 4 row 2, column 1, 3 column 2, 4

20

Graph the function f of x is equal to x cubed minus 3 x minus 2 Based on the graph, which value for x is a double root of this function?

A

negative 1

B

1

C

2

D

negative 2

N/A — Exam Answers

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