Question 1

Which expression is equivalent to $(4^4)^2 \cdot (4^7)^{-2}$?

Accepted Answer

$\frac{1}{4^6}$

Answer

$4^{11}$

Answer

$\frac{1}{4^3}$

Answer

$4^{30}$

Question 2

Which statement describes values of $x$ and $y$ such that $\frac{x}{y}$could be an irrational number?

Accepted Answer

The value of $x$ is the square root of an integer, and the value of $y$ is an integer
greater than zero

Answer

The value of $x$ is zero, and the value of $y$ is an integer less than zero.

Answer

The value of $x$ is a square root that can be simplified to an integer, and the value of $y$ is an
integer less than zero.

Answer

The value of $x$ is an integer less than zero, and the value of $y$ is an integer greater than zero.

Question 3

Which number is positive, rational, and has a value between $0$ and $1$?

Accepted Answer

$\sqrt\frac{1}{4}$

Answer

$^-0.\overline 2$

Answer

$\pi -3$

Answer

$\frac{3}{2}$

Question 4

A number is shown below.

$\qquad 0.\overline{56}$

Which statement about the number is true?

Accepted Answer

The number is rational and equivalent to $\frac{56}{99}$.

Answer

The number is irrational and cannot be represented as a fraction written with integers.

Answer

The number is rational and equivalent to  $\frac{56}{100}$.

Answer

The number is irrational and equivalent to  $\frac{1}{56}$.

Question 5

In the expression below, $c$ is an integer.

$\qquad 9^c\cdot9^{-c}$

Which value is equivalent to the expression?

Accepted Answer

$1$

Answer

$0$

Answer

$9$

Answer

$\frac{1}{9^{2c}}$

Question 6

Fran buys used DVDs. She pays $$\$2.75$$ for each DVD she buys. She graphs a line to show the total amount $(y)$, in dollars, she pays to buy $x$ used DVDs. Which equation correctly describes Fran's line?

Accepted Answer

$y = 2.75x$

Answer

$y = x + 2.75$

Answer

$y = 2.75x + 2.75$

Answer

$y = 2.75$

Question 7

Hank's Bicycle Rentals charges an initial fee of $$\$15$$ and an hourly rate of $$\$5$$ to rent a bicycle. Maria's Bicycle Rentals has the same hourly rate but charges an initial fee of $$\$12$$. To find the number of hours for which the two rental companies would charge the same amount to rent a bicycle, Cindy writes and solves the equation shown below.

$\qquad 15+5x=12+5x$

Which statement describes the number of hours for which the two rental companies charge the same amount to rent a bicycle?

Accepted Answer

The two companies never charge the same amount to rent a bicycle for the same
number of hours.

Answer

The two companies charge the same amount to rent a bicycle for $3$ hours.

Answer

The two companies always charge the same amount to rent a bicycle for the same
number of hours.

Answer

The two companies charge the same amount to rent a bicycle for $\frac{3}{5}$ hour.

Question 8

Which statement describing a function of $x$ is true?

Accepted Answer

The graph of $y = 3x + 9$ is linear and has a $y	ext{-intercept}$ of $9$.

Answer

The graph of $y = 3^2x + 9$ is nonlinear and passes through the point $(0, 9)$.

Answer

The graph of $y = 3x^2$ is linear and passes through the point $(0, 0)$.

Answer

The graph of $y = 3x$ is nonlinear and passes through the origin.

Question 9

Triangle $	ext{PQR}$ is graphed on the coordinate grid shown below.

To form triangle $	ext{P'Q'R'}$, triangle $	ext{PQR}$ will be rotated $90^\circ$clockwise about the origin. What will be the slope of side $	ext{Q'R'}$?

Accepted Answer

$\frac{1}{3}$

Answer

$^-3$

Answer

$\frac{^-1}{3}$

Answer

$3$

Question 10

Quadrilateral $	ext{ABCD}$ and quadrilateral $	ext{A'B'C'D'}$ are shown on the coordinate grid below.

Which sequence of transformations could be used to map quadrilateral  $	ext{ABCD}$ onto quadrilateral $	ext{A'B'C'D'}$?

Accepted Answer

a dilation centered at the origin with a scale factor of $0.5$, followed by a reflection across the $y	ext{-axis}$

Answer

a rotation of $180^\circ$ about the point $(0, ^-0.5)$, followed by a dilation centered at the origin with a scale factor of $0.5$

Answer

a translation $4$ units to the right, followed by a dilation centered at the origin with a scale factor of $0.5$

Answer

a reflection across the x-axis, followed by a dilation centered at the origin with a scale factor of $0.5$

Question 11

The side lengths of triangle $	ext{ABC}$ are listed below.

$\qquad\bullet\enspace 	ext{AB} = 7\, 	ext{mm}$
$\qquad\bullet\enspace 	ext{AC} = 12\, 	ext{mm}$
$\qquad\bullet\enspace 	ext{BC} = 6\, 	ext{mm}$

Which statement about triangle $	ext{ABC}$ is true?

Accepted Answer

Triangle$	ext{ABC}$ is not a right triangle.

Answer

Angle $	ext B$ is a right angle.

Answer

Angle $	ext C$ is a right angle.

Answer

Angle $	ext A$ is a right angle.

Question 12

Point R is located at $(1, 2)$ on a coordinate grid. Point $	ext S$ is located at $(4, ^-5)$ on the same coordinate grid. What is the distance from point $	ext R$ to point $	ext S$, rounded to the nearest tenth?

Accepted Answer

$7.6\,	ext{units}$

Answer

$3.2\,	ext{units}$

Answer

$10.0\,	ext{units}$

Answer

$4.6\,	ext{units}$

Question 13

Michael stacks $14$ identical disks to form a cylinder.

$\qquad\bullet\quad$ Each disk is $\frac{1}{4}\,	ext{inch}$ thick.
$\qquad\bullet\quad$ The diameter of each disk is $3\,	ext{inches}$.

Which measurement is CLOSEST to the volume, in cubic inches, of the stack of disks?

Accepted Answer

$25$

Answer

$99$

Answer

$7$

Answer

$396$

Question 14

The scatter plot below shows the rainfall, in millimeters, recorded each day during a $20$-day period.

On which day was the rainfall recorded an outlier?

Accepted Answer

$7$

Answer

$17$

Answer

$1$

Answer

$20$

Question 15

A scatter plot is graphed on the coordinate grid shown below.

Which equation BEST describes a line of best fit for the data?

Accepted Answer

$y = ^-0.8x + 8

Answer

$y = 0.8x + 8$

Answer

$y = ^-8x + 0.8$

Answer

$y = 8x + 0.8$

Question 16

Amy surveyed some families about whether they have cats and whether they have dogs. The results of her survey are shown in the two-way table below.

Based on the information shown in the two-way table, which statement about the families surveyed is true?

Accepted Answer

Of all the families surveyed, $32\%$ have either a cat or a dog, but not both a cat and a dog.

Answer

Of all the families surveyed, more than $\frac{1}{2}$ have neither a cat nor a dog.

Answer

Of all the families surveyed who do not have a dog, $\frac{3}{4}$ do have a cat.

Answer

Of all the families surveyed who do have a cat, $12\%$ do not have a dog.

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