Question 1

Which expression has a value between $-4$ and $-3$?

Accepted Answer

$\sqrt{20}-8$

Answer

$3\sqrt{5}-7$

Answer

$4 - \sqrt{15}$

Answer

$1 - 2\sqrt{10}$

Question 2

Craig uses a ruler to determine the length of two pieces of metal. He records the length of each piece of metal as a rational number. Which statement BEST explains whether the sum of the two lengths Craig recorded must also be a rational number?

Accepted Answer

When adding two rational numbers $\frac{a}{b}$ and $\frac{c}{d}$, the sum is $\frac{ad+bc}{bd}$, and both the numerator and denominator are integers. Therefore, the sum must be a rational number.

Answer

When adding two rational numbers a $\frac{a}{b}$ and $\frac{c}{d}$, the common denominator $bd$ does not have to be an integer. Therefore, the sum does not have to be a rational number.

Answer

When adding two rational numbers $\frac{a}{b}$ and $\frac{c}{d}$, the sum is$ \frac{ac}{bd}$,  and both the numerator and denominator are integers. Therefore, the sum must be a rational number.

Answer

When adding two rational numbers $\frac{a}{b}$ and $\frac{c}{d}$, the numerators a and c do not have to be integers. Therefore, the sum does not have to be a rational number.

Question 3

Which statement correctly describes the number $\frac{62}{495}$ and its equivalent decimal notation?

Accepted Answer

The number $\frac{62}{495}$ is a rational number and its equivalent decimal notation is a repeating decimal number.

Answer

The number $\frac{62}{495}$ is a rational number and its equivalent decimal notation is a terminating decimal number.

Answer

The number $\frac{62}{495}$ is an irrational number and its equivalent decimal notation is a repeating decimal number.

Answer

The number $\frac{62}{495}$ is an irrational number and its equivalent decimal notation is a terminating decimal number.

Question 4

Amanda graphed a linear function with the equation y$y=1.\overline 4x$. Which statement about the slope of Amanda's line is true?

Accepted Answer

The slope is a rational number that can be written as $\frac{13}{9}$.

Answer

The slope is an irrational number that can be written as $\frac{14}{10}$.

Answer

The slope is a rational number that can be written as $\frac{14}{10}$.

Answer

The slope is an irrational number that can be written as $\frac{13}{9}$.

Question 5

On the number line below, point $	ext P$ shows the location of an irrational number.

Which expression has a value that is GREATER than the irrational number represented by point $	ext P$?

Accepted Answer

$4+\sqrt 7$

Answer

$\sqrt 7-1$

Answer

$7-\sqrt 7$

Answer

$2\sqrt

Question 6

Which number is the CLOSEST APPROXIMATION of $\sqrt39$?

Accepted Answer

$6.2$

Answer

$6.5$

Answer

$7.7$

Answer

$7.5$

Question 7

Which number is irrational?

Accepted Answer

$9\sqrt3$

Answer

$9\sqrt4$

Answer

$4\sqrt9$

Answer

$3\sqrt9$

Question 8

Four numbers are shown below.

$\quad\pi \enspace \sqrt\enspace \pi \enspace \sqrt3 \enspace \sqrt8$

What is the order of the four numbers from LEAST to GREATEST?

Accepted Answer

$ \sqrt3 \enspace \sqrt\pi \enspace \sqrt8\enspace \pi $

Answer

$\pi \enspace \sqrt\pi \enspace \sqrt3 \enspace \sqrt8$

Answer

$ \sqrt3 \enspace \sqrt\pi \enspace \pi \enspace \sqrt8$

Answer

$ \sqrt\pi \enspace \sqrt3 \enspace \pi \enspace \sqrt8$

Question 9

Four points are graphed on the number line below.

Which point is located CLOSEST to the value of $-\sqrt5$?

Accepted Answer

point$ 	ext Y$

Answer

point$ 	ext X$

Answer

point$ 	ext W$

Answer

point$ 	ext Z$

Question 10

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 11

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 12

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  $\frac{1}{56}$.

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