AK STAR Grade 9 The Number System Practice

The Number System skills

N-RN.1–N-RN.3

N-Q.1–N-Q.3

Standards basis

Alaska Mathematics Standards — Alaska

How the AK STAR reports it

AK STAR is Alaska’s state summative assessment, built around Alaska’s own mathematics standards rather than a national consortium framework. Its math blueprint is organized into grade-level content strands/instructional areas and an adaptive growth component aligned to MAP Growth instructional areas.

Blueprint & weighting

The blueprint gives target item counts and point ranges by grade and strand, rather than fixed percentage weights. Grades 3-5 and 6-9 each include summative item counts plus additional growth items; grade 9 has no summative Geometry strand, with Geometry reported only through growth items.

Official sources

Alaska Department of Education and Early Development
Alaska Department of Education and Early Development
Alaska Department of Education and Early Development

8 free questions · 0/0 correct

Practice playmedium

Which expression is equivalent to $3\sqrt{20}+\sqrt{45}$ ?

$3\sqrt{20}=3\sqrt{4 \cdot 5}=3 \cdot 2\sqrt{5}=6\sqrt{5}$ and $\sqrt{45}=\sqrt{9 \cdot 5}=3\sqrt{5}$ . Adding like radical terms gives $6\sqrt{5}+3\sqrt{5}=9\sqrt{5}$ .

Practice playeasy

A concert venue gave each member of a fan club the same number of wristbands and the same number of parking passes. The club received $42$ wristbands and $63$ parking passes in all. Which could be the number of members in the fan club?

The number of members must divide both totals. The common factors of $42$ and $63$ greater than $1$ are $3$ , $7$ , and $21$ . Only $7$ is listed: $42 \div 7 = 6$ wristbands and $63 \div 7 = 9$ passes per member.

Practice playmedium

Given that $2 \le m \le 5$ and $3 \le n \le 8$ , what is the greatest possible value of $\dfrac{1}{m} + \dfrac{1}{n}$ ?

Each term $\dfrac{1}{m}$ and $\dfrac{1}{n}$ is greatest when its denominator is least: $\dfrac{1}{2} + \dfrac{1}{3} = \dfrac{5}{6}$ .

Practice playeasy

A recycling truck visits a neighborhood every $12$ days, and a compost truck visits the same neighborhood every $18$ days. Both trucks came today. In how many days will both trucks next visit on the same day?

The next day both trucks visit is the least common multiple of $12$ and $18\textsf{.}$ Since the GCF of $12$ and $18$ is $6\textsf{,}$ divide their product by the GCF: $\dfrac{12 \times 18}{6}=36\textsf{.}$ So they next coincide in $36$ days.

Practice playhard

If $\Large x$ and $\Large y$ are positive, which expression is equivalent to $\Large \sqrt[5]{x^8 y^{12}}$ ?

Divide each exponent by $\Large 5$ : $\Large x^{\tfrac{8}{5}} y^{\tfrac{12}{5}}$ .

Practice playmedium

The diagonal length, in inches, of a certain square television screen can be estimated by multiplying the screen's area, in square inches, by $2$ and then taking the square root of the product. According to this method, what is the estimated diagonal length, in inches, of a screen with an area of $216$ square inches?

The product is $216 \cdot 2 = 432$ . Factor $432 = 144 \cdot 3$ , where $144$ is the largest perfect-square factor. So $\sqrt{432} = \sqrt{144 \cdot 3} = 12\sqrt{3}$ , and $3$ is square-free.

Practice playeasy

Write $\sqrt[5]{x^3}$ as $x^{a/b}$ in lowest terms. What is $b$ ?

$\sqrt[5]{x^3} = x^{3/5}$ , so $b = 5$ .

Practice playeasy

Which expression is equivalent to $\sqrt{288}$ ?

$288 = 144 \cdot 2$ , so $\sqrt{288} = \sqrt{144 \cdot 2} = 12\sqrt{2}$ .

AK STAR Grade 9 The Number System. Practice it free.

The Number System skills

N-RN.1–N-RN.3

N-Q.1–N-Q.3

Topics mapped to this domain

Combining like square roots (ACT)

Common factor group size (ACT)

Fraction bounds extreme value (ACT)

LCM word problems (ACT)

Radical to exponent conversions

Radical word problems (ACT)

Rational exponents

Simplifying square roots (ACT)

Unit conversion word problems (ACT)

8 free questions · 0/0 correct

Turn the number system into game time.

More Grade 9 domains