ATLAS Algebra II Number and Quantity Practice

Number and Quantity skills

Extend the properties of exponents to rational exponents

Perform arithmetic operations with complex numbers

Represent complex numbers and their operations on the complex plane

Use vectors to model and solve problems

Perform operations with vectors and matrices as a tool in modeling

Standards basis

Arkansas Academic Standards for Mathematics (CCSS-M–aligned / Arkansas-adopted math standards) — Arkansas

How the ATLAS reports it

Arkansas’s statewide assessment system is ATLAS, which the ADE page says began serving in spring 2024. The official public page does not publish a math blueprint there, so the most defensible coverage map is the Arkansas math standards structure that ATLAS is aligned to.

Blueprint & weighting

ATLAS uses the Independent / state-specific framework (by grade domains structure).

Official sources

Arkansas DESE Assessment: Test Scores
Arkansas DESE home page
Arkansas DESE: 3–10 ATLAS Content Assessments

8 free questions · 0/0 correct

Practice playhard

Which of the following is equal to $(-3+4i)^{2}$ ?

Expand: $(-3+4i)^{2}=9-24i+16i^{2}$ . Since $i^{2}=-1$ , this is $9-24i-16=-7-24i\textsf{.}$

Practice playeasy

What is $(3i)^{2}$ ?

$(3i)^{2} = 9i^{2} = 9(-1) = -9$ .

Practice playeasy

Given $i = \sqrt{-1}$ , what is $\sqrt{49} + \sqrt{-4}$ ?

$\sqrt{49} = 7$ and $\sqrt{-4} = 2i$ . So $\sqrt{49} + \sqrt{-4} = 7 + 2i$ .

Practice playmedium

Which expression is equivalent to $\sqrt{27}+\sqrt{48}+\sqrt{75}$ ?

$\sqrt{27}=3\sqrt{3}$ , $\sqrt{48}=4\sqrt{3}$ , and $\sqrt{75}=5\sqrt{3}$ . Adding gives $3\sqrt{3}+4\sqrt{3}+5\sqrt{3}=12\sqrt{3}$ .

Practice playmedium

If $\Large u$ , $\Large v$ , and $\Large w$ are positive, which expression is equivalent to $\Large \sqrt[3]{u^{15} v^9 w^6}$ ?

Divide each exponent by $\Large 3$ : $\Large u^{\tfrac{15}{3}} v^{\tfrac{9}{3}} w^{\tfrac{6}{3}} = u^5 v^3 w^2$ .

Practice playeasy

The sound intensity level, in a simplified unit, of a certain speaker can be estimated by multiplying the speaker's power, in watts, by $8$ and then taking the square root of the product. According to this method, what is the estimated intensity level of a speaker with a power of $75$ watts?

The product is $75 \cdot 8 = 600$ . Factor $600 = 100 \cdot 6$ , where $100$ is the largest perfect-square factor. So $\sqrt{600} = \sqrt{100 \cdot 6} = 10\sqrt{6}$ , and $6 = 2 \cdot 3$ is square-free.

Practice playeasy

Evaluate $27^{-1/3}$ .

$27^{-1/3} = \dfrac{1}{27^{1/3}} = \dfrac{1}{3}$ .

Practice playeasy

Which matrix equals $-3\begin{bmatrix} 2 & -1 \\ 3 & 0 \end{bmatrix}$ ?

Multiply each entry by $-3$ : $\begin{bmatrix} -3(2) & -3(-1) \\ -3(3) & -3(0) \end{bmatrix} = \begin{bmatrix} -6 & 3 \\ -9 & 0 \end{bmatrix}$ .

ATLAS Algebra II Number and Quantity. Practice it free.

Number and Quantity skills

Extend the properties of exponents to rational exponents

Perform arithmetic operations with complex numbers

Represent complex numbers and their operations on the complex plane

Use vectors to model and solve problems

Perform operations with vectors and matrices as a tool in modeling

Topics mapped to this domain

Multiplying and squaring complex numbers (ACT)

Complex number operations

Rewriting complex numbers

Combining like square roots (ACT)

Radical to exponent conversions

Radical word problems (ACT)

Rational exponents

Scalar times 2×2 matrix (ACT)

Simplifying square roots (ACT)

8 free questions · 0/0 correct

Turn number and quantity into game time.

More Algebra II domains