NeSA Grade 8 The Number System Practice

What the test measures

The Number System skills

Know that there are numbers that are not rational and approximate them by rational numbers
Use rational approximations of irrational numbers
Work with square and cube roots
Use scientific notation and perform operations with numbers expressed in scientific notation
Understand integer exponents and apply properties of exponents

Standards basis

Nebraska College and Career Ready Standards for Mathematics (2019; Common Core–aligned domain structure) — Nebraska

How the NeSA reports it

Nebraska’s statewide math assessment is administered through NSCAS, but the official assessment page does not publish a test-specific math blueprint or reporting-category document on the page reviewed. In the absence of a public blueprint, the most defensible coverage map is the Nebraska College and Career Ready Standards for Mathematics, which are the state’s current standards basis and closely mirror Common Core-style grade-level domains.

Blueprint & weighting

No public test blueprint or per-domain item weighting was located on the Nebraska Department of Education assessment page reviewed. The page references NSCAS testing windows and general statewide assessment materials, but not math reporting-category percentages.

Official sources

Nebraska Department of Education – Statewide Assessment
Nebraska Department of Education – Press release noting current Nebraska College and Career Ready Standards approved in 2019

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playeasy

Simplify: $y^{6} \cdot y^{3}$ .

The Product of Powers Property says that powers with the same base are multiplied by adding the exponents, written $y^{m} \cdot y^{n} = y^{m+n}\textsf{.}$ Both factors have base $y$ , so $y^{6} \cdot y^{3} = y^{6+3} = y^{9}\textsf{.}$

Practice playeasy

Solve for the positive value of $x$ : $x^2 = 121$ .

$x = \sqrt{121} = 11$ because $11 \times 11 = 121$ .

Practice playhard

Let $f(t) = 6e^{2t}$ . Which of the following approximations, written as $a \times 10^n$ with one significant digit, is closest to the value of $f(5)$ ?

Substitute $t = 5$ : $f(5) = 6e^{10}$ . Since $e^{10} \approx 22{,}026$ , $f(5) \approx 6(22{,}026) = 132{,}156 \approx 1 \times 10^{5}$ .

Practice playeasy

$\sqrt{40}$ is between two consecutive integers. Enter the smaller one.

$6^2 = 36 < 40 < 49 = 7^2$ , so $\sqrt{40}$ is between $6$ and $7$ ; the smaller is $6$ .

Practice playeasy

$93{,}000{,}000 = c \times 10^7$ . What is $c$ ?

$9.3 \times 10^7 = 93{,}000{,}000$ , so $c = 9.3$ .

Practice playmedium

What is $\dfrac{7.2 \times 10^{-5}}{1.2 \times 10^{-2}}$ ?

Divide coefficients and subtract exponents: $7.2 \div 1.2 = 6$ and $-5-(-2)=-3$ . So the quotient is $6 \times 10^{-3}\textsf{.}$

Practice playeasy

Simplify: $\dfrac{b^{8}}{b^{4}}$ .

The Quotient of Powers Property says that powers with the same nonzero base are divided by subtracting the exponents, written $\dfrac{b^{m}}{b^{n}} = b^{m-n}\textsf{.}$ Here both the numerator and the denominator have base $b$ , so $\dfrac{b^{8}}{b^{4}} = b^{8-4} = b^{4}\textsf{.}$