ISAT Grade 8 The Number System Practice

The Number System skills

Know that there are numbers that are not rational, and approximate them by rational numbers

Work with radicals and integer exponents

Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p

Standards basis

Idaho Content Standards (Mathematics) — Idaho

How the ISAT reports it

Idaho ISAT is a state assessment administered to grades 3–8 and 11 and reported against Idaho grade-level content standards rather than a separate national testing framework. The public ISAT page points to summative blueprints and math specifications, while the Idaho Content Standards page shows the math program is organized by grade-band/domain progressions aligned to Idaho standards.

Blueprint & weighting

The public Idaho ISAT page references summative blueprints and item specifications, but the accessible official page content did not expose a published domain-by-domain percentage blueprint for math.

Official sources

Idaho Department of Education — Idaho Standards Achievement Test (ISAT)
Idaho Department of Education — Idaho Content Standards

8 free questions · 0/0 correct

Practice playeasy

What is $\sqrt[3]{64}$ ?

$4 \times 4 \times 4 = 64$ , so $\sqrt[3]{64} = 4$ .

Practice playeasy

$\dfrac{2^{7} \cdot 2^{4}}{2^{6}} = 2^{n}\textsf{.}$ What is $n\textsf{?}$

The Product of Powers Property says that powers with the same base are multiplied by adding the exponents, written $x^{m} \cdot x^{n} = x^{m+n}\textsf{.}$ The numerator is $2^{7} \cdot 2^{4} = 2^{7+4} = 2^{11}\textsf{.}$ The Quotient of Powers Property then subtracts the exponents of powers with the same base, written $\dfrac{x^{m}}{x^{n}} = x^{m-n}\textsf{.}$ So $\dfrac{2^{11}}{2^{6}} = 2^{11-6} = 2^{5}$ and $n = 5\textsf{.}$

Practice playmedium

Let $f(t) = 8e^{3t} + 50$ . Which of the following approximations, written as $a \times 10^n$ with one significant digit, is closest to the value of $f(2)$ ?

Substitute $t = 2$ : $f(2) = 8e^{6} + 50$ . Since $e^{6} \approx 403.4$ , $f(2) \approx 8(403.4) + 50 = 3{,}277 \approx 3 \times 10^{3}$ .

Practice playeasy

$0.0075 = c \times 10^{-3}$ . What is $c$ ?

Moving the decimal in $0.0075$ three places right gives $7.5$ , so $c = 7.5$ .

Practice playmedium

$(4 \times 10^{3})(5 \times 10^{4})$ equals

Multiply coefficients and add exponents: $4 \cdot 5 = 20$ and $3+4=7$ , giving $20 \times 10^{7}$ . Rewrite as $2 \times 10^{1} \times 10^{7}=2 \times 10^{8}\textsf{.}$

Practice playeasy

Which is closest to $\pi$ ?

$\pi \approx 3.14159$ .

Practice playeasy

If $x^2 = 169$ and $x > 0$ , what is $x$ ?

Take the positive square root: $x = \sqrt{169} = 13$ because $13 \times 13 = 169$ .

Practice playeasy

Rewrite $a^{-2}$ with a positive exponent.

The Negative Exponent Property says that a nonzero base raised to a negative exponent equals the reciprocal of that base raised to the positive exponent, written $a^{-n} = \dfrac{1}{a^{n}}\textsf{.}$ Applying the property, $a^{-2} = \dfrac{1}{a^{2}}\textsf{.}$