PSSA 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 x² = p and x³ = p

Use numbers expressed in the form of a single digit times an integer power of 10

Compare and order irrational numbers with rational numbers

Standards basis

Pennsylvania Academic Standards for Mathematics / Pennsylvania Assessment Anchors and Eligible Content — Pennsylvania

How the PSSA reports it

PSSA is Pennsylvania’s own standards-based, criterion-referenced assessment. Its math reporting structure is built on the Pennsylvania Academic Standards/Assessment Anchors and Eligible Content rather than a separate multi-state framework, and it closely mirrors CCSS-style grade-level domains.

Blueprint & weighting

The official PSSA page lists the Mathematics Test Design and grade-level item/scoring samplers, but the accessible source excerpt did not expose a usable per-domain percentage blueprint; no reliable item-weight table was recoverable from the available primary page text.

Official sources

Pennsylvania Department of Education — Pennsylvania System of School Assessment (PSSA)
Pennsylvania Department of Education — View Standards

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 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

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

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

Practice playeasy

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

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

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 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 $\dfrac{b^{8}}{b^{4}} = b^{8-4} = b^{4}\textsf{.}$

Practice playhard

Let $f(t) = 5e^{3t} + 200$ . Which of the following approximations, written as $a \times 10^n$ with one significant digit, is closest to the value of $f(4)$ ?

Substitute $t = 4$ : $f(4) = 5e^{12} + 200$ . Since $e^{12} \approx 162{,}755$ , $f(4) \approx 5(162{,}755) + 200 = 813{,}975 \approx 8 \times 10^{5}$ .