ILEARN 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 square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p
Use rational approximations of irrational numbers to compare the size of irrational numbers
Apply properties of integer exponents to generate equivalent numerical expressions
Use scientific notation to estimate very large or very small quantities

Standards basis

Indiana Academic Standards for Mathematics — Indiana

How the ILEARN reports it

Indiana iLEARN is a state assessment system aligned to Indiana’s Academic Standards rather than a shared national testing framework. The public iLEARN page says the math assessment is a computer-adaptive test measuring Indiana mathematics standards, and the through-year summative measures the full set of skills expected by year end ([Indiana DOE iLEARN](https://www.in.gov/doe/students/assessment/ilearn/)).

Blueprint & weighting

The iLEARN public page states that each Checkpoint measures a subset of skills and the summative measures the full set of skills by the end of the school year, but the official page and accessible sources retrieved here do not publish per-domain item percentages or weightings for math ([Indiana DOE iLEARN](https://www.in.gov/doe/students/assessment/ilearn/), [Indiana DOE Formative (Interim) Assessment Grant Guidance](https://www.in.gov/doe/files/2026-2027-Formative-Interim-Assessment-Grant-Guidance.pdf)).

Official sources

Indiana DOE iLEARN
Indiana DOE Formative (Interim) Assessment Grant Guidance

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playeasy

$(3 \cdot 7)^{4} = 3^{a} \cdot 7^{a}\textsf{.}$ What is $a\textsf{?}$

The Power of a Product Property says that a product raised to a power equals each factor raised to that power, written $(ab)^{n} = a^{n} \cdot b^{n}\textsf{.}$ Here $(3 \cdot 7)^{4} = 3^{4} \cdot 7^{4}$ , so $a = 4\textsf{.}$

Practice playhard

Let $f(t) = 2e^{3t} + 1{,}000$ . Which of the following approximations, written as $a \times 10^n$ with one significant digit, is closest to the value of $f(4)$ ?

Substitute $t = 4$ : $f(4) = 2e^{12} + 1{,}000$ . Since $e^{12} \approx 162{,}755$ , $f(4) \approx 2(162{,}755) + 1{,}000 = 326{,}510 \approx 3 \times 10^{5}$ .

Practice playeasy

$(3 \times 10^2)(3 \times 10^3) = 9 \times 10^n$ . What is $n$ ?

Coefficients multiply to $9$ ; exponents add: $2 + 3 = 5$ , so $n = 5$ .

Practice playeasy

Solve for all values of $x\textsf{.}$

$x^{2} = 81$

$9 \times 9 = 81$ and $(-9) \times (-9) = 81\textsf{,}$ so $x = \pm 9\textsf{.}$

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

$\sqrt{27}$ lies between two consecutive integers. Enter the larger one.

$5^2 = 25 < 27 < 36 = 6^2$ , so $\sqrt{27}$ is between $5$ and $6$ ; the larger is $6$ .

Practice playeasy

Simplify: $(y^{5})^{2}$ .

The Power of a Power Property says that a power raised to another power is simplified by multiplying the exponents, written $(y^{m})^{n} = y^{m \cdot n}\textsf{.}$ Here $y^{5}$ is raised to the second power, so $(y^{5})^{2} = y^{5 \cdot 2} = y^{10}\textsf{.}$

Practice playhard

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