KAP Grade 8 The Number System. Practice it free.

Works with irrational numbers and exponents, and understands properties of integer exponents and scientific notation. This Grade 8 reporting domain maps to 6 practice skills and 8 representative questions from the playable bank.

Grade 86 mapped skills

What the test measures

The Number System skills

Know that numbers that are not rational are irrational
Approximate irrational numbers
Use numbers expressed in the form of a single digit times an integer power of 10
Perform operations with numbers expressed in scientific notation
Use square root and cube root symbols to represent solutions to equations

Standards basis

Kansas College and Career Ready Standards for Mathematics (CCRS-M), closely aligned to Common Core State Standards for Mathematics (CCSS-M) — Kansas

How the KAP reports it

Kansas Assessment Program appears to be a state assessment program rather than a vendor framework like Smarter Balanced or PARCC. The public KAP site did not expose a math blueprint or reporting-category document in the pages I could access, so the safest official mapping is to the state's adopted mathematics standards structure that the assessment is built to.

Blueprint & weighting

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

Official sources

Kansas Assessment Program
KAP — About Our Tests (2017 Kansas Mathematics Standards; domains & clusters; reporting categories)
KSDE — Kansas Standards for Mathematics (KCCRS-M standards documents)

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playhard

Let $f(t) = 3e^{2t} + 10$ . Which of the following approximations, written as $a \times 10^n$ with one significant digit, is closest to the value of $f(5)$ ?

Substitute $t = 5$ : $f(5) = 3e^{10} + 10$ . Since $e^{10} \approx 22{,}026$ , $f(5) \approx 3(22{,}026) + 10 = 66{,}088 \approx 7 \times 10^{4}$ .

Practice playeasy

Between which two consecutive integers does $\sqrt{40}$ lie?

$6^{2} = 36$ and $7^{2} = 49\textsf{.}$ Since $36 < 40 < 49\textsf{,}$ $\sqrt{40}$ is between $6$ and $7\textsf{.}$

Practice playeasy

Write $720{,}000$ as $a \times 10^n$ where $1 \le a < 10$ . What is $n$ ?

$720{,}000 = 7.2 \times 10^5$ , so $n = 5$ .

Practice playeasy

$8 \times 10^{6}$ is how many times as large as $4 \times 10^{3}\textsf{?}$

$\dfrac{8 \times 10^{6}}{4 \times 10^{3}} = 2 \times 10^{3} = 2{,}000\textsf{.}$

Practice playeasy

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

$x^{2} = 400$

$20 \times 20 = 400$ and $(-20) \times (-20) = 400\textsf{,}$ so $x = \pm 20\textsf{.}$

Practice playeasy

What is $\sqrt{144}$ ?

$12 \times 12 = 144$ , so $\sqrt{144} = 12$ .

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 $f(5)$ ?