ISASP High School Functions Practice

Functions skills

Understand the concept of a function and use function notation

Interpret functions that arise in applications in terms of the context

Analyze functions using different representations

Build a function that models a relationship between two quantities

Construct and compare linear, quadratic, and exponential models and solve problems

Interpret expressions for functions in terms of the situation they model

Standards basis

Iowa Academic Standards / Iowa Core Mathematics — Iowa

How the ISASP reports it

ISASP is Iowa’s statewide assessment program administered by the state Department of Education and aligned to Iowa Academic Standards / Iowa Core rather than a multi-state blueprint like SBAC or ACT. The public materials accessible here establish the tested grades and that mathematics results are reported statewide, but I could not locate an official public math blueprint PDF on the Iowa DOE site in the available sources.

Blueprint & weighting

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

Official sources

Iowa Department of Education — Required Student Assessments
Iowa Department of Education — About the Iowa Department of Education
Iowa Academic Standards for Mathematics (April 2024) — full standards PDF, confirms K-8 domains/clusters and HS conceptual-category clusters are CCSS-M verbatim

8 free questions · 0/0 correct

Practice playmedium

The first five terms of an arithmetic sequence are $8, 14, 20, 26, 32$ . What is the $18$ th term?

The common difference is $d = 6$ . With $a_1 = 8$ , the $18$ th term is $a_{18} = 8 + 17(6) = 110$ .

Practice playeasy

The function $f$ is defined by $f(x) = 7x - 4$ . What is the value of $f(x)$ when $x = 3$ ?

Substitute $x = 3$ : $f(3) = 7(3) - 4 = 21 - 4 = 17$ .

Practice playeasy

The function $f$ is defined by $f(x) = \sqrt{2x + 1}$ . What is the value of $f(x)$ when $x = 4$ ?

Substitute $x = 4$ : $f(4) = \sqrt{2(4) + 1} = \sqrt{9} = 3$ .

Practice playeasy

For the function $p$ , $p(0) = 200$ . For each increase in $x$ by $1$ , the value of $p(x)$ decreases by $10\%$ . What is the value of $p(2)$ ?

Each step multiplies by $0.90$ . So $p(2) = 200 \cdot 0.90^2 = 200 \cdot 0.81 = 162$ .

Practice playeasy

$g = 9 - \dfrac{m}{4}$

The equation shown gives the estimated amount of paint $g\textsf{,}$ in gallons, remaining after covering $m$ square meters of wall, where $0 \le m \le 36\textsf{.}$ What is the estimated amount of paint, in gallons, remaining after covering $12$ square meters of wall?

Substitute $m = 12\textsf{:}$ $g = 9 - \dfrac{12}{4} = 9 - 3 = 6\textsf{.}$ The estimated amount remaining is $6$ gallons.

Practice playeasy

What is the value of $\log_{4}16\textsf{?}$

$4^{2} = 16\textsf{,}$ so $\log_{4}16 = 2\textsf{.}$

Practice playmedium

A charity drive starts with $80$ donors. Each day after the first day, a model estimates that the number of donors increases by $25\%$ of the number of donors the previous day. Which equation defines this model, where $d(n)$ is the estimated number of donors $n$ days after the drive begins?

The starting number is $80$ , and a $25\%$ daily increase means multiplying by $1.25$ each day, so $d(n) = 80(1.25)^n$ .

Practice playeasy

A $32$ -milligram sample of a radioactive isotope has a half-life of $1$ year.

Choose the function model that correctly calculates the amount remaining after $4$ years.

The remaining amount after $t$ years is $A(t) = 32\left(\dfrac{1}{2}\right)^{\textstyle\frac{t}{h}}\textsf{,}$ where $h$ is the half-life. Here $t = 4$ and $h = 1\textsf{,}$ so $A(4) = 32\left(\dfrac{1}{2}\right)^{\textstyle\frac{4}{1}} = 32\left(\dfrac{1}{2}\right)^{4} = 2\textsf{.}$

ISASP High School Functions. Practice it free.

Functions skills

Understand the concept of a function and use function notation

Interpret functions that arise in applications in terms of the context

Analyze functions using different representations

Build a function that models a relationship between two quantities

Construct and compare linear, quadratic, and exponential models and solve problems

Interpret expressions for functions in terms of the situation they model

Topics mapped to this domain

Arithmetic sequence nth term

Evaluating functions

Evaluating functions at a value

Evaluating functions from percent change

Evaluating functions in context

Evaluating logarithms (ACT)

Writing exponential equations from context (SAT)

Exponential functions

Exponential functions in context (SAT)

Exponential and log formulas

Factored polynomial x-intercepts (SAT)

Function table composition (ACT)

8 free questions · 0/0 correct

Turn functions into game time.

More High School domains