CMAS 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

Build new functions from existing functions

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

Standards basis

Colorado Academic Standards (mathematics) — Colorado

How the CMAS reports it

CMAS is Colorado’s statewide summative assessment system aligned to the Colorado Academic Standards rather than a national framework like SBAC or NAEP. The official CMAS page and Colorado standards materials indicate the math assessment is built from Colorado Academic Standards, but the retrieved official CMAS page did not expose a separate math blueprint document.

Blueprint & weighting

No official CMAS math domain weighting/percent-of-items blueprint was available in the retrieved primary CMAS materials.

Official sources

Colorado Department of Education CMAS page
Colorado Department of Education Colorado Academic Standards and Essential Skills page

8 free questions · 0/0 correct

Practice playeasy

The first five terms of an arithmetic sequence are $2, 6, 10, 14, 18$ . What is the $17$ th term?

The common difference is $d = 4$ . With $a_1 = 2$ , the $17$ th term is $a_{17} = 2 + 16(4) = 66$ .

Practice playeasy

The function $f$ is defined by $f(x) = x^{2} - 10$ . What is the value of $f(x)$ when $x = 6$ ?

Substitute $x = 6$ : $f(6) = 6^{2} - 10 = 36 - 10 = 26$ .

Practice playeasy

The function $f$ is defined by $f(x) = \sqrt{x + 5}$ . What is the value of $f(x)$ when $x = 11$ ?

Substitute $x = 11$ : $f(11) = \sqrt{11 + 5} = \sqrt{16} = 4$ .

Practice playeasy

For the function $f$ , $f(0) = 160$ . For each increase in $x$ by $1$ , the value of $f(x)$ decreases by $50\%$ . What is the value of $f(3)$ ?

A decrease of $50\%$ multiplies by $0.50$ each step. So $f(3) = 160 \cdot 0.50^3 = 160 \cdot 0.125 = 20$ .

Practice playeasy

$b = 100 - 4h$

The equation shown gives the estimated battery charge $b\textsf{,}$ as a percent, remaining on a laptop after $h$ hours of use, where $0 \le h \le 20\textsf{.}$ What is the estimated battery charge, as a percent, remaining on the laptop after $12$ hours of use?

Substitute $h = 12\textsf{:}$ $b = 100 - 4(12) = 100 - 48 = 52\textsf{.}$ The estimated charge remaining is $52$ percent.

Practice playeasy

The function $L$ is defined by $L(w) = 180(0.88)^{w/2}$ . The function $L$ models the light output, in lumens, from a bulb, where $w$ is the number of weeks the bulb has been in use. According to the model, what is the estimated light output, in lumens, after $2$ weeks of use?

When $w = 2$ , the exponent is $2/2 = 1$ . So $L(2) = 180(0.88)^1 = 158.4$ lumens.

Practice playeasy

A substance has a half-life of $5$ years. What fraction remains after $10$ years?

$10 \div 5 = 2$ half-lives. Remaining: $\left(\dfrac{1}{2}\right)^{2} = \dfrac{1}{4}$ .

Practice playeasy

For which value of $x$ does the graph of $y = -(x + 8)(x - 2)$ meet the $x$ -axis?

Set $y = 0$ : $-(x + 8)(x - 2) = 0$ . The factor $-1$ is nonzero, so the zeros come from $x + 8 = 0 \Rightarrow x = -8$ and $x - 2 = 0 \Rightarrow x = 2$ . Of the choices, $-8$ is an x-coordinate of an x-intercept.

CMAS 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

Build new functions from existing functions

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

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

Exponential functions in context (SAT)

Exponential and log formulas

Factored polynomial x-intercepts (SAT)

Finding inverse functions (ACT)

Function table composition (ACT)

Function transformation descriptions

Function transformations

8 free questions · 0/0 correct

Turn functions into game time.

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