DC CAPE Algebra II Linear, Quadratic, and Exponential Models Practice

Linear, Quadratic, and Exponential Models skills

interpret expressions for functions in terms of the situation they model

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

Standards basis

Common Core State Standards (CCSS-M) — District of Columbia

How the DC CAPE reports it

DC CAPE math continues DC’s PARCC-era alignment to the Common Core State Standards and uses the same general development/review approach described by OSSE. The page says DC Math follows the same rigorous development and review process and measures the knowledge and skills that matter most for DC students, while also explicitly tying the assessments to CCSS.

Blueprint & weighting

DC CAPE uses the PARCC-derived / Common Core-based framework (by grade domains structure).

Official sources

OSSE DC CAPE
OSSE DC CAPE page content on CCSS and test specifications

8 free questions · 0/0 correct

Practice playeasy

The function $I$ is defined by $I(t) = 275(1.04)^t$ . The function $I$ models the balance, in thousands of dollars, of an investment account, where $t$ is the number of months after the account was opened. According to the model, what is the estimated balance, in thousands of dollars, of the account $1$ month after it was opened?

When $t = 1$ , $I(1) = 275(1.04)^1 = 275 \cdot 1.04 = 286$ thousand dollars.

Practice playeasy

You invest $\text{\char36}400$ at $25\%$ annual interest for $1$ year. What is the total?

$400 \times 1.25 = 500$ .

Practice playmedium

Candle height, in cm, after $x$ hours:
$\begin{array}{c|c} x & f(x) \\ \hline 0 & 20 \\ 1 & 18 \\ 2 & 16 \\ 3 & 14 \end{array}$
The height is $f(x)=mx+20\textsf{.}$ What is $m\textsf{?}$

Slope-intercept form is $f(x) = mx + b\textsf{.}$ The height decreases by $2$ centimeters each hour, so $m = -2\textsf{.}$

Practice playmedium

The table shows values of a linear function $h\textsf{.}$
$\begin{array}{c|cccc} x & 1 & 2 & 3 & 4 \\ \hline h(x) & 7 & 10 & 13 & 16 \end{array}$
Which of the following is $h(x)\textsf{?}$

The outputs increase by $3$ each time $x$ increases by $1\textsf{,}$ so the constant rate is $3\textsf{.}$ Using the point $(1, 7)$ gives $3(1) + b = 7\textsf{,}$ so $b = 4\textsf{.}$ Therefore $h(x) = 3x + 4\textsf{.}$

Practice playeasy

A line has slope $4$ and passes through the point $(-1, 2)$ . Which equation represents this line in point-slope form?

Point-slope form is $y - y_1 = m(x - x_1)$ . With $m = 4$ and $(x_1, y_1) = (-1, 2)$ , the equation is $y - 2 = 4(x - (-1))$ , or $y - 2 = 4(x + 1)\textsf{.}$

Practice playmedium

Solve $e^{-x}=6$ for the real value of $x$ .

Take $\ln$ of both sides: $-x=\ln 6$ . Since $-x=(-1)x$ , divide both sides by $-1$ to get $x=-\ln 6\textsf{.}$

Practice playmedium

A warehouse begins a clearance week with $640$ boxes. Each week, half of the boxes still in the warehouse are shipped out. Which equation gives the number of boxes, $b$ , still in the warehouse after $w$ weeks?

The warehouse starts with $640$ boxes, and each week the remaining amount is multiplied by $\dfrac{1}{2}$ . After $w$ weeks, $b = 640\left(\dfrac{1}{2}\right)^w$ .

Practice playeasy

The function $c$ is defined by $c(x) = 40(1.25)^{x}$ . The function models the number of colonies of bacteria $x$ hours after a culture is started. Which statement is the best interpretation of the growth factor $1.25$ in this context?

The growth factor is $1.25$ . Each time $x$ increases by $1$ , the number of colonies is multiplied by $1.25$ . That means each hour the number of colonies is $125\%$ of the previous hour's number, a $25\%$ increase.

DC CAPE Algebra II Linear, Quadratic, and Exponential Models. Practice it free.

Linear, Quadratic, and Exponential Models skills

interpret expressions for functions in terms of the situation they model

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

Topics mapped to this domain

Exponential functions in context (SAT)

Exponential and log formulas

Linear functions from tables (ACT/SAT)

Linear rule from a function table (ACT)

Slope-point line equations (ACT/SAT/PSAT 8/9/10)

Solving exponential equations with logarithms (ACT)

Writing exponential equations from context (SAT)

Interpreting exponential parameters

Interpreting linear parameters

Linear coefficient interpretations (SAT/PSAT 8/9/10)

8 free questions · 0/0 correct

Turn linear, quadratic, and exponential models into game time.

More Algebra II domains