NJSLA Algebra I Linear, Quadratic, and Exponential Models Practice

Linear, Quadratic, and Exponential Models skills

F-LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions

F-LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs

F-LE.A.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly

F-LE.B.4 For exponential models, interpret the parameters in terms of a context

F-LE.B.5 Interpret the parameters in a linear or exponential function in terms of a context

F-LE.B.6 Calculate and interpret the average rate of change of a function over a specified interval

F-LE.B.7 Distinguish between situations that can be modeled with linear functions and with exponential functions

Standards basis

New Jersey Student Learning Standards for Mathematics (NJSLS-M), aligned to Common Core State Standards for Mathematics (CCSS-M) — New Jersey

How the NJSLA reports it

NJSLA math is built on the New Jersey Student Learning Standards for Mathematics, which closely follow the Common Core domain structure and progressions. The assessment is organized by grade-level and end-of-course reporting aligned to those standards rather than by a separate proprietary framework.

Blueprint & weighting

NJDOE publishes statewide assessment administration information and grade/course coverage, but no official public math-domain weighting blueprint was located in the retrieved primary materials.

Official sources

New Jersey Department of Education - Assessment
New Jersey Department of Education - 2023 NJSLS-Mathematics
NJDOE - Statewide Assessment Testing Schedule 2026-27

8 free questions · 0/0 correct

Practice playeasy

The equation of a line is $y + 7 = 2(x + 4)\textsf{.}$ What is the slope of the line?

Point-slope form is $y - y_1 = m(x - x_1)\textsf{.}$ The slope is the coefficient of $(x - x_1)\textsf{,}$ so $m = 2\textsf{.}$

Practice playeasy

The $x$ -intercept of the graph of $y = 2x - 8$ in the coordinate plane is $(x, 0)$ . What is the value of $x$ ?

At the $x$ -intercept, $y = 0$ , so $0 = 2x - 8$ , $2x = 8$ , and $x = 4\textsf{.}$

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

An $80$ -milligram sample of a radioactive isotope has a half-life of $5$ years.

Choose the function model that correctly calculates the amount remaining after $10$ years.

The remaining amount after $t$ years is $A(t) = 80\left(\dfrac{1}{2}\right)^{\textstyle\frac{t}{h}}\textsf{,}$ where $h$ is the half-life. Here $t = 10$ and $h = 5\textsf{,}$ so $A(10) = 80\left(\dfrac{1}{2}\right)^{\textstyle\frac{10}{5}} = 80\left(\dfrac{1}{2}\right)^{2} = 20\textsf{.}$

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 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.

Practice playeasy

The given equation represents the number of pages $p$ read, where $h$ represents the number of hours spent reading.

$p = 42h$

Which of the following is the best interpretation of $42$ in this context?

In $p = 42h$ , the number $42$ is the reading rate: $42$ pages for each hour spent reading.

NJSLA Algebra I Linear, Quadratic, and Exponential Models. Practice it free.

Linear, Quadratic, and Exponential Models skills

F-LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions

F-LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs

F-LE.A.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly

F-LE.B.4 For exponential models, interpret the parameters in terms of a context

F-LE.B.5 Interpret the parameters in a linear or exponential function in terms of a context

F-LE.B.6 Calculate and interpret the average rate of change of a function over a specified interval

F-LE.B.7 Distinguish between situations that can be modeled with linear functions and with exponential functions

Topics mapped to this domain

Slope and point from point-slope form

Slope-intercept intercepts (SAT/PSAT 8/9/10)

Writing exponential equations from context (SAT)

Exponential functions

Exponential functions in context (SAT)

Exponential and log formulas

Interpreting exponential parameters

Interpreting linear parameters

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

Linear functions from tables (ACT/SAT)

Linear rule from a function table (ACT)

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

8 free questions · 0/0 correct

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

More Algebra I domains