DC CAPE Algebra I Creating Equations Practice

Creating Equations skills

create equations that describe numbers or relationships

create equations in two or more variables to represent relationships

create inequalities in one variable and use them to 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 playmedium

Devin is paid $\text{\char36}22$ per hour in his first year at a clinic and works $2{,}000$ hours that year. He receives the same dollar-per-hour raise each year and is paid $\text{\char36}26$ per hour in his fifth year, still working $2{,}000$ hours annually. What is the total of Devin's earnings over his five years?

Devin works $2{,}000$ hours each year, so Year 1 earnings are $\text{\char36}44{,}000$ and Year 5 earnings are $\text{\char36}52{,}000$ . Subtract: $\text{\char36}52{,}000 - \text{\char36}44{,}000 = \text{\char36}8{,}000$ . Over five years there are four equal annual increases, so divide by $5 - 1 = 4$ to get $x = \text{\char36}2{,}000$ . Add $\text{\char36}2{,}000$ each year after the first: $\text{\char36}44{,}000$ , $\text{\char36}46{,}000$ , $\text{\char36}48{,}000$ , $\text{\char36}50{,}000$ , $\text{\char36}52{,}000$ . Sum all five years: $\text{\char36}240{,}000$ .

Practice playeasy

What is the $x$ -intercept of the line $y = 2x - 8$ ?

Set $y = 0$ : $2x - 8 = 0$ , so $x = 4$ .

Practice playmedium

A line passes through the points $(1, -4)$ and $(5, 4)$ . Which equation represents this line in slope-intercept form?

The slope is $m = \dfrac{4 - (-4)}{5 - 1} = 2$ . Substitute $(1, -4)$ : $-4 = 2(1) + b$ , so $b = -6$ . The equation is $y = 2x - 6$ .

Practice playmedium

If $x=8$ and $x=-5$ are solutions of $x^{2}-3x+m=0$ , what is the value of $m$ ?

If the zeros are $x=8$ and $x=-5$ , that means the factors of the equation are $(x-8)$ and $(x+5)$ . The product of these factors is $x^{2}-3x-40$ . Comparing with $x^{2}-3x+m$ , the missing constant is $m=-40$ .

Practice playeasy

At a craft fair, making a pair of earrings takes $12$ minutes and making a bracelet takes $20$ minutes. A vendor spends a total of $280$ minutes making $x$ pairs of earrings and $y$ bracelets. Which equation represents this situation?

Making $x$ pairs of earrings takes $12x$ minutes and making $y$ bracelets takes $20y$ minutes. The total time is $280$ minutes, so $12x + 20y = 280$ .

Practice playeasy

On a certain road, traffic cameras record speeds $s$ , in miles per hour, that are at least $25$ mph and no more than $55$ mph. Which inequality represents the possible values of $s$ ?

At least $25$ and no more than $55$ include both endpoints, so $25 \le s \le 55$ .

Practice playmedium

Twice a number $n$ is no more than $18\textsf{.}$ Which inequality shows the possible values of $n\textsf{?}$

Twice $n$ is $2n\textsf{.}$ No more than $18$ means $2n \le 18\textsf{.}$

Practice playeasy

At a cafe, burgers cost $b$ dollars each and fries cost $f$ dollars each. One order of $4$ burgers and $3$ orders of fries cost $\text{\char36}30\textsf{.}$ Another order of $2$ burgers and $5$ orders of fries cost $\text{\char36}22\textsf{.}$ What is the price of one order of fries?

The system is $4b + 3f = 30$ and $2b + 5f = 22\textsf{.}$ Double the second equation: $4b + 10f = 44\textsf{.}$ Subtract the first: $7f = 14\textsf{,}$ so $f = 2\textsf{.}$

DC CAPE Algebra I Creating Equations. Practice it free.

Creating Equations skills

create equations that describe numbers or relationships

create equations in two or more variables to represent relationships

create inequalities in one variable and use them to solve problems

Topics mapped to this domain

Linear raise total earnings

Linear equation forms

Linear equation from two points (SAT)

Quadratic missing coefficient from roots (ACT)

Writing a two-variable equation from context

Compound inequality situations

Linear inequality situations (ACT/SAT/PSAT 8/9/10)

Linear system word problems (ACT/SAT)

Writing systems from context

Literal equations (SAT)

Literal quadratic equations (ACT)

Sum of consecutive integers (ACT)

8 free questions · 0/0 correct

Turn creating equations into game time.

More Algebra I domains