Algebra 2 Review

Features of :linear functions (slope & intercepts)

100

What is the slope and y- intercept of y= 2x +3

Slope: 2

y- intercept: (0,3)

200

Find the x and y intercept of y = -3x + 6 

y- intercept: (0,6)

x- intercept: (2,0)

300

Rewrite 4x + 2y = 10 in slope- intercept form and state the slope and intercepts 

y = -2x + 5

Slope: -2

y- intercept: (0,5)

x- intercept: (5/2,0)

400

Find the slope and both intercepts of 3x + 4y = 12

Slope: -3/4

y-intercept: (0,3)

x-intercept: (4,0)

500

A line passes through (0,7) and has slope -1/2. What is the x-intercept? 

(14,0)

Writing linear functions (equation from 2 points)

100

Write the equation of the line with slope 3 and y-intercept -2 

y= 3x - 2

200

Find the equation of the line through (0,-3) and (4,1).

y= x - 3

300

Find the equation of the line through (2,6) and (-2,4).

y = 1/2x + 5

400

Find the equation of the line through (-1,2) and (2,-4).

y = -2x

500

Write the equation of the line through (3,-2) and (3,5).

x=3 (vertical line) 

Solving Linear equations

100

Solve: 2x + 5=11

x=3

200

Solve: 5x - 7 =18

x = 5

300

Solve: 3(2x + 5) - 2(2x -3) = 12

x= -9/2

400

Solve: 4x - 3(x-2) = 2x + 5

x = 1

500

Solve: 5(x - 1) + 2 = 3x +4

x = 7/2

Error Analysis

100

What mistake is made if someone solves 7x=2 as x =27

they divided incorrectly; x= 2/7

200

A student writes 2(x+ 3) as 2x + 3, what is wrong?

Incorrect distribution; it should be 2x + 6

300

A student combines 3x - 4x as 7x. What is the mistake?

Wrong sign; correct is -x

400

A student solves 3x + 2 - 2(2x-3) = 13 as 7x =2. What's their main error? 

Mis-distributed -2(2x-3) 

500

Rewrite a short "note to the author" explaining how to avoid mistakes when distributing and combining like terms.

Always use parentheses, distribute carefully to each term, and combine only like terms. Double-check by plugging your answer back into the equation.

Domain and Range

100

What is the domain and range of y = 2x +3

Domain: (-inf, inf)

Range: (-inf, inf) 

200

What is the domain and range of y= 5

Domain: (-inf, inf)

Range: y = 5

300

What is the domain and range of y = x²

Domain: (-inf, inf)

Range: 0 ≤ y < inf OR [0, inf) 

400

What is the domain and range of y = (x-2)²+ 1  

 

Domain: [0, inf) OR 0 ≤ x < inf

Range: [1,inf) OR 1 ≤ y < inf

500

What is the domain and range of y = sqrt(x+4)

Domain: [-4, inf) OR -4 ≤ x < inf

Range: [0 , inf) OR 0≤ y < inf