2023 / 2024 Algebra Review

Quadratics

100

Find the solutions to the following quadratic equation:

(x-5)(x+9)=0

x = 5 and x = -9

200

Find the roots to the quadratic equation:

2x²=200

x = 10 and x = -10

300

What is the discriminant of the following and how many solutions does it have:

2m² + 2m − 12 = 0

100; 2 solutions because it is positive

400

Find the solutions to the following quadratic:

2x² − 3x − 5 = 0

x = 5/2

x = -1

500

A water balloon is catapulted into the air so that its height h, in meters, after t seconds is

 h = -4.9t² + 24.5t + 1.  What is the maximum height of the balloon?  Round to the nearest tenth.

h = 31.6 meters

Functions

100

Algebra: Is this a function: {(1, 2), (-2, 3), (2, 4)} 

Yes, the domain does not repeat.

200

Algebra: simplify: 4(6ac - 3) + 5ac

Algebra: 29ac-12

300

Algebra: Solve for a: abc + 2h

Algebra: a = -2h/bc

400

Simplify: a(b - c) - 2a(c + b)

-1ab - 3ac

500

Algebra: What's the domain of a quadratic function? 

All Real Numbers

Slope Intercept/Linear Equations

100

Algebra: What is the slope-intercept of a linear equation perpendicular to y = 2/3x+9

-3/2

200

Write the following equation in slope-intercept form:  6(x + 3y) = 12

y = -1/3+2/3

300

Write an equation in point-slope form with a slope of 1/5 and passes through the point (2, -6).

y + 6 = 1/5 (x - 2)

400

Write an equation parallel to the equation y = 2x+3 and goes through the point (-8, 1) in slope-intercept form.

y = 2x+17

500

Write an equation perpendicular to y = -0.25x + 3 and goes through the point (5, -2) in slope-intercept form.

y = 4x-22

Systems of Equations

100

Julia traveled to Argentina and Chile for a total of 16 days.  In Argentina, she learned 125 new words per day.  In Chile, she learned 140 new words per day.  She learned a total of 2145 words.  Write a system of equations using x for Argentina and y for Chile.

x + y = 16

125x + 140y = 2145

200

Solve the following system of equations:

6x − 12y = 24 

−x − 6y = 4

(2, -1)

300

Solve the following system of equations:

x + 7y = 0 

2x − 8y = 22

(7, -1)

400

Solve the following system of equations:

−8x − 10y = 24 

6x + 5y = 2

(7, -8)

500

If two lines intersect, then the solution to the system is:

a.  One solution

b.  Infinitely Many Solutions

c. No solution

One solution

Exponents

100

Simplify x³y²/x^-2y⁴

x⁵/y²

200

Simplify (4⁵)²

4¹⁰

300

 Factor the following polynomial.

x² -5x - 24

 

(x-8)(x+3)

400

Find the product of (x - 2)(x² + 3x -4)

x³ + x² - 10x +8

500

Factor the following polynomial.

25x²-64

(5x+8)(5x-8)

Absolute Value

100

Solve the equation: 

|x|-5=7

x = 12 and x = -12

200

Solve the equation.

2|x-5| = 12

x = 11 or x = -1

300

Solve: 

4|x+3|-11=5

x = 1 or x = -7

{1,-7}

400

Solve the equation.  

-3|x-1|+5=8

No Solution.

500

Solve the equation. 

0.8|x+4|-3=1

x = -9 or x = 1 

Random

100

What country is the largest in the world?

Russia

200

What occasion corresponds to the longest day of the year?

The summer solstice

300

What is an eight-sided shape called

Octagon

400

On what day is the Algebra EOC?

April 17

500

What does EOC stand for?

End of Course