Algebra 2 Semester 1 Final Benchmark Review

Quadratics

100

What is the y-intercept?
y=2x²-3x+7

(0, 7)

200

Find the vertex.
y = -x²+2x-5

(1,-8)

300

Solve by factoring.
x²-x-6

x = -2, 3

400

Solve using the quadratic formula.
x²-4x+68=0

2+8i

500

Solve using the quadratic formula
2x²-12x+15=0

6 +/- sqrt(6) / 2

Rationals

100

What is the restricted value(s) of the rational expression?

6x+1/(x² - x - 20)

x= -4 and x = 5

200

What is the sum of the rational expressions

5x/(x+9)   +   (2x -7)/(x+9)

(7x - 7)/(x + 9)    or   7(x-1)/(x+9)

300

What is the difference of the rational expressions 

(3x² + 5x)/2  and  (7x - 4)/2

(3x² -2x + 4)/2

400

What is the solution to the equation? 

(x +3)/4 = x/3

x = 9 

500

What is unique about the solution to the rational equation

(x² -7x - 18)/(x+2) = x - 9

All real solutions 

Polynomials

100

Add.
(9x+5)+(-2x²+10x)

-2x²+19x+5

200

Multiply.
(x-3)(3x-8)

3x²-17x+24

300

Multiply.
(2x+1)(x²-6x+7)

2x³-11x²+8x+7

400

Multiply.
(4x²+5x+4)(x²-3x+1)

4x⁴-7x³-7x²-7x+4

500

Divide using long division
4x³-22x²+11x-5 / x-5

4x²-2x+1

Random Trivia

100

According to Bloomberg, which artist officially entered the billionaire's club in 2023?

Beyonce, Jay-Z, Taylor Swift, Kanye West

Taylor Swift

200

Which actor from the sitcom 'Friends' passed away on October 28, 2023?

Matthew Perry 

300

Which country was projected to surpass China as the most populous in the world in 2023?

India

400

Which two NFL teams were in the last Superbowl? 

Philadelphia Eagles and Kansas City Chiefs

500

What became the fastest-growing app in history by gaining over 100 million users in less than one week in 2023?

Threads

Algebra #2 Miscellaneous

100

Simplify.
x⁵y²/2x²

2x⁷y²

200

Simplify.

18xy⁴/6x⁴y³

3y/x³

300

Solve for x.
-9x - (-3x+3) > 6x - 14

x < 11/12

400

Solve for x.
-5(-3x-3) + 5x + 4= -1

x = -1

500

Simplify.
12y⁵m/4(y³m⁴)^-2

3y¹¹m⁹