Algebra 1 2nd Semester Final Exam Review

Data and Probability

100

Find the mean and median of the following data set

3, 5, 8, 6, 2, 4, 8

What is 

Mean = 5.14

Median = 5

200

You are picking markers out of a bag with 4 blue, 2 red, 4 green, and 5 yellow markers, replacing the markers each time. Find the probability that you pick a blue marker and a yellow marker. 

What is P(blue and yellow) = 5/49

300

The function y = 2(1.08)^t represents a bacterial population y, over t minutes. Predict the number of bacteria after 50 minutes. 

What is 93.8 bacteria? 

400

John is eating chips out of a bag. The number of chips in the bag, y, over x minutes is represented by the equation y = 253 - 12.2x. What is the meaning of the -12.2 in the context of the question?

What is he eats an average of 12.2 chips every 1 minute?

500

The function y = 23.5 + 8.7x represents a student's score on the final exam, y, compared to the hours they spent preparing, x. 

Predict the score for a student who spends 8 hours preparing. 

That student actually got a 92%. Calculate and interpret their residual. 

What is 93.1%, r = -1.1, the student actually scored 1.1% lower than was predicted?

Exponents

100

x² * x³

What is x⁵

200

x^6/x^4

x²

300

(25x^-3)/(5x^2)

What is

5/(x^5)

400

(6(m^2n^4)^2)/(2(m^3n^-2)^-3)

What is 3m¹⁰n²

500

((7x^-3y^-5)^0)/(2x^-3y^6)

What is

x^3/(2y^6)

Factoring

100

Factor completely

x² - 16

What is (x - 4)(x + 4)

200

Factor completely

x² - 12x + 27

What is (x - 9)(x - 3)

300

Factor

8x^3-2x^2+12x-3

What is  

(2x^2+3)(4x-1)

400

Factor completely

(12x³ - 75x)

What is 

3x(2x+ 5)(2x-5)

500

Factor completely

70x⁵  - 12x⁴ - 16x³

What is 2x³(5x+2)(7x-4) ?

Exponential

100

 y = 12(3)^x

Give the starting value

12

200

Write an equation to represent when you invest $500 at 3% interest compounded yearly, in terms of t.

What is 500(1.03)^t?

300

The b for y = a(b)^x  for a 

$30,000 car, which depreciates 12% a year for 5 years.

What is .88?

400

You invest $1000 at 4% interest compounded yearly. How much do you have after 5 years?

What is $1216.65

500

A car loses 20% of its value each year. 

State the value of a $40,000 car after 3 years.

What is $20,480?

Quadratics

100

The solutions of x² - x - 20 = 0

What are x = -4 and x = 5

200

The vertex of y=(x - 4)² + 8

What is (4, 8)

300

Solve the following equation

f(x)= 10x² - 21x + 9

What is x = 3/2 and x = 3/5?

400

Give axis of symmetry and vertex for

y = x² + 4x - 5 

What is x=-2, (-2, -9)

500

Solve, round to the nearest hundredth 

y=4x^2-5x-10

What is x = -1.07, 2.32?