Algebra 1 Final Exam Review

Systems of Equations

100

Solve the system of equations by elimination. -3x-y=-5 2x-2y=-2

(1,2)

200

Solve by substitution: 2y=x+1 -2x-y=7

(-3,-1)

300

The sum of two numbers is 17. The total of four times the smaller number and two times the larger number is forty-four. Find the two numbers.

5 and 12

400

A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test?

5 multiple choice questions

500

The Lakers scored a total of 80 points in a basketball game against the Bulls. The Lakers made a total of 37 baskets. Assuming all points were from two- or three- point shots, how many two-point shots did the Lakers make? How many three-point shots?

31 two-point shots 6 three-point shots

Exponents

100

Simplify (2a)³

8a³

200

2x⁴y^-4/8x⁷y³

1/4x⁴y⁶

300

Write an example of exponential growth in the real world. 

Examples may vary. 

400

Find a bank account balance if the account starts with $100, has an annual rate of 4%, and the money is left in the account for 12 years. 

$160.10

500

An adult takes 400 mg of ibuprofen. Each hour, the amount of ibuprofen in a person's system decreases by about 29%. How much ibuprofen is left after 6 hours. 

51.24 mg. 

Polynomials

100

Simplify: (2x^2+7x+3)-(x^2-7x+1)

x^2+14x+2

200

Factor the expression 64x²-81

(8x-9)(8x+9)

300

Factor the expression: 4x²-15x-25 

(n-5)(4n+5)

400

Factor 10v²-27vw+18w²

(2v-3w)(5v-6w)

500

What is the product of: (2x+3)(4x²-5x+6)

8x³+2x²-3x+18

Quadratics

100

Find the coordinates of the vertex of the graph of the function. y=2x^2 + 12x + 10

(-3,-8)

200

Solve using square roots: 1/2 x^2=32

x=8,-8

300

Solve by factoring: 5p^2-9p-2=0

p=-1/5, 2

400

Find the solutions using the quadratic formula: 8x²+7x-8

-7+-root305/16

500

A ball is thrown into the air. The height, h, in feet, of the ball can be modeled by the equation h=-16t^2+20t+6, where t is the time, in seconds, the ball is in the air. When will the ball hit the ground? Round your answer to nearest hundredth if necessary.

1.5 seconds

Radicals

100

Define rational number. Then, give two examples. 

A rational number can be written as a fraction. 

200

Simplify the radical expression: The square root of 45

3 root 5

300

Simplify the square root of 512m³

16m root 2m

400

Graph the function square root of x+6        -2 on your graph. 

See graph

500

Find the vertex of the following: 1/3(x-15)²+25

(15, 25)