Algebra Final Exam Review

Systems of Equations

100

Solve: 

y=2x-3

x+y=15

(6,9)

200

Solve:

3x=y-2

6x=4-2y

(0,2)

300

The difference of two numbers is 3. Their sum is 13. Find the numbers.

5 and 8

400

You and a friend go to Tacos Galore for lunch. You order three soft tacos and three burritos and your total bill is $11.25. Your friend's bill is $10.00 for four soft tacos and two burritos. How much do soft tacos cost? How much do burritos cost?

1 burrito costs $2.50 & 1 soft taco costs $1.25

500

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.

senior ticket is $8 and the child ticket is $14

Rules of Exponents

100

2x³*2x²

4x⁵

200

(x⁵y⁶)/(xy²)

x⁴y⁴

300

(52x⁶)/(13x^-7)

4x¹³

400

(2x⁴y^-4)/(8x⁷y³)

1/4x³y⁷

500

(-2a³b²c⁰/3a²b³c⁷)^-2

9b²c¹⁴/4a²

Linear Equations

100

Find the slope: y = 3x + 5

Slope: 3

200

What is the slope of the line that crosses these two points:

(2,5) & (4,13)

Slope: 4

300

The equation of the line through (0,4) with a slope of -2

y=-2x+4

400

What is the slope of the following equation:

2x + 2y = 8

slope = -1

500

A plumber charges $25 for a service call plus $50 per hour of service. Write an equation in slope-intercept form for the cost, C, after h hours of service. What will be the total cost for 8 hours of work?

C=50h+25

After 8 hours, the cost will be 425

Exponential Equations

100

What is the multiplier of the following exponential equation: 

y=4(6)^x

multiplier: 6

200

What is the multiplier of the exponential equation that goes through the points: (2,3) & (3,9)

Multiplier: 3

300

Write an exponential equation with an initial value of 100 and a multiplier of 1/2.

y=100(1/2)^x

400

What is the value of y when x=3 in the following equation: y=10(3)^x

y=270

500

Kristin’s grandparents started a savings account for her when she was born. They invested $500 in an account that pays 8% interest compounded annually. Write an equation and find out how much money is in the account for Kristin's 16th birthday.

Equation: y=500(1.08)^x

For Kristin's 16th birthday, she will have $1712.97 

Quadratic Equations

100

Factor: x²-2x-15

(x+5)(x-3)

200

What is the vertex of the following equation:

y=(x-6)²-4

vertex: (6,-4)

300

Use the Zero Product Property to find the roots of:

4x²-28x=0

x=0, x=7

400

Use the quadratic formula to solve the following equation: 

x²+5x-14

x=-7, x=2

500

What is the vertex of the following quadratic equation: x²+4x-5

vertex: (-2,-9)