Algebra 1 Final Review

Rules of Exponents

100

Simplify: (xy)²(xy)

x³y³

200

(x²y^-2)(xy²)

x³

300

[(x²y)(x^-4y^-5)(xy)³]⁰

1

400

(xyz)^-2(x²y⁵z³)

y³z

500

This rule of exponents tells us to "flip" the place of the variable.

What is the negative exponent rule?

Exponential Equations

100

Solve. 2^x=8

x=3

200

4^3x=8^x+1

x=1/3

300

3^3x+1=27^x

No solution

400

(1/2)^2X-3=2^X+3

X=0

500

The half life of carbon-14 is 5730 years.  If 15 grams are present to begin with, how old is something if 10 grams are left?

3352 years

Graphing Quadratics

100

This form of quadratics gives the vertex in the equation.

What is vertex form?

200

This equation determines the x-value of the vertex in intercept form.

What is x=(p+q)/2?

300

This value determines how narrow/wide a graph of a quadratic is.

What is "a"?

400

This process converts quadratics in standard form to intercept form.

What is factoring?

500

Johnny found the x-value of the vertex of f(x)=2x²+16x-5 by calculating x=16/2(2) = 16.  What is mistake did he make?

PARENTHESES AROUND THE DENOMINATOR.

Solving Quadratics

100

Solve: x²+4x-12=0

x=-6,2

200

x²+10x+16=0

x=-8,-2

300

x²+2x-5=0

x=(-2+V24)/2, (-2-V24)/2

400

Solve: x²-2=x

x=2,-1

500

Solve: x²+4x+4=0

x=-2

Quadratic Applications

100

The width of a rectangle is 4 more than its length.  If the area is 45 square units, find the dimensions.

L = 5, W = 9

200

The length of a rectangle is 3 more than twice its width.  If the area of the rectangle is 65 square units, find the dimensions

L = 13, W = 5

300

The long leg of a right triangle is 1 more than the short leg.  The hypotenuse is 2 more than the short leg.  Find all 3 sides of the triangle.

3,4,5

400

In a right triangle, the long leg is 1 less than twice the short leg.  The hypotenuse is 1 more than twice the short leg.  Find all 3 sides.

8,15,17

500

The product of two consecutive positive odd integers is 3 more than 4 times the smaller.  What are the integers?

3,5