Algebra 1 Semester 2 Review

Exponents

100

Simplify.

(x²)³

x⁶

200

Simplify (5x²)³

125x⁶

300

Simplify.

(4x⁰y³)²

16y⁶

400

Simplify (3x⁵)(x⁶) 

3x¹¹

500

Simplify.

(2b^-4)²

4/b⁸

Polynomials

100

Multiply:

3x(5x+8)

15x²+24x

200

Simplify:

2x²(4x-x²+3)

-2x⁴+8x³+6x²

300

Simplify:

(3x²-6)+(5x²+9)

8x²+3

400

Simplify:

(x²+5x-4)-(3x²-2x+5)

-2x²+7x-9

500

Simplify and write in standard form: 

3x²(2x+4)+8x³-4x+5x³

19x³+12x²-4x

Quadratics

100

List the x-intercepts for y=x²-4x-32

x= {8,-4} 

(8,0) and (-4,0)

200

Solve. 

4x²=64

x={4,-4}

300

Complete the square by filling in the blanks:

x²+12x+_____=15 + ______

36 and 36

400

Solve using the quadratic formula. 

x²-3x-2=0

x=3 +- square root(17) / 2

500

Answer all parts to this question correctly.

y=-2(x+3)²+4

-Vertex:_____(min/max)

-Axis of symmetry:______

-Leading coefficient:______

-Opens:______

vertex:(-3,4) 

axis of symmetry: -3

leading coefficient:-2

Opens downward, therefore vertex is the max.

Mix-up

100

What does a negative exponent do?

Moves the variable or number to the opposite part of the fraction.

200

The shape of a quadratic function is______.

U-shaped (Parabola)

300

5x³-3x²+1

List how many terms this polynomial has.

List the leading coefficient.

List the constant(s).

List the degree.

3 terms

Leading coefficient: 5

Constant: 1

Degree: 3

400

Explain the difference between the parent functions of a linear equation and a quadratic equation. 

Linear functions create straight lines and the equation used is y=mx +b. There are no exponents in the equation.

Quadratic functions create a parabola and have an exponent of 2 in the equation. (y=ax²+bx+c)

500

Solve. Explain what you should do first in order to solve.

5x+6=-2x+27

3

You need to combine like terms first.

Mix-up

100

What is the degree of this polynomial?

15x-3x⁴+2x²

4

200

Factor.

6n²+6n-36

6(n+3)(n-2)

300

What are the solutions of (8x+1)(x-2)=0?

x={-1/8, 2}

400

Simplify 5x⁰

5

500

Simplify:

14xy² divided by 4x²y

7y/2x