Algebra Final Review

Quadratics

100

Graph y = x²+3

See Desmos.  

200

Graph y = -1/4 x²

See Desmos.

300

Graph y = -(x-3)²-1

See Desmos.  

400

When c=7, what is the value of 20+60-25+15+10/c+9

5

500

Which value of x satisfies the equation 4(x-2)+3=3-2(x-3)

A=7/3

Functions

100

Find f(x) + g(x)

f(x) = -3x-6 and g(x) = 5x +2

2x - 4

200

Let f(x) = 4x+5 and g(x) = -6x-7,

find f(x) - g(x)

10x+12

300

If f(x) = 2x+3 and g(x) =4x², find f(g(x)).

8x²+3

400

If f(x)= 2x + 3 and g(x) = 3x², find f(g(-2))

27

500

Find the inverse of f(x) = 4x+8

f^-1(x)=1/4 x -2

Exponents

100

Simplify (-3c³d⁴e⁶)²

9c⁶d⁸e¹²

200

Simplify (y²/z⁴)⁵

y¹⁰/z²⁰

300

Find the sum:

(6q⁵+8q²+3) + (8q⁵-3q-7)

14q⁵+8q²-3q-4

400

Evaluate the expression ((3)/(4))^(-2)

(16)/(9)

500

Evaluate the expression ((243)/(32))^(4/5)

5(1/16)

Polynomials

100

Find the sum:

(6q⁵+8q²+3) + (8q⁵-3q-7)

14q⁵+8q²-3q-4

200

Evaluate p(x) = -3x³+x²-12x-5 when x = 2

p(2) = -49

300

If you need to divide (x⁴+3x²-4x-2) by the factor x-2 using synthetic division, what special situation do you need to remember when you set up the problem?

You need to use a zero place holder for the x³ term.  

400

Divide using synthetic division. 

(6m²-5m+9) / (m-1)

6m+1 + 10/m-1

500

Divide (3x³ - 4x² - x + 1) by (x + 1) using polynomial long division.

  -7x

Mixed

100

What is the domain of the function? f(x)=(1)/((x-6)(x+6))

Domain: All real numbers, x can't be 6 

200

Find the inverse of f(x) = (2x+5)/3

f^-1(x)=3/2 x - 5/2

300

Find the root of y=x^2+4x

(-4+\sqrt((4)^(2)-4(1)(0)))/(2(10)) = -4

400

How many different ways can you select 15 jelly beans from a bag of 15?

15 14 13 12 11= 360360/5 = 3003 ways

500

If you wrote numbers from 1 to 1000, how many numbers have the digits of 4?

4 14 24 34 40 41 42 43 44 45 46 47 48 49... 19 numbers contain 4 from 1 to 100 400..499.. 100 contain 4 9*19+100= 271 numbers.