Grade 11 College Math Review

Quadratics

100

Given:

y = 5(x - 4)² - 7 

What is the vertex?

(4, -7)

200

Given:

y = -4(x + 6)(x - 3)

What is the axis of symmetry?

x = - 1.5

300

Consider:

y = 5(x +2)²

^{What is the y-intercept?}

y-intercept = 20

400

Consider:

y = x² -12x - 28

Rewrite this equation in factored form. 

y = (x + 2)(x - 14)

500

Consider:

y = -7(x + 1) (x -7)

What is the vertex?

Vertex:  (3, 112)

Exponents

100

y⁵ . y³

y⁸

200

(6x²)(2x³)

12x⁵

300

(9x⁴y³)(3x²y⁴)

27x⁶y⁷

400

Solve for b. 

(3x^by³)(5x^-7y⁵) = 15x⁵y⁸

b = 12

500

Divide:

(36x⁷y⁵z) / (-6x^-2y³)

-6x⁹y²z

Factoring

100

Factor:

x² - 49

(x - 7)(x+7)

200

Factor:

x² - 9x +14

(x - 7)(x -2)

300

5x² - 45

5(x - 3)(x + 3)

400

Factor completely:

3x² - 15x + 12

3(x - 4)(x - 1)

500

Factor:

25x² - 36

(5x - 6)(5x + 6) 

Expanding

100

Expand and simplify:

(x - 4) (x +3)

x² - x -12

200

Expand and simplify:

(x - 3)²

x² -6x + 9

300

Expand and simplify:

5(x +3)(x - 4) - 3

5x² -5x -63

400

Solve for b. 

(3x - 5)(2x - 7) = 6x² +bx +35

b = -31

500

Solve for c. 

(6x - 9)(2x +5) = 12x² + 12x + c

c = -45

More Exponents

100

Simplify:

x¹² / x³

x⁹

200

(5y²)²

25y⁴

300

(4x⁵y³)²/(2xy²)

8x⁹y⁴

400

Solve for x. 

7^x-4=7¹² x 7⁸

x =16

500

2^{3x - 5} = 4^x+2

x = 9