Free Printable Solving quadratic and simplifying algebraic fractions

1.

Which of the following equations matches standard form of a quadratic?

a)

ax + by = c

b)

y = a(x - h)² + k

c)

y = ax² + bx + c

d)

y = mx + b

2.

Determine the values of a, b, and c for the quadratic equation:

4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

3.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

No Real Solution

b)

c)

d)

4.

The first step in solving quadratic equations is to . . .

a)

factor

b)

write the equation in standard form

c)

use quadratic formula

d)

complete the square

5.

find x for the following equation using the quadratic formula.
2x²-8x-24=0

a)

x= 6, -2

b)

x= 2, -6

c)

x= 4, 2

d)

x= 2, 6

6.

The discriminant is

a)

aX² + bX + c

b)

b - 4ac

c)

b² - 4ac

d)

b² + 4ac

7.

Is $\sqrt{-4}$ a real or imaginary number?

a)

real

b)

imaginary

8.

Find the missing value "c" to complete the square:

x² + 22x + ___

a)

11

b)

22

c)

121

d)

2121

9.

Rewrite the equation in completing the square form.

y = x² + 6x - 5

a)

y=(x+3)² - 14

b)

y=(x-3)² + 4

c)

y=(x+9)² - 14

d)

y=(x-9)² + 4

10.

What do you do to the b value to correctly complete the square?

a)

square it

b)

divide it by 2 and square the result

c)

divide it by 2 and take the square root of the result

d)

divide it by 2 only

11.

Which of the following equations shows the completring square form of a quadratic?

a)

x = -b/2a

b)

x = (-b ±√b² - 4ac)/2a

c)

y = ax² + bx + c

d)

y = a(x - h)² + k

12.

Solve by completing the square:
k² − 12k + 23 = 0

a)

{6 + √13, 6 - √13}

b)

{-6 + √13, -6 - √13}

c)

{6 + √59, 6 - √59}

d)

{-6 + √59, -6 - √59}

13.

Solve by completing the square.
x² − 10x - 11= 0

a)

x = −1 and 11

b)

x = 1 and −11

c)

x = −10 and 11

d)

x = −5 and 25

14.

$\frac{8x^4}{2x^2}$

a)

$4x^3$

b)

$\frac{4x^2}{2}$

c)

$4x^2$

d)

$\frac{8x^2}{2}$

15.

$\frac{33a^2b^2}{44a^3b}$

a)

$\frac{3ab}{4ab}$

b)

$\frac{3b}{4a}$

c)

$\frac{3ab}{4}$

d)

$\frac{3}{4ab}$

16.

$\frac{6x+8}{2}$

a)

$\frac{3x+4}{2}$

b)

$3x+4$

c)

$\frac{14x}{2}$

d)

$7x$

17.

$\frac{x^2+6x+9}{x^2-2x-15}$

a)

$\frac{x+3}{x+5}$

b)

$\frac{x+5}{x-3}$

c)

$\frac{x-5}{x+3}$

d)

$\frac{x+3}{x-5}$

18.

Simplify:

a)

x(x-5)/(x+5)(x-5)

b)

x/(x-5)

c)

x/(x+5)

d)

(x+5)/x

19.

Simplify each radical expression.

$\frac{2x^2+5x-3}{4x^2-8x+3}$

a)

(x - 3)/(2x + 3)

b)

(x + 3)/(2x - 3)

c)

(x + 3)/(2x + 3)

d)

(x - 3)/(2x - 3)

20.

Simplify the algebraic fraction by factorising.

$\frac{7x^2-29x+4}{x^2-8x+16}$

(a)

Solving quadratic and simplifying algebraic fractions - chap 14

Total questions: 20

Worksheet time: 2hrs 40mins

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