Free Printable Algebra

1.

$x^2+5x+6=0$ Solve this equation.

a)

$x=-3,\ -2$

b)

$x=3,\ 2$

c)

$x=-6,\ 1$

d)

$x=6,\ -1$

2.

$\frac{2}{3}x^2+\frac{1}{3}x-\frac{1}{3}=0$ Solve this equation.

a)

$x=1,\ -\frac{1}{2}$

b)

$x=-1,\ -\frac{1}{2}$

c)

$x=-1,\ \frac{1}{2}$

d)

$x=1,\ \frac{1}{2}$

3.

$4x^2-17x+13=0$ Solve this equation.

a)

$x=\frac{13}{4},\ 1$

b)

$x=\frac{15}{4},\ 1$

c)

$x=\frac{13}{4},\ -1$

d)

$x=\frac{15}{4},\ -1$

4.

2x^2-11x-9=0

Solve this equation (surd)

a)

$x=\frac{11\pm\sqrt{193}}{4}$

b)

$x=\frac{-11\pm\sqrt{193}}{4}$

c)

$x=\frac{11\pm2\sqrt{3}}{4}$

d)

$x=\frac{-11\pm2\sqrt{3}}{4}$

5.

$5x^2-14x-9=0$ Solve this equation (1d.p.)

a)

$x=\ -3.3,\ 0.5$

b)

$x=\ -3.3,\ -0.5$

c)

$x=3.3,\ -0.5$

d)

$x=3.3,\ 0.5$

6.

$3x=20-8x^2$ Solve this equation (3 d.p.)

a)

$x=-1.405,\ -1.780$

b)

$x=1.405,\ -1.780$

c)

$x=1.405,\ 1.780$

d)

$x=-1.405,\ 1.708$

7.

Form a quadratic equation from the roots:

x=-5,\ -4

a)

$x^2-9x-20=0$

b)

$x^2+9x-20=0$

c)

$x^2-9x+20=0$

d)

$x^2+9x+20=0$

8.

A frog is sitting on the ground when he is scared by a big dog. His movement is modeled by the equation h = -6t²+ 6t where h is the frog's height at any given time, t . How many seconds until the frog is back on the ground?

a)

0.5 seconds

b)

1 second

c)

1.5 seconds

d)

2 seconds

e)

3 seconds

9.

Your nephew is standing on his deck, which is 4 feet off the ground. He tosses his toy up into the air. The equation

h = -2t²+ 7t + 4 models the toy's height, h, from the ground at t seconds after he threw it. How high is the toy after 1 second?

a)

2

b)

4

c)

9

d)

10

e)

15

10.

If you square 5 more than a positive number, the result is 88 more than 12 times the number. Find the numbers.

a)

-9, 7

b)

√75

c)

9, -7

d)

15, -5

11.

The product of two consecutive negative even integers is 24. Find the integers.

a)

6, 8

b)

6, 4

c)

-6, -8

d)

-6, -4

12.

The product of two consecutive positive numbers is 132. Find the numbers.

a)

11, 12

b)

-11, -12

c)

-11, 12

d)

11, -12

13.

The area of a playground is 336 yd2 . The width of the playground is 5 yd longer than its length. Find the length and width of the playground

a)

length = 26 yd, width = 21 yd

b)

length = 21 yd, width = 26 yd

c)

length = 21 yd, width = 16 yd

d)

length = 16 yd, width = 21 yd

14.

What is the smallest of 3 consecutive positive integers if the product of the smaller two integers is 5 less than 5 times the largest integer?

a)

10

b)

-5

c)

5

d)

-10

15.

A rectangle has an area of 24 square units. The width is 5 units less than the length. What is the length, in units, of the rectangle?

a)

6

b)

8

c)

3

d)

19

16.

$25x^2-81=0$ Solve this equation.

a)

$x=--\frac{9}{5},\ \frac{9}{5}$

b)

$x=\frac{81}{25},\ -\frac{81}{25}$

c)

$x=\frac{9}{25},\ -\frac{9}{25}$

d)

$x=\frac{81}{5},\ -\frac{81}{5}$

17.

Factor by grouping:
4p³+8p²+3p+6

a)

(2p²+3)(p+2)

b)

(2p²+6)(p+4)

c)

(4p²+3)(p+2)

d)

(4p²+8p)(3p+6)

18.

Factor by grouping:
x³+7x²-2x-14

a)

(x²-2)(x-7)

b)

(x²+2)(x-7)

c)

(x²+2)(x+7)

d)

(x²-2)(x+7)

19.

$3a=\frac{b+c}{2}$

Express b in terms of a and c.

a)

$b=3a\ +\frac{c}{2}$

b)

$b=6a\ -c$

c)

$b=6a-2c$

d)

$b=3a-\frac{c}{2}$

20.

$\frac{p}{2}-\frac{3q}{5}=\frac{c}{10}$
Express c in terms of p and q.

a)

$c\ =5p-6q$

b)

$c=5p-3q$

c)

$c=2p-15q$

d)

$c=20p-30q$

Algebra

Total questions: 20

Worksheet time: 2hrs 17mins

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