Free Printable Algebra 12

1.

Which of the following inequalities matches the given graph?

a)

y ≥ 2/5x + 1

b)

y ≥ -2/5x + 1

c)

y≤ 2/5x + 1

d)

y ≥ -2/5x - 1

2.

Which of the following inequalities matches the given graph?

a)

x ≥ -1

b)

x ≤ -1

c)

x > -1

d)

x < -1

3.

Which of the following inequalities matches the given graph?

a)

y ≤ -3/4 x + 3

b)

y ≥ -3/4 x + 3

c)

y < -3/4 x + 3

d)

y > -3/4 x + 3

4.

Consider the equation:
y=-x+4
Identify the slope and y-intercept.

a)

m=4, b=-x

b)

m=-x, b=4

c)

m=1, b=4

d)

m=-1, b=4

5.

How can I tell if an inequality will have a solid line?

a)

It has an equal sign.

b)

The symbol is greater than.

c)

The symbol has "or equal to."

d)

You just guess.

6.

Which ordered pair is a solution of the inequality?

y ≥ 4x – 5

a)

(3, 4)

b)

(3, 0)

c)

(2, 1)

d)

(1, 1)

7.

Which point below is NOT part of the solution set?

a)

(0, 0)

b)

(-10, 20)

c)

(3, 5)

d)

(0, -2)

8.

Write the linear inequality in standard form for this situation: Ms. Savva is ordering pizzas and breadsticks for a school party and has a budget of no more than $81. An order of breadsticks costs $7 and a pizza costs $13.

a)

7x + 13y < 81

b)

7x + 13y ≥ 81

c)

7x + 13y ≤ 81

d)

7x + 13y > 81

9.

Write the linear inequality in standard form for this situation: The CRHS science department can spend no more than $2700 on textbooks this year. The department needs to buy both Biology text books, which cost $57 each, and Chemistry textbooks, which cost $72 each.

a)

57x + 72y ≥ 2700

b)

57x + 72y > 2700

c)

57x + 72y < 2700

d)

57x + 72y ≤ 2700

10.

Select the correct graph for each inequality.

a)

A

b)

B

c)

C

d)

_D

11.

Select the correct graph for each inequality.

a)

A

b)

B

c)

C

d)

D

12.

Select the correct graph for each inequality.

a)

A

b)

B

c)

C

d)

D

13.

In an equation or inequality, you want to get the variable...

a)

on one side

b)

to disappear

c)

isolated (by itself)

14.

When graphing an inequality, you use a dotted line when you use which symbol?

a)

<, >

b)

≤, ≥

15.

Solve the inequality.
x + 5 ≤ 13

a)

x ≥ 8

b)

x ≥ 18

c)

x ≤ 8

d)

x ≤ 18

16.

Consider the function y<2x+3. Which is true?

a)

The line would be solid with shading above.

b)

The line would be dashed with shading above.

c)

The line would be solid with shading below.

d)

None of these.

17.

Solve the inequality.
x + 5 ≤ 13

a)

x ≥ 8

b)

x ≥ 18

c)

x ≤ 8

d)

x ≤ 18

18.

Solve the inequality.
x + 5 ≤ 13

a)

x ≥ 8

b)

x ≥ 18

c)

x ≤ 8

d)

x ≤ 18

19.

c - 7 > 8

a)

c < 15

b)

c > 15

c)

c < - 15

d)

c >, = 15

20.

Solve
y - 4 > 12

a)

y > 16

b)

y < 16

c)

y > 8

d)

y < 8

21.

What inequality does the number line graph represent?

a)

x ≤ 4

b)

x ≥ -4

c)

x < -4

d)

x < 4

22.

The sign below means...
≥

a)

Greater Than

b)

Less Than

c)

Greater Than or Equal to

d)

Less Than or Equal to

23.

<

a)

equal

b)

less than

c)

less than or equal to

d)

at least

24.

≤

a)

equal

b)

less than

c)

less than or equal to

d)

at least

25.

≥

a)

equal

b)

greater than

c)

greater than or equal to

d)

at most

26.

>

a)

equal

b)

greater than

c)

greater than or equal to

d)

at most

27.

m - 5 > 10

a)

m is less than 15

b)

m is greater than 5

c)

m is greater than 15

d)

m is less than 5

28.

If you were to graph x > 2, what would you do?

a)

put a closed dot on 2 and to the right

b)

put a closed dot on 2 and to the left

c)

put an open dot on 2 and to the right

d)

put an open dot on 2 and to the left

29.

What do you do to solve the graph of the inequality:
-2x ≤ 10

a)

divide by -2

b)

multiply by -2

c)

multiply by -2 and flip the inequality

d)

divide by -2 and flip the inequality

30.

Which is the solution of
-6a ≥ -36

a)

a ≥ 6

b)

-6 ≥ a

c)

a ≤ 6

d)

6 ≤ a

31.

How many answers are there in an inequality?

a)

0

b)

1

c)

2

d)

multiple

32.

Which of the following inequalities would require you to flip the sign when solving?

a)

2x < 3

b)

3x > - 9

c)

-4x ≥ 10

d)

5x ≤ 15

33.

Solve the inequality

-2y+4>6

a)

$y<1$

b)

$y>-1$

c)

$y<-1$

d)

$y>1$

34.

Solve the inequality $-3-d>2d-7$

a)

$d<\frac{4}{3}$

b)

$d<-\frac{4}{3}$

c)

$d>\frac{4}{3}$

d)

$d>-\frac{4}{3}$

35.

Given the inequality $x>-5$ , Find the values of x.

a)

$x=All\ negative\ and\ positive\ numbers\ except\ -5$

b)

$x=from\ -5\ to\ negative\ numbers$

c)

$x=-4,-3,-2,1,0\ and\ all\ positive\ numbers$

d)

$x=-5,-4,-3,-2,-1,0\ and\ positive\ numbers$

36.

This are the notations that represent the relationships between numbers by using signs $>,<,\ge,\le or\ \ne$ .

(a)

37.

The number before the variable is called (a) ?

38.

Solve the inequality $2\left(c-3\right)\ge1$

a)

$c\ge-3.5$

b)

$c\le3.5$

c)

$c\le-3.5$

d)

$c\ge3.5$

39.

2c+1\ge c>3c-20,\

Find the values of x.

(a)

40.

Find the smallest integer value of x that satisfy the inequality

27-2x\le8

,Write your answer in complete sentence.

(a)

41.

Find the integer values of x that satisfy the inequalities

-10\le x<-4

. Write your answer in complete sentence.

(a)

42.

From the equation (x ÷ 4) + 3 = 15, what is the correct answer?

a)

35

b)

-35

c)

48

d)

-48

43.

From the equation (2x – 5) ÷ 3 = 9, what is the solution to this equation?

a)

32

b)

27

c)

18

d)

16

44.

From the equation 9(y -3) = 72, what is the solution to the equation?

a)

8

b)

11

c)

69

d)

45

45.

From the equation 12(z + 10) = 156, what is the solution to the equation?

a)

3

b)

-3

c)

61

d)

-61

46.

From the equation X + 16 = 14, what is the solution to the equation?

a)

2

b)

-2

c)

1

d)

-1

47.

From the equation 83 = X - 15, what is the solution to the equation?

a)

98

b)

99

c)

100

d)

101

48.

From the equation 12X = 108, what is the solution to the equation?

a)

6

b)

7

c)

8

d)

9

49.

From the equation X ÷ 14 = 5, what is the solution to the equation?

a)

50

b)

60

c)

70

d)

80

50.

From the equation 500 + X = 1,275, what is the solution to the equation?

a)

700

b)

772

c)

774

d)

775

51.

From the equation (X + 10) + X = 76, what is the solution to the equation?

a)

33

b)

34

c)

35

d)

36

52.

$What\ are\ the\ factors\ of\ \ x^2\ -5x\ +6\ ?$

a)

(x - 2)(x - 3)

b)

(x - 1)(x +6)

c)

(x+2)(x-3)

d)

(x +1)(x -6)

53.

$What\ are\ the\ factors\ of\ \ x^2\ +5x\ +6\ ?$

a)

(x - 2)(x - 3)

b)

(x +1)(x +6)

c)

(x+2)(x+3)

d)

(x -1)(x -6)

54.

Factor: x² + 2x – 3

a)

(x - 2)(x + 1)

b)

(x + 1)(x - 3)

c)

(x + 2)(x - 1)

d)

(x - 1)(x + 3)

55.

Factor:
x²+ 7x - 30

a)

(x + 10)(x - 7)

b)

(x - 10)(x + 3)

c)

(x + 10)(x + 3)

d)

(x + 10)(x - 3)

56.

Factor
x² + x - 6

a)

(x + 2)(x + 3)

b)

(x + 6)(x -1)

c)

(x + 3)(x - 2)

d)

(x +1)(x - 6)

57.

Factor
a² - a - 12

a)

(a - 4)(a + 3)

b)

(a + 6)(a - 4)

c)

(a - 6)(a + 4)

d)

(a + 4)(a - 3)

58.

Factor
3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

59.

x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

60.

The final factors of 4x²- 64y²are :

a)

4( x - 4y) (x + 4y)

b)

( 2x - 32y) (2 x + 32y)

c)

( 2x - 8y) (2 x - 8y)

d)

( 2x - 8y) (2 x + 8y)

61.

25x²y²- 100

a)

( 5xy - 10) (5xy + 10)

b)

( 5xy + 10) (5xy + 10)

c)

Prime

d)

( 5xy - 50) (5xy + 50)

62.

x²+ 81

a)

Prime

b)

( x - 9 ) ( x + 9 )

c)

( x + 9 ) ( x + 9 )

d)

( x - 9 ) ( x - 9 )

63.

What is the factored form of x³+7x²-2x-14?

a)

(x²-2)(x-7)

b)

(x²+2)(x-7)

c)

(x²+2)(x+7)

d)

(x²-2)(x+7)

64.

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

65.

What is the factored form of 2x³-x²+x-2?

a)

(2x²+x+2)(x - 1 )

b)

2(x - 1)(x²+1)

c)

2(x²+x+2)(x - 1 )

d)

(2 - x)(x - 1)(x²+x+1)

66.

What is the factored form of x³ + 2x² - x-2

a)

(x+1)(x - 1 )(x+2)

b)

(x+1)(x - 2 )(x+2)

c)

(x²+1)(x+2)

d)

(2 +x)(x² - 1)

67.

What is the factored form of x³ + 2x²+2x+1

a)

(x+1)(x²+x+1)

b)

(x+1)(x² - x +1)

c)

(x-1)(x² - x +1)

d)

(x+1)(x+1)(x+1)

68.

What is the factored form of x² +y²- z² - 2xy?

a)

(x - y - z)(x - y+z)

b)

(x + y - z)(x - y - z)

c)

(x - y + z)(x + y+z)

d)

(x - y - z)(x + y+z)

69.

What is the factored form of x² - y²- z² - 2yz?

a)

(x - y - z)(x - y+z)

b)

(x + y - z)(x - y - z)

c)

(x - y + z)(x + y+z)

d)

(x - y - z)(x + y+z)

70.

What is the factored form of x⁴+x²+1?

a)

(x² +x+1)(x² +x+1)

b)

(x² - x+1)(x² -x+1)

c)

(x² +x+1)(x² - x +1)

d)

(x² +x -1)(x² +x+1)

71.

The factors of

16x^4+36x^2y^2+81y^4

are :

a)

$\left(4x^2+6xy+9y^2\right)\left(4x^2-6xy+9y^2\right)$

b)

$\left(2x-3y\right)^2\ \left(2x+3y\right)^2$

c)

undefined

d)

$\left(4x^2+6xy+9y^2\right)\left(4x^2+6xy+9y^2\right)$

Algebra 12

Total questions: 71

Worksheet time: 5hrs 51mins

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