Free Printable Algebraic Reasoning Fall Semester Review

1.

Solve: (2×10)+4

a)

20

b)

26

c)

7

d)

24

2.

Solve: (3+12)-3²

a)

4

b)

6

c)

2

d)

7

3.

5x + 3y + 5 + 4x + 3y + y + 8

a)

9x + 7y + 13

b)

6x + 2y + 2

c)

25x + 2y + 3

d)

x + 7y + 12

4.

Simplify the expression:

3x²- x + 7 + 5x + 2 - 2x²

a)

x²+ 4x + 9

b)

5x²+ 9

c)

15

d)

15x

5.

Simplify the Expression:

3x²y + 4x - 6y + 4x²y -2y

a)

11x²y - 8y

b)

3y

c)

7x²y - 4y

d)

7x²y + 4x - 8y

6.

Evaluate the following expression:
-3x² - 5x + 7 when x = -2

a)

5

b)

10

c)

12

d)

7

7.

Evaluate the expression. Let g = 3 h = 9
4h + 2g + 4

a)

42

b)

46

c)

34

d)

58

8.

m² – 15
m = 8

a)

12

b)

32

c)

49

d)

32

9.

What is the solution for x + 9 = 21

a)

10

b)

12

c)

11

d)

13

10.

Solve for b
2b = -16

a)

8

b)

4

c)

-8

d)

3

11.

2d + 7 = 9

a)

1

b)

7

c)

4

d)

3

12.

11 = 3z + 5

a)

2

b)

6

c)

1

d)

4

13.

2s - 4 = 6

a)

5

b)

3

c)

-5

d)

2

14.

$24\ =\ 3\left(3x\ -7\right)$

a)

$x\ =\ -9$

b)

$x\ =\ 5$

c)

$x\ =3$

d)

$x\ =\ 7$

15.

8v - 4(v + 8) = 8

a)

2

b)

10

c)

4

d)

-4

16.

3x + 2(4x - 4) = 3

a)

4

b)

3

c)

2

d)

1

17.

What is the solution?

a)

x = 4

b)

x = 6

c)

x = 96

d)

x = 144

18.

Solve the equation:
3(x - 1) = 2x + 9

a)

x = 12

b)

no solution

c)

x = 10

d)

x = 6

19.

Solve the equation:
3x - x + 2 = 4(2x - 1)

a)

infinite solutions

b)

x = 1

c)

x = -1

d)

no solution

20.

When do you "flip the inequalities sign"?

a)

When you add or subtract a negative

b)

When it's a 1-step problem

c)

When you multiply or divide a negative

d)

When it's a 2-step problem

21.

2x > 12

a)

x > 6

b)

x < 6

c)

x ≥ 6

d)

x ≤ 6

22.

-3x ≤ 18

a)

x ≤ -6

b)

x ≤ 6

c)

x ≥ 6

d)

x ≥ -6

23.

Solve 3x + 7 < 22

a)

x < -29/3

b)

x < -5

c)

x < 29/3

d)

x < 5

24.

2<x+2<5

a)

0<x<3

b)

4<x<7

c)

4<x<3

d)

0<x<7

25.

x+2<-4 or -5x<-15

a)

-6<x<3

b)

x<-3 and x>6

c)

x<-6 or x>3

d)

No Solution

26.

Write an inequality for Graph 4.

a)

-2 < x < 5

b)

x < -2 or x > 5

c)

x ≥ -2 OR x < 5

d)

-2 ≤ x ≤ 5

27.

What is the range of the graph?

a)

[-7, 5)

b)

(-3, 1]

c)

[-3, 1)

d)

(-7, 5]

28.

What is the domain?

a)

[-2, 3]

b)

[-2, 3)

c)

(-2, 3]

d)

[-3, 4]

e)

(-3, 4]

29.

What is the domain?

a)

$\left(-\infty,\ -3\right]$

b)

$\left[3,\ -\infty\right)$

c)

$\left(-\infty,3\right]$

d)

$\left(-\infty,\infty\right)$

e)

None of the answer choices

30.

What is the range of the graph?

a)

(-∞,∞)

b)

[-1,0]

c)

[-1,3]

d)

[3,∞)

31.

Is this mapping a function or not a function?

a)

Function

b)

Not a Function

32.

Is the relation a function?
{(4,5), (4,-7), (4,2), (4,0), (4,9)}

a)

Yes

b)

No

33.

Is this table a function or not a function?

a)

Function

b)

Not a Function

34.

Is this a function? Explain.

a)

Yes; it passes the horizontal line test.

b)

No; it is not a straight line.

c)

Yes; it passes the vertical line test.

d)

No; there is a line connecting the dots.

35.

What is the equation of a line with a slope of 4 and a y-intercept of 2?

a)

y = -4x + 2

b)

y = -2x + 4

c)

y = 4x + 2

d)

y = 2x + 4

36.

What would the slope of the graph be?

a)

Positive

b)

Negative

c)

0

d)

Undefined

37.

What kind of slope does the graph have?

a)

Positive

b)

Negative

c)

0

d)

Undefined

38.

What kind of slope does the graph have?

a)

Positive

b)

Negative

c)

0

d)

Undefined

39.

What kind of slope does the graph have?

a)

Positive

b)

Negative

c)

0

d)

Undefined

40.

Which equation matches the graph?

a)

y = 5

b)

y = -5

c)

x = -5

d)

x = 5

41.

Which equation matches the graph?

a)

y = 5

b)

y = -5

c)

x = -5

d)

x = 5

42.

Convert the standard form equation into slope-intercept form.
x + y = -1

a)

y = x - 1

b)

y = 27, 239, 430

c)

y = -1x

d)

y = -x - 1

43.

Convert the standard form equation into slope-intercept form.
x + 5y = -25

a)

y = -⅕x - 5

b)

y = -x - 5

c)

x = 20

d)

y = 27, 239, 430

44.

Which is the graph of y= -x + 2?

a)

A

b)

B

c)

C

d)

D

45.

what is the slope intercept form of

-x + 4y = 11

a)

$y=x+11$

b)

$y=\frac{1}{4}x+11$

c)

$y=\frac{1}{4}x+\frac{11}{4}$

46.

Select the graph for 5x+ y ≤ -1 .

a)

A

b)

B

c)

C

d)

D

47.

Select the correct graph for each inequality. y≤ -¾x -1

a)

A

b)

B

c)

C

d)

D

48.

Describe the transformation that is applied to the parent function.
f(x) = IxI -5

a)

Shifts left 5

b)

Shifts right 5

c)

Shifts up 5

d)

Shifts down 5

49.

Write the equation for a graph that is vertically compressed by a factor of 2/5 and shifted up 6.

a)

y=6|x|-2/5

b)

y=2/5|x|+6

c)

y=2/5|x+6|

d)

y=2/5|x-6|

50.

Describe the transformation of the equation below from the parent function of y = I x I
y = -2 I x - 3 I + 3

a)

reflected over x axis, stretched by 2, right 3, up 3

b)

reflected over x axis, stretched by 2, left 3 up 3.

c)

reflected over x axis, shrunk by 2, right 3, up 3

d)

reflected over the x axis, shrunk by 2, left 3, up 3

51.

What is the equation of the absolute value function?

a)

f(x)= |x+4|

b)

f(x)= |x-4|

c)

f(x)= |x| + 4

d)

f(x)= |x| - 4

52.

Which function defines the graph?

a)

f(x) = |x - 4| + 3

b)

f(x) = |x - 3| + 4

c)

f(x) = |-x + 4| + 3

d)

f(x) = |x + 4| + 3

53.

What is the equation of the graph below?

a)

f(x) = I x + 2 I

b)

f(x) = I x I + 2

c)

f(x) = I x I - 2

d)

f(x) = I x - 2 I

54.

What is the domain of the following graph?

a)

$\left(-\infty,\infty\right)$

b)

$\left[0,\infty\right]$

c)

$\left(-\infty,0\right]$

d)

[0,0]

55.

What is the vertex of the following function?
y=2|x-3|+1

a)

(2,3)

b)

(-3,1)

c)

(2,-3)

d)

(3,1)

56.

Which interval notation is represented by the graph?

a)

$\left(-20,\ -10\right)$

b)

$\left[-20,\ -10\right]$

c)

$\left(-20,\ -10\right]$

d)

$\left[-20,\ -10\right)$

57.

What is the range of the absolute value function?

a)

(-infinity, infinity)

b)

[3, infinity)

c)

[0, infinity)

d)

(-infinity, 3]

58.

Describe the transformations of the absolute value equation.

a)

Reflects over x-axis, compresses by a factor of 3, shifts right 1 unit

b)

Reflects over x-axis, compresses by a factor of 3, shifts up 1 unit

c)

Reflects over x-axis, stretches by a factor of 3, shifts right 1 unit

d)

Reflects over x-axis, stretches by a factor of 3, shifts up 1 unit

59.

Which graph represents the parent function of an Absolute Value?

a)

Black

b)

Blue

c)

Orange

d)

Red

60.

What type of shape is an absolute value function?

a)

Line

b)

V

c)

U

d)

Z

Algebraic Reasoning Fall Semester Review

Total questions: 60

Worksheet time: 15hrs 0mins

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