Free Printable Algebraic Reasoning 2nd Semester Review

1.

Solve for x
l 2x−1 l = 9

a)

x = 5 and x =-4

b)

x = 5 and x = -5

c)

Only x = 5

d)

No Solution

2.

Solve for x
l 2x−1 l +4 = 8

a)

x = 2.5 and x = -1.5

b)

x = 2 and x = -1

c)

x = -2 and x = 9

d)

No Solution

3.

Evaluate each expression.
| x + 9 | = -5

a)

-14

b)

-4

c)

{-14, -4}

d)

no solution

4.

| x + 2 | > 5

a)

x < - 7 or x > 3

b)

x > 7 or x < 3

c)

x < -7 and x > 3

d)

x > -3 and x < 7

5.

| m - 2 | < 8

a)

m > 8 or m < 9

b)

m < -6 or m > 2

c)

m > -6 and m < 10

d)

0 > m < 0

6.

|v + 8| − 5 = 2

a)

{-1,-15}

b)

{-1,-5}

c)

{-15,15}

d)

No Solution

7.

Solve:
|x + 3| > 8

a)

x > 5 or x < -11

b)

x > 5

c)

all real numbers

d)

no solution

8.

What is the solution?

a)

No solution

b)

(0, 2)

c)

(0, -4)

d)

(3, -3)

9.

Where do these two lines intersect?

a)

No solution

b)

(-2, 3)

c)

(3, -2)

d)

(2, 3)

10.

Solve the system of equations by graphing.

a)

(4, 7)

b)

(3, 5)

c)

(6, 7)

d)

(5, 3)

11.

Solve the system of equations by graphing.

a)

(-1, 4)

b)

(1, 0)

c)

No Solution

d)

(0, 2)

12.

When you graph the exact same equation twice,

a)

you will have no solution.

b)

you will have one solution.

c)

you will have infinite solutions.

d)

you will graph a giraffe.

13.

Solve for x and y
3x + 2y = 16
7x + y = 19

a)

(-2,5)

b)

(-2,-5)

c)

(2,-5)

d)

(2,5)

14.

What is the solution to this system?

a)

One Solution

b)

No solution

c)

Infinitely Many Solutions

15.

Solve the system of equations:

a)

( -1, 6, 1)

b)

( 1, 6, -1)

c)

None of these

d)

( -6, -1, 1)

16.

Determine which ordered triple is a solution of the systems of equations?
2x+y=0
x+3y-z=-11
7x+5y+4z=21

a)

(0,0,11)

b)

(1,-2,6)

c)

(-1,2,-16

d)

(0,1,-14)

17.

Which of the following is an example of a quadratic function?

a)

b)

c)

d)

18.

Where is the vertex?

a)

$\left(0,\ -3\right)$

b)

$\left(1,\ -4\right)$

c)

$\left(-1,\ 0\right)$

d)

$\left(3,\ 0\right)$

e)

$\left(1,\ 0\right)$

19.

Does the graph have a maximum or a minimum?

a)

Maximum

b)

Minimum

c)

Both

d)

Neither

20.

Does the graph have a maximum or a minimum?

a)

Maximum

b)

Minimum

c)

Both

d)

Neither

21.

Use the graph to determine the X-intercepts

a)

(-1,0) and (-3,0)

b)

(1,0) and (3,0)

c)

(0,1) and (0,3)

d)

(0,-1) and (0,-3)

22.

What is the equation for axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

23.

What is the vertex of the quadratic function:
y = x² - 6x + 11?

a)

(3,2)

b)

(-3,-2)

c)

(-3,2)

d)

(3,-2)

24.

Determine the vertex of the parabola:
y = 5x²- 20x + 13

a)

(5, -7)

b)

(-2, -7)

c)

(2, -7)

d)

(-7, -2)

25.

What are the x- intercepts?

a)

x=0 and x=-4

b)

x=0 and x=4

c)

x=0

d)

x=2

26.

Which transformation transforms the graph of

f(x) = x² to the graph of g(x) = (x + 4)²?

a)

shift 4 units up

b)

shift 4 units down

c)

shift 4 units to the left

d)

shift 4 units to the right

27.

What are the transformations?

y=(x-2)²+4 (Choose ALL that apply.)

a)

shift right 2

b)

shift left 2

c)

shift up 4

d)

shift down 4

28.

y= -(x-11)²+6

*Mark all that apply.

a)

right 11

b)

reflection across x-axis

c)

VC

d)

up 6

29.

Write the equation of this transformation: up 8

a)

y=(x+8)²

b)

y= x²+8

c)

y= x²-8

d)

y=8x²

30.

Write the equation of this transformation: reflection across x-axis, left 2, down 5

a)

y= -(x+2)²+5

b)

y= -(x+2)²

c)

y= (x-2)²-5

d)

y= -(x+2)²-5

31.

$\sqrt{50}$

a)

$5\sqrt{2}$

b)

$\sqrt{5}$

c)

$2\sqrt{5}$

d)

$25\sqrt{2}$

32.

$\sqrt{243}$

a)

$3\sqrt{3}$

b)

$9\sqrt{3}$

c)

$81\sqrt{3}$

d)

$3\sqrt{81}$

33.

$\sqrt{112}$

a)

$4\sqrt{7}$

b)

$16\sqrt{3}$

c)

$16\sqrt{7}$

d)

$4\sqrt{3}$

34.

√169 =

a)

3√7

b)

13

c)

7√3

d)

7√7

35.

3x² = 12

a)

± 2

b)

2

c)

± √12

d)

± 4

36.

x² + 4 = 68

a)

± 8

b)

± √8

c)

8

d)

± 64

37.

3x² - 1 = 14

a)

5

b)

-√5

c)

-√5, √5

d)

√5

38.

x² + 4 = 68

a)

± 8

b)

± √8

c)

8

d)

± 64

39.

Solve the following equation:

x^2+8=13

a)

$x=\pm5$

b)

$x=\pm\sqrt{5}$

c)

$x=\pm21^2$

40.

Simplify using the 9 Laws of Exponents:

a)

b)

c)

d)

41.

Simplify using the 9 Laws of Exponents:

a)

b)

c)

d)

42.

(2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

43.

4⁰

a)

0

b)

1

c)

4

d)

-4

44.

Simplify the exponential expression:

a)

10x^-2

b)

2x²

c)

2x¹²

d)

10x¹²

45.

Simplify the exponential expression.

a)

2x⁶y¹²

b)

2x⁵y⁷

c)

8x⁶y¹²

d)

8x⁵y⁷

46.

(3y⁴)²

a)

9y⁸

b)

9y⁶

c)

6y⁸

d)

6y⁶

47.

n²⋅n⁴⋅n⁵

a)

n¹¹

b)

n⁴⁰

c)

n¹³

d)

n²²

48.

According to exponent rules, when we multiply the same base we _______ the exponents.

a)

Multiply

b)

Add

c)

Divide

d)

Subtract

49.

According to exponent rules, when we divide the same base we _______ the exponents.

a)

Multiply

b)

Add

c)

Divide

d)

Subtract

50.

Simplify:
(x⁵)⁴

a)

x⁹

b)

x²⁰

c)

x

d)

x⁵⁴

51.

According to exponent rules, when we raise the power to a power we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

52.

Anything raised to a power of zero is always:

a)

0

b)

1

c)

itself

d)

negative

53.

Simplify
(-7y²)(5y⁴)

a)

-35y⁶

b)

-2y⁶

c)

-35y⁸

d)

-2y⁸

54.

Simplify (-4r⁵)(2r⁸)

a)

-8r¹³

b)

-2r¹³

c)

-8r⁴⁰

d)

-2y⁴⁰

55.

6v(2v + 3)

a)

12v+18

b)

15v² + 8v

c)

12v² + 18v

d)

12v² + 18v²

56.

(x+10)(x-10)

a)

x² - 100

b)

x² + 100

c)

x² + 20x - 100

d)

x² -20x + 100

57.

(x + 7)(x + 9)

a)

x² + 63x + 16

b)

x² + 16x + 63

c)

x² + 79

d)

x² + 16x + 2

58.

(x + 7)(x - 2)

a)

x² - 5x + 5

b)

x²- 9x - 14

c)

x² - 5x - 14

d)

x² + 5x - 14

59.

Multiply
x²(2x+3)

a)

x²+2x+3

b)

2x+3

c)

2x²+3x

d)

2x³+3x²

60.

2x³(x²−2x − 3)

a)

2x⁶- 4x³ - 6x³

b)

2x⁵−4x⁴ − 6x³

c)

-2x⁵−4x⁴ − 6x³

d)

-2x⁶−4x³ − 6x³

Algebraic Reasoning 2nd Semester Review

Total questions: 60

Worksheet time: 15hrs 0mins

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