Free Printable 5/30/22 Math 3 Study Guide

1.

Find the slope

a)

-5/3

b)

-3/5

c)

5/3

d)

3/5

2.

What is the slope in the equation y=2x + 3?

a)

2

b)

3

c)

5

d)

Cannot be Determined

3.

Find the slope of the line that passes through
(10, 1) and (5, 2)

a)

1/5

b)

-1/5

c)

5

d)

-5

4.

What does "m" represent in y=mx+b?

a)

y-intercept

b)

slope

c)

macaroni

d)

nothing

5.

What is the equation of this line?

a)

y = 2x +2

b)

y = 2x -2

c)

y = -x + 2

d)

Cannot be Determined

6.

Evaluate 2a + 4b
if a = 10 and b = 6

a)

20

b)

24

c)

44

d)

4

7.

Which property is demonstrated by the following equation:

4x-6y = 3(x-1)?

a)

Distributive

b)

Closure

c)

Associative

d)

Commutative

8.

3x - 4 = x + 10

a)

x = 7

b)

x = -7

c)

x = 0

d)

x = 4

9.

x + 7 = 2x + 2

a)

x = -4

b)

x = -5

c)

x = 3

d)

x = 5

10.

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

a)

4

b)

3

c)

2

d)

1

11.

7(1 - y) = -3(y - 2)

a)

x = 1/4

b)

x = 4

c)

x = 5

12.

2x - 3 ≥ 4x - 1

a)

x ≤ -1

b)

x ≥ -1

c)

x ≤ 1

d)

x ≥ 1

13.

-1(2x + 4) ≥ 6

a)

x ≤ -5

b)

x ≥ -5

c)

x ≤ -1

d)

x ≥ -1

14.

|v + 8| − 5 = 2

a)

{-1,-15}

b)

{-1,-5}

c)

{-15,15}

d)

No Solution

15.

|−2n| + 10 = −50

a)

{30, -30}

b)

{20,-20}

c)

{-5,5}

d)

No Solution

16.

|2a - 10| = 6

a)

a = 8, a = 5

b)

a = 2

c)

a = 8

d)

a = 8, a = 2

17.

| x + 3 | ≤ 2

a)

No Solution

b)

All Real Numbers

c)

-5 ≤ x ≤ -1

d)

1 ≤ x ≤ 5

18.

| n + 2 | - 3 ≥ -6

a)

No Solution

b)

All Real Numbers

c)

n ≤ -5 or n ≥ 1

d)

-5 ≤ n ≤ 1

19.

What is the solution to the system?

a)

(3, -1)

b)

(2, -6)

c)

No Solution

d)

(6, -2)

20.

Solve the system by elimination.
−4x − 4y = 0
4x + 4y = 0

a)

(−6, −4)

b)

Infinite number of solutions

c)

(−6, 10)

d)

(6, 4)

21.

What is the y-intercept of this graph?

a)

(0,1)

b)

(0,-2)

c)

(0,0)

d)

(0,3)

22.

Solve by elimination:

4x+9y=28

-4x-y=-28

a)

(-7,0)

b)

(6,0)

c)

(-6,0)

d)

(7,0)

23.

Solve:
y = 5x + 9
2y + 2x = -18

a)

(5, 0)

b)

(3, 6)

c)

(-3, -6)

d)

(1, 16)

24.

What is the solution to this system?
x= 7 - 2y
2x + y = 5

a)

(-1,4)

b)

(4,-1)

c)

(1,3)

d)

(3,1)

25.

When graphed, where is the solution to a system of equations?

a)

The y-intercept

b)

The x-intercept

c)

The point of intersection

d)

The origin

26.

If a system of linear equations has no solution, what do you know about the graphs of the equations?

a)

The lines are parallel

b)

The lines are perpendicular

c)

The lines intersect

d)

The lines have different slopes

27.

If a system has infinitely many solutions, what must be true?

a)

The lines have the same slope and y-intercept

b)

The lines have the same slope but different y-intercepts

c)

The lines have different slopes but the same y-intercept

d)

The lines have different slopes and y-intercepts

28.

Solve the system.
x − y = 11
2x + y = 19

a)

(-1, 10)

b)

(30, 19)

c)

(19, 30)

d)

(10, -1)

29.

Solve the system of equations.

a)

(10, 3)

b)

(6, 3)

c)

(15, 3)

d)

No solution

e)

Infinite Solution

30.

The solution (x, y) to a system of equations is the point where they...?

a)

Run off the graph

b)

Don't touch

c)

Intersect

d)

Exist

31.

Parallel Lines never intersect because...

a)

they have the same slopes.

b)

they have the same y-intercept.

c)

they have different slopes.

d)

they have different y-intercepts.

32.

Which equation is being represented by this line?

a)

y = -1x + 2

b)

y = 1/2x + 2

c)

y = 3x -4

d)

y = -3x +2

33.

Find the x and y intercepts
4x - 5y = 40

a)

x intercept is 10
y intercept is 8

b)

x intercept is 10
y intercept is 20

c)

x intercept is 8
y intercept is 10

d)

x intercept is 10
y intercept is -8

34.

Find the value of y when x = 2.

a)

2

b)

6

c)

7

d)

8

35.

Find the slope of the line.

a)

Undefined

b)

0

c)

1/1

d)

-1/1

36.

Which equation represents the graph?

a)

x = 2

b)

y = 2

c)

y = 2x

d)

y = undefined

37.

What is coordinate L?

a)

(6,6)

b)

(2,5)

c)

(2,3)

d)

(5,2)

38.

Slope is describe as

a)

$\frac{rise}{run}$

b)

$\frac{run}{rise}$

39.

y -intercept is where the line ______________.

a)

begins

b)

crosses the x-axis

c)

crosses the y-axis

d)

crosses each other

40.

Which trig function would you use with this diagram?

a)

^Sin

b)

^Cos

c)

^Tan

d)

^Wha??

41.

What is the cosine of angle P?

a)

p/q

b)

q/r

c)

p/r

d)

r/q

42.

What does SOH stand for

a)

hypotenuse over opposite

b)

adjacent over opposite
opposite over adjacent

c)

opposite over hypotenuse

d)

adjacent over adjacent

43.

What does CAH stand for

a)

cosine is the adjective over the hypotenuse.

b)

cosine is the adjacent side over the hypotenuse side.

c)

cosine is the adjacent side over the hippopotamus.

d)

cosine is the hypotenuse side over the adjacent side.

44.

Use a calculator to find sin 45.

a)

.707

b)

1

c)

.809

d)

1.4

45.

Use a calculator to find the cos 70.

a)

.12

b)

2.7

c)

.94

d)

.34

46.

Use a calculator to find cos 0

a)

4

b)

3

c)

2

d)

1

47.

Find cosA

a)

30/16

b)

30/34

c)

30/15

d)

16/34

48.

FInd tanX

a)

32/40

b)

40/24

c)

32/24

d)

24/32

49.

We can use SOH-CAH-TOA for...

a)

Any triangle ever

b)

Non-right triangles only

c)

Right Triangles only

d)

Never

50.

What is the length of side x?

a)

130 cm

b)

112 cm

c)

150 cm

d)

105 cm

51.

Find the measure of ∠A

a)

18

b)

28

c)

25

d)

24

52.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

53.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

54.

What is the size of the matrix below? Always do Rows x Columns.

a)

3 x 4

b)

4 x 3

55.

What is the size of the matrix below?

a)

0 x 1

b)

1 x 0

c)

3 x 3

d)

3 x 0

56.

Which element is located in A₂₃?

a)

-3

b)

5

c)

-9

d)

2

57.

What is the location of 5?

a)

A₁₂

b)

A₂₁

c)

A₂₅

d)

A₁₃

58.

What are the dimensions of this matrix?

a)

4x3

b)

3x4

c)

3

d)

4

59.

Add

a)

11 8
-4 2

b)

3 2
-6 -6

c)

-3 2
-4 -6

d)

10 8
-6 2

60.

What is a Matrix?

a)

An equation of over 5 numbers or symbols

b)

A set of numbers in rows and columns

c)

A method of finding the n^th value of a series

d)

A complicated number system

61.

Find A+B

a)

8 10
8 1

b)

12 25
7 1

c)

10 30
0 1

d)

can't add two together because the rows dont match columns

62.

How many rows are in a 7 x 3 matrix?

a)

7

b)

3

c)

21

d)

10

63.

Multiply

a)

20 15 -10
30 -5 0

b)

-20 15 -10
30 -5 0

c)

1 8 3
11 4 5

d)

20 -15 10
-30 5 0

64.

The number of columns in a 2x12 matrix is?

a)

10

b)

24

c)

12

d)

2

65.

Find B-A

a)

-4 0
6 -1

b)

1 0
1 -4

c)

4 0
-6 1

d)

not possible because rows do not match columns

66.

What must be true in order to ADD two matrices?

a)

They must be square.

b)

The dimensions must be equal.

c)

The determinant can't equal 0.

d)

The column of the 1st must equal the row of the 2nd.

67.

Find the determinant of the above matrix.

a)

-23

b)

23

c)

-7

d)

7

68.

When setting up Cramer's Rule, what is the 2x2 determinant for the numerator for the x in the system?

a)

$\left|-4\ \ \ -2\right|$
$\left|-5\ \ \ -4\right|\$

b)

$\left|-4\ \ \ -16\right|$
$\left|-5\ \ -26\right|$

c)

$\left|-16\ \ \ -2\right|$
$\left|-26\ \ \ \ -4\right|$

d)

$\left|-4\ \ -4\right|$
$\left|-2\ \ -5\right|$

69.

When setting up Cramer's Rule, what is the 2x2 determinant for the numerator for the y in the system?

a)

$\left|-4\ \ \ -2\right|$
$\left|-5\ \ \ -4\right|\$

b)

$\left|-4\ \ \ -16\right|$
$\left|-5\ \ -26\right|$

c)

$\left|-16\ \ \ -2\right|$
$\left|-26\ \ \ \ -4\right|$

d)

$\left|-4\ \ -4\right|$
$\left|-2\ \ -5\right|$

70.

a)

$\left[-3\ -5\right]$

b)

$\left[-5\ -3\right]$

c)

$\left[5\ \ -4\right]$

d)

Undefined

71.

Use Cramer's Rule to solve the system. What is the solution?

a)

$\left(1,5\right)$

b)

No unique solution

c)

$\left(3,\ -4\right)$

d)

$\left(2,4\right)$

72.

Evaluate the determinant of the matrix.

a)

$-30$

b)

$-10$

c)

$10$

d)

$-55$

73.

What is the solution to the 4x5 Matrix?

a)

( 3, 4, 9, 6 )

b)

( 3, 4, 9, -6 )

c)

( -6, 9, 4, 3 )

d)

( 6, 9, 4, 3 )

74.

Solve!

a)

(2,7,5)

b)

(-8,7,5)

c)

(-8,2,5)

d)

(-3,2,5)

75.

What is an appropriate first row command to solve this by Gaussian Elimination?

a)

2R2 + R2 -> R2

b)

-2R1 + R2 -> R2

c)

R3 +R2 --> R3

d)

2R1 + R2 --> R2

76.

Can the system of equations be solved without performing any further row operations? Why or why not?

a)

No, you need to continue row operations until you get a row with all zeros on the left side.

b)

Yes, the last row tells you what z is, you can use that in the second row to find y, and you can use both in the first row to find x.

c)

Yes, you can tell from these rows that there are infinitely many solutions because one row is a multiple of another row.

d)

No, you need to continue row operations until you get all zeros and ones on the right side.

77.

What is the common monomial factor of $6x^3+3x^2-12x$ ?

a)

$3$

b)

$2x$

c)

$3x$

d)

$3x^2$

78.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

79.

factor:x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

80.

Factor:
x²+ 7x - 30

a)

(x + 10)(x - 7)

b)

(x - 10)(x + 3)

c)

(x + 10)(x + 3)

d)

(x + 10)(x - 3)

81.

Factor
a² - a - 12

a)

(a - 4)(a + 3)

b)

(a + 6)(a - 4)

c)

(a - 6)(a + 4)

d)

(a + 4)(a - 3)

82.

Which of the following is a factor of
r² -16r + 60 ?

a)

r + 6

b)

r + 10

c)

r - 6

d)

r -30

83.

Factor completely:
$r^2+r-6$

a)

$\left(r+2\right)\left(r+3\right)$

b)

$\left(r+4\right)\left(r-7\right)$

c)

$\left(r-2\right)\left(r-3\right)$

d)

$\left(r-2\right)\left(r+3\right)$

84.

Which of the following is a difference of perfect squares?

a)

x² - 18

b)

4x² + 36

c)

9x² - 100

d)

x² + 4

85.

Factor:
x² - 9

a)

( x -9) (x - 9)

b)

(x + 3) (x + 3)

c)

(x + 3) (x - 3)

d)

( x + 9) (x-9)

86.

x²- 400

a)

( x - 200) ( x + 200)

b)

( x + 20) ( x + 20)

c)

Prime

d)

( x - 20) ( x + 20)

5/30/22 Math 3 Study Guide

Total questions: 86

Worksheet time: 22hrs 30mins

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