Free Printable Functions and Linear Programming Review

1.

What is the slope of the following table?

a)

$m=-3$

b)

$m=-\frac{1}{3}$

c)

$m=-2$

d)

$m=-\frac{1}{6}$

2.

Determine the equation for the following linear function.

a)

$f\left(x\right)=-7x+9$

b)

$f\left(x\right)=9x-7$

c)

$f\left(x\right)=-3x+2$

d)

$f\left(x\right)=2x-3$

3.

Determine the equation for the following linear function.

a)

$f\left(x\right)=4x+16$

b)

$f\left(x\right)=16x+4$

c)

$f\left(x\right)=-21x+4$

d)

$f\left(x\right)=4x-21$

4.

Determine the slope for the following linear function.

a)

$m=-4$

b)

$m=-3$

c)

$m=-\frac{4}{3}$

d)

$m=-\frac{3}{4}$

5.

Determine the equation for the following linear function.

a)

$f\left(x\right)=-2x+\frac{1}{4}$

b)

$f\left(x\right)=\frac{1}{4}x-2$

c)

$f\left(x\right)=4x-2$

d)

$f\left(x\right)=-2x+4$

6.

What is the slope of the following linear function?

7x-4y=4

a)

$m=\frac{4}{7}$

b)

$m=\frac{7}{4}$

c)

$m=-1$

d)

$m=-\frac{1}{4}$

7.

What is the x-intercept of the following linear function?

5x-3y=-6

a)

$\frac{5}{3}$

b)

$2$

c)

$-\frac{6}{5}$

d)

$-\frac{5}{6}$

8.

What is the y-intercept of the following linear function?

-8x+2y=-8

a)

$-4$

b)

$4$

c)

$1$

d)

$-1$

9.

Determine the slope of the line that passes through the following two points.

\left(-3,\ 4\right)\ and\ \left(-6,\ 7\right)

a)

$m=-1$

b)

$m=1$

c)

$m=-\frac{11}{9}$

d)

$m=-\frac{9}{11}$

10.

Determine the slope of the line that passes through the following two points.

\left(5,\ 1\right)\ and\ \left(-4,\ -9\right)

a)

$m=8$

b)

$m=-8$

c)

$m=\frac{9}{10}$

d)

$m=\frac{10}{9}$

11.

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

a)

A

b)

B

c)

C

d)

D

12.

Describe the slope of the line.

a)

negative slope

b)

0 slope

c)

positive slope

d)

undefined slope

13.

Write the equation of the line.

a)

y= -1x-3

b)

y= -3x-1

c)

y=(-1/3)x-1

d)

y= -3x-3

14.

Which equation matches the graph?

a)

y = 2x

b)

y = 1/4 x + 2

c)

y = 1x + 4

d)

y = -2x

15.

Write down the equation of this line.

a)

y= 2x+1

b)

y= −2x+1

c)

y= 2x−½

d)

None of the above

16.

Find the slope between the two given points: (-2,1) and (5,7)

a)

7/6

b)

2

c)

6/7

d)

-2

17.

(-4,4),(-2,2)

a)

(3,2)

b)

(-3,3)

c)

(4,5)

d)

(6,7)

18.

Find the y-coordinate of the midpoint of the line

a)

1

b)

2

c)

-2

d)

3

19.

What is the midpoint between (3, -1) and (7, -5)

a)

(5, -2)

b)

(10, -6)

c)

(5, -3)

d)

(2, -2)

20.

What is the midpoint between (10, 9)
and (-10, -5)

a)

(10, 2)

b)

(0, -2)

c)

(0, 2)

d)

(2, -2)

21.

Find the midpoint of the segment with the endpoints:
(-7, -8) and (4, 7)

a)

(-5.5, -7.5)

b)

(-1.5, -0.5)

c)

(-3, -1)

d)

(0.5, 1.5)

22.

What is the slope in the equation: y=4x+3

a)

3

b)

4x

c)

4

d)

3x

23.

Slopes of parallel lines are...

a)

negative reciprocals.

b)

opposites.

c)

the same.

d)

always 7.

24.

Slopes of perpendicular lines are...

a)

negative reciprocals.

b)

opposites.

c)

the same.

d)

always 7.

25.

y = 3x +2
y = 3x - 3
These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

d)

The same line

26.

y = -2/3x + 2
y = 3/2x + 9
These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

27.

What slope is perpendicular to:
m = 5/8

a)

-5/8

b)

5/8

c)

-8/5

d)

8/5

28.

What slope is parallel to:
m = 4

a)

4

b)

-1/4

c)

-4

d)

1/4

29.

y = 6x + 2
y = -6x + 2
These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

30.

Choose the linear equation that is parallel to the following line

$y=-\frac{1}{4}x-1$

a)

$y=-\frac{1}{4}x+5$

b)

$y=\frac{1}{4}x-1$

c)

$y=-4x-1$

d)

$y=4x-1$

31.

Choose the linear equation that is perpendicular to the following line

$y=-\frac{1}{4}x-1$

a)

$y=-\frac{1}{4}x+5$

b)

$y=\frac{1}{4}x-1$

c)

$y=-4x-1$

d)

$y=4x-3$

32.

Choose the linear equation that is perpendicular to the following line

$y=\frac{4}{3}x+1$

a)

$y=\frac{3}{4}x+1$

b)

$y=-\frac{3}{4}x+6$

c)

$y=-\frac{4}{3}x+1$

d)

$y=\frac{4}{3}x+5$

33.

Write an equation in slope int. form of the line through (4,-1) with slope of -3

a)

y = 3x - 6

b)

y = -3x +11

c)

y = -3x - 11

d)

y = -3x -6

34.

In the equation y=mx+b, what does the m represent?

a)

slope

b)

y-intercept

c)

linear

d)

point-slope

35.

Convert the equation of the line

y + 5 = -3(x - 6)

into slope intercept form.

a)

y = -3x - 23

b)

y = -3x - 13

c)

y = -3x - 11

d)

y = -3x + 13

36.

Write the equation in point-slope form

for the line that contains the points

(3, -5) and (5, - 1)

a)

y - 5 = 2(x + 3)

b)

y + 5 = 2(x - 3)

c)

y - 3 = 2(x + 5)

d)

y + 3 = 2(x - 5)

37.

The line with the equation

y + 1 = -3(x - 5),

contains the point (5, -1)

and has a slope of _______.

a)

-1

b)

1

c)

-3

d)

5

38.

What is the equation in Point-Slope form

of the line that goes through

the point (6,1) and has a slope of -3?

a)

y - 6 = -3(x - 1)

b)

y + 6 = -3(x + 1)

c)

y - 1 = -3(x - 6)

d)

y + 1 = -3(x + 3)

39.

For the equation
y - 3 = 2(x + 4),
the line has a slope of 2 and contains what point?

a)

(-4, 3)

b)

(3, -4)

c)

(-3, -4)

d)

(-4, -3)

40.

For the equation

y + 2 = 5(x - 4),

the line has a slope of 5 and contains what point?

a)

(4,−2)

b)

(−4,2)

c)

(5,0)

d)

(4,2)

41.

For the equation

y - 3 = 2(x + 4),

the line has a slope of 2 and contains what point?

a)

(-4, 3)

b)

(3, -4)

c)

(-3, -4)

d)

(-4, -3)

42.

Write the equation in point-slope form of the line that passes through the given point and has the given slope.

(4, -7); m = -1/4

a)

y + 7 = -1/4(x - 4)

b)

y - 4 = -1/4(x + 7)

c)

y + 7 = 4(x - 4)

d)

y - 7 = -1/4(x - 4)

43.

Write the equation in point-slope form of the line that passes through the given point and has the given slope:

(-2, -1); m= -3

a)

y + 1 = -3(x - 2)

b)

y + 1 = -3(x + 2)

c)

y - 1 = 3(x - 1)

d)

y + 2 = -3(x + 1)

44.

Find the solution to the quadratic equation:

x^2+6x+5=0

a)

x = {6, 5}

b)

x = {-6, -5}

c)

x = {-5, -1}

d)

x = {1, 5}

45.

Find the solution to the quadratic equation:

x^2-10x-24=0

a)

x = {-24, -10}

b)

x = {10, 24}

c)

x = {-12, 2}

d)

x = {-2, 12}

46.

Find the solution(s) to the quadratic equation:

x^2-81=0

a)

x = {9}

b)

x = {-9}

c)

x = {-9, 9}

d)

No solution

47.

What are the roots of the function
f(x)= (x - 2)(x + 3)?

a)

x = - 2 or x = 3

b)

x = 2 or x = -3

c)

The are no real roots

d)

x = 2 or x = 3

48.

What are the zeros of the quadratic function?
y = x² - 2x - 15

a)

x = -2
x = -15

b)

x = -3
x = 5

c)

x = 3
x = -5

d)

x = 1
x = -16

49.

Solve by Factoring Completely: 3x² + 18x +15 = 0 Hint: Factor GCF first.

a)

x=5 x=-1

b)

x=3 x = 1

c)

x= -5 x= - 1

d)

x= -5 x = 1

50.

Which of the following equations matches standard form of a quadratic?

a)

ax + by = c

b)

y = a(x - h)² + k

c)

y = ax² + bx + c

d)

y = mx + b

51.

Convert the equation y= x²-2x-5 into vertex form.

a)

y= (x-1)²-6

b)

y= -(x-1)²-6

c)

y= (x+1)²-6

d)

y= -(x+6)²-1

52.

Which of the following shows
f(x) = x² + 12x - 2
written in vertex form?

a)

f(x) = (x + 6)² + 142

b)

f(x) = (x + 6)² - 34

c)

f(x) = (x + 6)² - 38

d)

f(x) = (x + 6)² + 34

53.

Which of the following shows
f(x) = x² - 8x + 1
written in vertex form?

a)

f(x) = (x - 4)² - 15

b)

f(x) = (x - 4)² + 17

c)

f(x) = (x - 4)² - 17

d)

f(x) = (x - 4)² + 65

54.

If given the equation
y = 3(x + 5)² - 4,
what is the vertex of the parabola?

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

55.

Which function is equivalent to
y = x² - 6x + 10?

a)

y = (x + 3)² - 1

b)

y = (x - 3)² + 1

c)

y = (x + 6)² - 10

d)

y = (x - 6)² + 10

56.

Convert the equation

f(x) = x²- 12x + 40

into vertex form

a)

f(x) = (x + 6)²- 4

b)

f(x) = (x + 6)²+ 4

c)

f(x) = (x - 6)²- 4

d)

f(x) = (x - 6)²+ 4

57.

Identify the vertex and whether the graph opens up or down.

a)

(5, 2); opens up

b)

(5, 2); opens down

c)

(-5, 2); opens up

d)

(-5, 2); opens down

58.

Factor

x^{3\ }-\ 27

a)

$\left(x-3\right)\left(x^{2\ }+3x+9\right)$

b)

$\left(x+3\right)\left(x^{2\ }+3x+9\right)$

c)

$\left(x-3\right)\left(x^{2\ }-3x+9\right)$

59.

Factor

x^{3\ }+\ 4x^{2\ }+\ 9x+36

a)

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

b)

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

c)

$\left(x+3\right)\left(x-3\right)\left(x+4\right)$

60.

Factor

2x^{3\ }+\ 3x^{2\ }-\ 26x-39

a)

$\left(x^2-13\right)\left(2x+3\right)$

b)

$\left(x^2+13\right)\left(2x+3\right)$

c)

$\left(x^2-13\right)\left(2x+3\right)\left(2x-3\right)$

61.

Factor completely

3x^{3\ }+\ x^{2\ }-\ 27x-9

a)

$\left(x-3\right)\left(x+3\right)\left(3x-1\right)$

b)

$\left(x-3\right)\left(x-3\right)\left(3x-1\right)$

c)

$\left(x-3\right)\left(x+3\right)\left(3x+1\right)$

62.

Which method of factoring should be used for...

x^2-\ 9

a)

Difference of Squares

b)

Difference of Cubes

c)

X - Method

d)

Factoring by Grouping

63.

Which method of factoring should be used for...

18x^3+27x^2-8x-12

a)

Difference of Squares

b)

Sum of Cubes

c)

X - Method

d)

Factoring by Grouping

64.

Sofia is factoring the following problem:

3x^{3\ }+7x^{2\ }-12x+c

Her factors are

\left(x-2\right)\left(x+2\right)\left(3x+7\right)

What number is the

c

in her original problem?

a)

-28

b)

14

c)

-14

d)

Not enough information

65.

(2x³ - 5x² + 3x + 7) ÷ (x - 2)

a)

2x³ - x² + x + 9

b)

2x² - x + 1

c)

2x² - x + 1 + 9/x-2

d)

2x² - 9x - 15 - 23/x-2

66.

(3x³ - 2x² - 7x + 6) ÷ (x + 1)

a)

3x³ - 5x² - 2x + 8

b)

3x² + x - 6

c)

3x² - 5x - 2 + 8/x+1

d)

3x³ + x² - 6x

67.

For synthetic division, what would be the number in the left hand box?

a)

0

b)

1

c)

2

d)

3

68.

(2x³ + 5x² + 9) ÷ (x + 3)

a)

2x² - x + 3

b)

2x³ - x² + 3x

c)

2x² + 11x + 33 + 108/x+3

d)

2x² - 5x + 12

69.

Is (x – 2) a factor

$f\left(x\right)\ =\ x^3+4x^2\ +x\ -6$

a)

Yes f(2) = 0

b)

No, f(2) = 20

c)

Yes, f(2) = 20

d)

No, f(2) = 0

70.

Is (x + 3) a factor

$f\left(x\right)\ =\ x^3+4x^2\ +x\ -6$

a)

Yes f(-3) = 0

b)

No, f(-3) = 20

c)

Yes, f(3) = 0

d)

No, f(3) = 60

71.

Is (x - 1) a factor

$f\left(x\right)\ =\ x^3+4x^2\ +x\ -6$

a)

Yes f(1) = 0

b)

No, f(1) = -2

c)

Yes, f(-1) = 0

d)

No, f(-1) = -2

72.

Solve

27^x=81.

a)

$x=\frac{4}{3}$

b)

$x=\frac{3}{4}$

c)

$x=-\frac{4}{3}$

d)

$x=-\frac{3}{4}$

73.

Solve

4^x=32.

a)

$x=\frac{3}{4}$

b)

$x=\frac{2}{5}$

c)

$x=\frac{5}{2}$

d)

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

74.

Solve

8^x=4.

a)

$x=-\frac{2}{3}$

b)

$x=\frac{2}{3}$

c)

$x=\frac{3}{2}$

d)

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

75.

Solve

3^x=\frac{1}{27}.

a)

$x=-2$

b)

$x=3$

c)

$x=-3$

d)

$x=9$

76.

Solve

3^{\left(x+1\right)}=27.

a)

$x=2$

b)

$x=4$

c)

$x=-4$

d)

$x=-2$

77.

Find the solution for

5^{\left(x+7\right)}=25^x.

a)

$x=2$

b)

$x=-2$

c)

$x=-7$

d)

$x=7$

78.

Find the value of x for

5^{\left(2x+3\right)}=\frac{1}{125}.

a)

$x=-2$

b)

$x=-3$

c)

$x=2$

d)

$x=3$

79.

Solve

\left(\frac{1}{2}\right)^x=8^{\left(x-2\right)}.

a)

$x=-3$

b)

$x=3$

c)

$x=-\frac{3}{2}$

d)

$x=\frac{3}{2}$

80.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

81.

Convert 6^(x+2)=216 to logarithmic form

a)

log₂₁₆(x+2)=6

b)

log₆(x+2)=216

c)

log₆(216)=x+2

d)

log_(x+2)(216)=6

82.

Solve for x:
log₄ x = 3

a)

4

b)

12

c)

32

d)

64

83.

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

84.

log₉(x)+log₉(x+2)=log₉(35)

a)

5

b)

-7

c)

5, -7

d)

-7, -13

85.

log(216)=(x-4)log(6)

a)

1

b)

3

c)

7

d)

0

86.

2log₅7 = 3x+1 log₅49

a)

1

b)

-1

c)

5

d)

0

87.

Solve the equation for x.

a)

22.198

b)

e

c)

1.131

d)

21.66

88.

Name this person

a)

Michelle Obama

b)

Aretha Franklin

c)

Beyonce

d)

Mariah Carey

89.

What equation matches the graph?

a)

f(x) = 3^x

b)

f(x) = (⅓)^x

c)

f(x) = log₃(x)

90.

Expand the logarithm
log₁₀ 7x

a)

(log₁₀ 7)(log₁₀ x)

b)

log₁₀ 7 + log₁₀ x

c)

7log₁₀ x

d)

xlog₁₀ 7

91.

Sarah makes small purses (x) and big purses (y). She can make no more than 8 purses a week.
Which inequality represents the situation?

a)

x + y ≤ 8

b)

x + y ≤ 6

c)

2x + 3y ≤ 6

d)

x + y ≤ 10

92.

It takes Sarah 2 hours to make small purses and 3 hours to make big purses. She has a maximum of 18 hours a week. Which inequality represents this situation?

a)

2x + 3y ≤ 18

b)

x + y ≤ 6

c)

x + y ≤ 9

d)

3x + 2y ≤ 18

93.

a)

(0, 0), (0, 6), (6, 2), (8, 0)

b)

(0, 0), (6, 0), (2, 6), (0, 8)

94.

Sarah makes $30 for each small purse (x) and $50 for each big purse (y). What is the objective quantity?

a)

P = 30x + 50y

b)

P = 50x + 30y

95.

a)

(0,0)

b)

(6,2)

c)

(8,0)

d)

(0,6)

96.

Objective quantity:
P = 30x + 50y
Corner that maximizes profit: (0, 6)
What is the profit?

a)

300

b)

280

c)

400

d)

240

97.

Rachel owns a car and a moped. She has at most 12 gallons of gas to be used between the car and the moped. The car's tank holds at most 10 gallons and the moped's 3 gallons. The mileage for the car is 20 mpg and for the moped is 100 mpg. What are the variables you need to define?

a)

x is gas, y is mileage

b)

x is car, y is moped

c)

x is gas, y is moped

d)

x is car, y is mileage

98.

What do you call the area where all the shading overlaps?

a)

the answer

b)

the feasible region

c)

the void

d)

the objective function

99.

Rachel owns a car and a moped. She has at most 12 gallons of gas to be used between the car and the moped. The car's tank holds at most 10 gallons and the moped's 3 gallons. The mileage for the car is 20 mpg and for the moped is 100 mpg.
What are the constraints?

a)

x≤10, y≤3, x+y≤12

b)

0≤x≤10, 0≤y≤3, x+y≤12

c)

x≥0, y≥0, 10x+3y≤12

d)

x≤10, y≤3, 10x+3y≤12

100.

A farmer can plant up to 6 acres of land with soybeans and corn. Her use of a necessary pesticide is limited by federal regulations to 15 gallons for her entire 6 acres. Soybeans require 2 gallons of pesticide for every acre planted and corn requires 3 gallons per acre. The profit the farmer makes by earning $4,000 for every acre of soybeans she plants and $3,000 for every acre she plants with barley can be modeled by P=4000x+3000y . If x represents acres of soybeans and y represents acres of corns, which inequalities represent the possible solutions to her situation?

a)

x≥0

y≥0

x+y≥6

3x+2y≥15

b)

x≥0

y≥0

x+y≤6

2x+3y≤15

c)

x≥0

y≥0

4000x+y≤6

2x+600y≤15

d)

P=4000x+3000y

101.

Solve the system of inequalities. The feasible region is shown by the darkest blue shading.

a)

b)

c)

d)

102.

x + 3 ≤ 4y

a)

b)

c)

d)

103.

2x + 9 ≥ 3y

a)

b)

c)

d)

104.

A manufacturing company makes two types of television sets; one is black and white (x) and the other is colour (y). The company has resources to make at most 300 sets a week. It takes Rs 1800 to make a black and white set and Rs 2700 to make a coloured set. The company can spend not more than Rs 648000 a week to make television sets. Constraints are

a)

$x+y\le300,\ 2x+3y\le720$

b)

$x+y\le300,\ 2x+3y\ge720$

c)

$x+y\ge300,\ 2x+3y\le720$

d)

$x+y\ge300,\ 2x+3y\ge720$

105.

Which graph represents:

3x+5y\le15000

3x+16y\ge24000

y\le x

a)

b)

c)

d)

106.

Objective quantity:
P = 30x + 50y
Corner that maximizes profit: (0, 6)
What is the profit?

a)

300

b)

280

c)

400

d)

240

107.

a)

y < -2/5x - 4

b)

y > -2/5x - 4

c)

y ≤ -2/5x - 4

d)

y ≥ -2/5x - 4

Functions and Linear Programming Review

Total questions: 107

Worksheet time: 5hrs 3mins

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