Free Printable Third Nine Weeks Review

1.

Lloyd solves the equation 24x + 18(x – 2) = 216 for x. Some of his steps are shown. Which statement best describes what Lloyd did to get from Step 3 to Step 4?

a)

combined liked terms

b)

used the distributive property

c)

used the addition property of equality

d)

used the multiplicative inverse property

2.

What would be the best first step?

$5\left(x+6\right)=2x-3$

a)

Distribute the 5.

b)

Combine the 2x and 3.

c)

Combine the x and 6.

d)

Subtract 2x on both sides.

3.

What value of x satisfies the equation $\frac{x}{3}+\frac{x}{6}=5$ ?

(a)

4.

A company has 500 employees and plans to increase the workforce by 10 employees per month until it has doubled in size. Which of the equations below could be used to determine the number of months, m, it will take until the company has doubled in size?

a)

500 + 10 = 2m

b)

2(500) = 10m

c)

(500 + 10)2 = m

d)

500 + 10m = 2(500)

5.

Which of the following graphs represents the solution to the inequality $x-6x\le-25$ ?

a)

b)

c)

d)

6.

Tori can spend up to $5.00 at the fruit stand. She wants to buy peaches (p) that are $0.40 each and apples (a) that are $0.30 each. The graph shows the possible numbers of peaches and apples Tori can purchase.

Which of these is a combination of peaches and apples Tori can buy with $5.00?

a)

2 peaches and 17 apples

b)

4 peaches and 10 apples

c)

10 peaches and 4 apples

d)

12 peaches and 2 apples

7.

The graph of which inequality is shown in the accompanying diagram?

a)

y < x + 1

b)

y > x + 1

c)

y > -x + 1

d)

y ≥ x + 1

8.

The graph of y ≤ 2x – 3 is shown. Which set contains only points that satisfy the inequality?

a)

{(3, 3), (-4, -1), (-1, -8), (5, 0)}

b)

{(5, 7), (-3, -10), (5, -7), (-1, -4)}

c)

{(-1, -10), (5, 7), (-4, -13), (3, -2)}

d)

{(-4, -12), (-1, -5), (3, 4), (5, 6)}

9.

A group of friends will buy at most 8 snacks at a movie theater and spend no more than $42. They will pay $4 for each box of candy and $7 for each bag of popcorn. Which combination of boxes of candy and bags of popcorn could the group buy?

a)

2 boxes of candy and 6 bags of popcorn

b)

3 boxes of candy and 4 bags of popcorn

c)

5 boxes of candy and 4 bags of popcorn

d)

8 boxes of candy and 1 bag of popcorn

10.

Which of the following graphs shows the solution to this system of inequalities?

y < -x + 3

y > x - 1

a)

b)

c)

d)

11.

Frank wants to go bowling. The bowling alley charges $4 per game and a one-time charge of $3 for bowling shoes. The equation y = 4x + 3 represents this scenario (where y is the total cost of bowling and x is the number of games bowled).

Based on the information, which statement is true?

a)

The total cost will increase by $4 for every game bowled.

b)

The total cost will increase by $3 for every game bowled.

c)

The total cost will increase by $4 for every 3 games bowled.

d)

The total cost will increase by $3 for every 4 games bowled

12.

Which of the following situations could be represented by the equation y = 3x + 5?

a)

A bricklayer lays 5 bricks in 3 minutes. What is the total number of bricks he can lay in x minutes?

b)

An express package costs $5 plus $3 per pound to ship. What is the total cost for x pounds?

c)

A jogger is 3 miles from home, jogging toward home at 5 miles per hour. What is the total number of minutes it will take her to get home?

d)

A math teacher gave some problems worth 5 points and a bonus problem worth 3 points. What was the total value of the problems?

13.

Webster found this table in his algebra book. What are the y-intercept and slope of the line represented by this data?

a)

y-intercept = 0; slope = 2

b)

y-intercept = 3; slope = 1⁄2

c)

y-intercept = 2; slope = 3

d)

y-intercept = 3; slope = 2

14.

Which is an equation of the line that passes through the point (5, -2) and has a slope of -3?

a)

y = -3x – 13

b)

y = 3x – 13

c)

y = -3x + 13

d)

y = -x – 3

15.

A jar contains q quarters and d dimes. There are 7 coins in the jar, and the total value of the coins is $1.00. Which system of equations can be used to find out how many of each type of coin the jar has?

a)

0.10q + 0.25d = 1.00

q + d = 7

b)

25q + 10d = 1

q + d = 7

c)

0.25q + 0.10d = 1.00

q + d = 7

d)

0.25q + 0.10d = 7.00

q + d = 1

16.

Consider the system of equations below.

2x + 3y = 8

2x + 6y = 12

What could be the first step in solving the system of equations using elimination?

a)

Add the two equations.

b)

Add 4 to both sides of the first equation.

c)

Multiply the first equation by -1.

d)

Multiply the second equation by 2

17.

What is the BEST first step?

2x - 3y = 14

x + 3y = -11

a)

solve each equation for y

b)

add the equations to eliminate the y's

c)

subtract the equations to eliminate the y's

18.

Ruben bought 2 large popcorn buckets and 4 small drinks for $20. Lucia bought 2 large popcorn buckets and 2 small drinks for $14. How much did the large popcorn cost? The small drink?

a)

The large popcorn cost $4 and small drink cost $3.

b)

The large popcorn cost $2 and the small drink cost $4.

c)

The large popcorn cost $5 and the small drink cost $3.

d)

The large popcorn cost $3 and the small drink cost $2.

19.

What value of x satisfies the system of equations below?

x = 8 – 2y

x + 3y = 12

a)

16

b)

0

c)

4

d)

5

20.

Which system of equations represents the graph?

a)

y = 2x – 5

2x + 4y = 8

b)

y = 3x – 5

2x + 4y = 8

c)

y = 3x – 5

4x + 2y = 8

d)

y = 2x – 5

4x + 2y = 8

21.

One equation in a system of equations is y = 2x + 10. Which equation below would have to be the second equation so that the system has infinitely many solutions?

a)

y = 5x – 8

b)

y = 2x – 10

c)

y + 2x = 10

d)

y = 2(x+5)

22.

A system of equations is shown below.

2x + 4y = 8

x + 2y = 4

Which statement about the ordered pair (-2, 3) is true?

a)

It is the only solution to the system of equations.

b)

It is one of many solutions to the system.

c)

It is not a solution to either equation.

d)

It is a solution to the first equation but not the second equation.

23.

Which of the following systems of equations has infinitely many solutions?

a)

b)

c)

d)

24.

What is the solution set of the equation 2x² + x – 3 = 0?

a)

x = 1/2 and x = -3

b)

x = -3/2 and x = 1

c)

x = -1/2 and x = -3

d)

x = 3/2 and x = 1

25.

What are the roots of the equation 2x² – 8x = 0?

a)

-2 and 2

b)

0 and -4

c)

0, -2, and 2

d)

0 and 4

26.

What are the solutions to x² – 16 = 0?

a)

x = -16 and x = 16

b)

x = -4 and x = 4

c)

x = 0 and x = -16

d)

x = 16 and x = 8

27.

An equation and the first step in its solution are shown below.

Equation: x² + 5x – 7 = 0

Step 1: x² + 5x + h = 7+ h

What value of h is used to solve the equation by the method of completing the square?

a)

$\frac{7}{2}$

b)

$\frac{5}{2}$

c)

$\left(\frac{5}{2}\right)^2$

d)

$\left(\frac{7}{2}\right)^2$

28.

What quantity should be added to both sides of this equation to complete the square?

x² – 8x = 5

a)

4

b)

-4

c)

16

d)

-16

29.

Leanne correctly solved the equation x² + 4x = 6 by completing the square. Which equation is part of her solution?

a)

(x + 2)² = 8

b)

(x + 2)² = 10

c)

(x + 4)² = 10

d)

(x + 4)² = 22

30.

What are the values of x in the equation x² + 4x – 1 = 0?

a)

$-4\pm\sqrt[]{5}$

b)

$-4\pm\sqrt[]{3}$

c)

$-2\pm\sqrt[]{5}$

d)

$-2\pm\sqrt[]{3}$

31.

Solve the quadratic equation 2x² + 5x – 1 = 0 by using the quadratic formula.

a)

$\frac{5\pm\sqrt[]{17}}{4}$

b)

$\frac{-5\pm\sqrt[]{17}}{4}$

c)

$\frac{5\pm\sqrt[]{33}}{4}$

d)

$\frac{-5\pm\sqrt[]{33}}{4}$

32.

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the expression –16t² + 64t + 80.

What is the meaning of the 80 in the expression?

a)

The object took 80 seconds to reach its maximum height.

b)

The object took 80 seconds to reach the ground.

c)

The object reached a maximum height of 80 feet.

d)

The object was thrown from a height of 80 feet.

33.

The first 3 figures in a pattern are shown. Which of the following functions represents f(n), the number of small squares in figure n?

a)

$n^2-1$

b)

$2n^2+1$

c)

$\left(n+1\right)^2+1$

d)

$\left(n+1\right)^2-1$

34.

a)

$y=x^2-x-3$

b)

$y=x^2+x+3$

c)

$y=x^2-x+3$

d)

$y=x^2+x-3$

35.

The points (0, 2), (1, 3), (2, 6), and (3, 11) are on the graph of a function. Which equation represents that function?

a)

$h(x)=x+2$

b)

$h(x)=2x^2$

c)

$h(x)=x^2+2$

d)

$h(x)=0.5x^2+1.5$

36.

A rectangle has a length of 30 inches and a width of 2 feet. What is the perimeter, in inches, of the rectangle?

a)

54 inches

b)

64 inches

c)

108 inches

d)

120 inches

37.

Peyton is a sprinter who can run the 40-yard dash in 4.5 seconds. He converts his speed into miles per hour, is shown.

Which ratios is written incorrectly to convert his speed?

a)

$\frac{3\ feet}{1\ yard}$

b)

$\frac{5280\ ft}{1\ mile}$

c)

$\frac{60\ \sec}{1\ \min}$

d)

$\frac{60\ \min}{1\ hr}$

38.

What is the sum of 3x² − 2x + 5 and x² + 2x − 8, expressed as a trinomial?

a)

4x² + 3

b)

4x² − 3

39.

Simplify: (4x² − 3x + 4) - (3x² − 7x + 6)

a)

−x² − 4x + 2

b)

x² − 10x − 2

c)

x² + 4x − 2

40.

Binomial (-2x – 8) and trinomial (-3x² + 4x + 5) are the factors of which polynomial?

a)

$-3x^2+2x-3$

b)

$-3x^3-8x^2-42x-40$

c)

$6x^3+24x^2-50x-40$

d)

$6x^3+16x^2-42x-40$

41.

The expression below represents the area, in square meters, of a rectangle.

x² + 5x – 24

Which of the following pairs of expressions could represent the length and width, in meters, of the rectangle?

a)

(x – 4) and (x + 6)

b)

(x – 3) and (x + 8)

c)

(x – 6) and (x + 4)

d)

(x – 8) and (x + 3)

42.

Which expression is equivalent to x² +7x +6?

a)

(x+6)(x+1)

b)

(x+3)(x+2)

c)

(x+1)(x+7)

d)

x(x + 7)

43.

Which function represents the function g(x) = 2x² + 7x – 15 as the product of factors?

a)

g(x) = (2x + 3)(x – 5)

b)

g(x) = (2x – 3)(x + 5)

c)

g(x) = (2x + 3)(x + 5)

d)

g(x) = (2x – 3)(x – 5)

44.

Which of the following is equivalent to the expression 9x² – 16?

a)

$(3x-4)^2$

b)

(9x – 4)(9x + 4)

c)

(3x – 8)(3x + 8)

d)

(3x – 4)(3x + 4)

45.

Which function has zeros at 2 and -5?

a)

$y=x^2+3x+10$

b)

$y=x^2-3x+10$

c)

$y=x^2+3x-10$

d)

$y=x^2-3x-10$

46.

A ball is thrown in the air from a platform. The height of the ball, in feet, can be represented by the function h(t) = –16t²+ 32t + 48, where t is the time, in seconds, since the ball was thrown. Which of the following shows the function rewritten in the form that would be best to use to identify the maximum height of the ball?

a)

$h(t)=-16(t-2)^2+112$

b)

$h(t)=-16(t-2)^2+96$

c)

$h(t)=-16(t-1)^2+80$

d)

$h(t)=-16(t-1)^2+64$

47.

Which ordered pair is the vertex of f(x) = x² + 6x + 5?

a)

(-3, -4)

b)

(-2, -3)

c)

(-1, 0)

d)

(0, -5)

48.

What is the rewritten form of the radical $3\sqrt[]{8}$ ?

a)

$12\sqrt[]{2}$

b)

$\sqrt[]{24}$

c)

$6\sqrt[]{2}$

d)

$8.4$

49.

Evaluate $\sqrt[]{63}-4\sqrt[]{7}$ .

a)

$\sqrt[]{7}$

b)

$-\sqrt[]{7}$

c)

$-4\sqrt[]{56}$

50.

Anna has $12.00 and saves $4.00 each week. The equation below represents how much money she will have saved.

f(x) = 4x + 12

Which is the correct graph for this equation?

a)

b)

c)

d)

51.

What is the slope and y-intercept of the linear function given by the equation 4x - 3y = 6

a)

The slope is 4/3 and the y-intercept is -2

b)

The slope is 4 and the y-intercept is 2

c)

The slope is -4/3 and the y-intercept is -2

d)

The slope is 4 and the y-intercept is -2

52.

A salesperson earns 25% of her total sales in addition to a base pay. The graph below represents her total pay for a given day. How much does she earn if she does not make any sales on a given day?

a)

$0

b)

$25

c)

$75

d)

$175

53.

Which phrase describes characteristics for the graph of the line connecting the points in this table?

a)

A line with a negative slope that crosses the x-axis at 5.

b)

A line with a negative slope that crosses the y-axis at 5.

c)

A line with a positive slope that crosses the x-axis at 5.

d)

A line with a positive slope that crosses the y-axis at 5.

54.

A car travels at a rate of 45 miles per hour for 5 hours. Let y be the distance, in miles, the car travels for a given amount of time, x, in hours. This situation can be modeled by a function. Which of these describes the domain of the function?

a)

0 ≤ x ≤ 5

b)

0 ≤ y ≤ 5

c)

0 ≤ x ≤ 45

d)

0 ≤ y ≤ 45

55.

The graph describes the labor cost for a mechanic.

Which of the following describes the domain of the function?

a)

All real numbers

b)

All real numbers greater than or equal to 0

c)

All whole numbers greater than 1

d)

All whole numbers greater than 75

56.

A local theater sells admission tickets for $9.00 on Thursday nights. At capacity, the theater holds 100 customers. The function M(n) = 9n represents the amount of money the theater takes in on Thursday nights, where n is the number of customers. What is the domain of M(n) in this context?

a)

All whole numbers

b)

All non-negative rational numbers

c)

All non-negative integers that are multiples of 9

d)

All non-negative integers less than or equal to 100

57.

Which statement below is true? Select all that apply.

a)

f(3) > g(3)

b)

The y-intercept of f(x) is greater than the y-intercept of g(x)

c)

The functions f(x) and g(x) have the same value at x = 1

d)

Both functions have a domain of all real numbers

58.

The functions f(x) = 2x² + 2 and g(x) = 2^{x + 1}+ 2 are graphed on the coordinate plane.

For what x-values is g(x) > f(x)? Select all that apply.

a)

$0\le x<2$

b)

$2<x<4$

c)

$x>4$

59.

Bob threw a ball across a basketball court. The graph below shows the relationship between the horizontal distance of the ball and its height. How many feet from Bob did the ball land?

a)

10 feet

b)

12 feet

c)

18 feet

d)

21 feet

60.

The accompanying diagram shows a parabola.

Which statement is not true?

a)

The equation of the axis of symmetry is x = 2.

b)

The parabola has a minimum point.

c)

The turning point of the parabola is (2, 0).

d)

The parabola has two x-intercepts.

61.

Which graph represents the function below? $f\left(x\right)=-\left(x-4\right)^2+1$

a)

b)

c)

d)

62.

A baseball is hit into the air. The height of the baseball, in feet, as a function of time, in seconds, is represented in the graph.

What is the average rate of change between 5 and 8 seconds?

a)

-80 feet per sec

b)

-240 feet per sec

c)

-0.0125 feet per sec

d)

-30 feet per sec

63.

Translate f(x) = x² right 5 units and up 4 units.

a)

(x - 5)² + 4

b)

(x + 5)² - 4

c)

(x + 5)² + 4

d)

(x - 5)² - 4

64.

The coordinate plane below shows the graphs of Function A and Function B. Which of these translations maps Function A onto Function B?

a)

Function A is translated 1 unit left and 2 units up

b)

Function A is translated 2 units right and 1 unit up

c)

Function A is translated 2 units left and 1 unit down

d)

Function A is translated 1 unit right and 2 units down

65.

Paul graphs the equation y = 3^x + 4. Where does the graph intersect the y-axis?

a)

(0, -4)

b)

(0, -3)

c)

(0, -1)

d)

(0, 5)

66.

Which statements are true about the graph of the exponential function f(x)? Select all that apply.

a)

The y-intercept is 3.

b)

The x-intercept is 2.

c)

The domain is all real numbers.

d)

The asymptote is y = -1.

e)

As x increases, f(x) approaches, but never reaches, -1.

67.

The exponential function f(x) has a horizontal asymptote at y = 3. What is the end behavior of f(x)

a)

As x decreases, f(x) approaches, but never reaches, 0.

As x increases, f(x) increases.

b)

As x decreases, f(x) approaches, but never reaches, 3.

As x increases, f(x) increases.

c)

As x decreases, f(x) approaches, but never reaches, 3.

As x increases, f(x) decreases.

d)

As x decreases, f(x) decreases.

As x increases, f(x) approaches, but never reaches, 3.

68.

Use the equation below to answer the following question.

y = 3^x

As the value of x becomes negative and continues to decrease, what happens to the value of y?

a)

y becomes negative

b)

y gets closer to 1

c)

y gets closer to 0

d)

y gets closer to x

69.

a)

a

b)

b

c)

c

d)

d

Third Nine Weeks Review

Total questions: 69

Worksheet time: 3hrs 27mins

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