PSABDSX6 - Grade 10 Mathematics Practice Test 2019
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Which of the following is equivalent to this expression?

 

−5x(−6x2 + 1)

 

A. 30x3 − 4x
B. 30x3 − 5x
C. −11x3 − 4x
D. −11x3 − 5x

 

Select one:

 

Consider this function.

 

f(x) = x(18 − x)


What are the values of f(0), f(5), and f(18)?

 

Select one:

 

This diagram shows a circle with an inscribed right triangle and some of its measurements, in units.

Based on the diagram, what is the circumference, in units, of the circle?

 

Select one:

 

On a coordinate plane, a single transformation will be performed on square RSTU.


Select three transformations of square RSTU that would result in a congruent figure.

 

Select all that apply:

 

Consider this system of equations.


h + c = 2.25
h − c = 1.75

 

What value of h makes the system of equations true?

 

Type your answer below as a number (example: 5, 3.1, 4 1/2, or 3/2):

 

Which of the following is equivalent to this expression?

 

4k4 + 16k3 + 10k2

 

A. 4k2(k2 + 4k + 2)
B. 2k2(2k2 + 8k + 5)
C. 2(2k4 + 14k3 + 8k2)
D. 2k2(2k2 + 16k + 10)

 

Select one:

 

Consider this inequality.

 

y ≥ x − 4

 

Which of the following graphs represents the solution set of the inequality?

 

 

 

Select one:

 

Line w is represented by this equation.


y = 5x +3

 

Which of the following equations represents a line that is perpendicular to line w?

 

Select one:
Part A)

 

A line and a parabola are graphed on a coordinate plane. The equation of the line and the equation of the parabola are shown in this table.

 

Graph

Equation

 Line

y = –3x + 5
Parabola y = –x2 + 2x + 1

 

A. What is the value of y for the line when x = −4? 

 

Type your answer below as a number (example: 5, 3.1, 4 1/2, or 3/2):
Part B)

Show or explain how you got your answer.

Type your answer below:
Part C)

B. What is the value of y for the parabola when x = −4? 

 

 

Type your answer below as a number (example: 5, 3.1, 4 1/2, or 3/2):
Part D)

Show or explain how you got your answer.

Type your answer below:
Part E)

C. The line and the parabola intersect at two points. The distance, in units, between the two points is represented by this expression.

 

 

Simplify the expression to determine the distance, in units, between the two points.

Type your answer in the following format: 

sqrt(7) for  or 12sqrt(7) for 

with no spaces

 

 

 

Type your answer below:
Part F)

 Show or explain how you got your answer.

Type your answer below:
Part G)

D. The area, in square units, of the region on the coordinate plane enclosed by the parabola and the line is represented by this expression.

 

 

Simplify the expression to determine the area, in square units, of the enclosed region. 

 

 

Type your answer below as a number (example: 5, 3.1, 4 1/2, or 3/2):
Part H)

Show or explain how you got your answer.

Type your answer below:

 

A waiter recorded the amount of money he earned in tips each weekday for a two-week period. His data are shown in this table.

 

Which statement about the data in the table is true?


A. The median and the range for week 1 are equal to the median and the range for week 2.
B. The median and the mode for week 1 are equal to the median and the mode for week 2.
C. The mean and the median for week 1 are equal to the mean and the median for week 2.
D. The mean and the range for week 1 are equal to the mean and the range for week 2.

 

Select one:

 

Line segment KL is shown on this coordinate plane.

 

 

What are the coordinates of the midpoint of line segment KL?

 

Select one:
Part A)

 

Shayla and Carlos each have a bag that contains 5 green marbles, 5 red marbles, and 10 yellow marbles. The marbles are all the same size and shape.

 

A. Shayla will select two marbles from her bag at random. She will not return the first marble to the bag before selecting the second marble. Which expression represents the probability that Shayla will select two red marbles?

 

Select one:
Part B)

B. Carlos will select two marbles from his bag at random. He will not return the first marble to the bag before selecting the second marble. The first marble Carlos selects will not be yellow. What is the probability that the second marble he selects will be yellow?

 

Select one:

 

What are the solutions of this equation?


x2 + 7x + 12 = 0

 

Select one:
Part A)

 

This double bar graph shows the amounts of time, in minutes, an athlete spent on aerobic training and strength training each day for 5 days.

 

 

 

A. On what day did the athlete spend the longest total amount of time training? Show or explain how you got your answer.

 

Select one:
Part B)

Show or explain how you got your answer.

Type your answer below:
Part C)

B. What is the median total number of minutes the athlete spent training each day?  

 

Do not include units (minutes) in your answer. 

Type your answer below as a number (example: 5, 3.1, 4 1/2, or 3/2):
Part D)

Show or explain how you got your answer.

Type your answer below:
Part E)

C. What percent of the total number of minutes the athlete spent training for the 5 days was spent on strength training? 

 

Do not include the percent symbol (%) in your answer.

Type your answer below as a number (example: 5, 3.1, 4 1/2, or 3/2):
Part F)

Show or explain how you got your answer.

Type your answer below:
Part G)

D. Determine whether the sum of the mean number of minutes spent on aerobic training and the mean number of minutes spent on strength training is equal to the mean total number of minutes spent training. Show or explain how you got your answer.

 

 

Type your answer below:

 

A rectangular garden that is 16 1/4 feet wide and 11 3/4 feet long will be covered with soil. If a bag of soil covers an area of 20 square feet, which of the following is closest to the number of bags of soil needed to cover the garden?

 

Select one:
Part A)

 

Four triangles and some of their angle measures are shown.

Based on the angle measures, which of the following similarity statements is true?

 

A. △FGE ~ △TUS

B. △GEF ~ △QPR

C. △LMN ~ △PQR

D. △NML ~ △TSU

 

Select one:
Part B)

B. These two triangles are similar.

 

Which of the following similarity statements about the triangles are true? Select the two true statements.

 

A. △EFG ~ △ZYX
B. △EGF ~ △XYZ
C. △FEG ~ △XZY
D. △FGE ~ △YZX
E. △GFE ~ △YXZ

 

Select all that apply:

 

Which of the following is equivalent to this expression?

 

x2 + 5x − 84

 

Select one:

 

Triangle KLM, shown on this coordinate plane, will be dilated by a scale factor of 1/2 with respect to the origin.

 

 

What are the ordered pairs that represent the vertices of the image of triangle KLM after the dilation? Select the three ordered pairs.

 

Select all that apply:
Part A)

 

A. Which of the following statements is true?

 

Select one:
Part B)

B. Which of the following statements is true?


A. The sum of π/2 and π/2 is rational, and the product of 1/2 and π is rational.

B. The sum of π/2 and π/2 is rational, and the product of 1/2 and π is irrational.

C. The sum of π/2 and π/2 is irrational, and the product of 1/2 and π is rational.

D. The sum of π/2 and π/2 is irrational, and the product of 1/2 and π is irrational.

 

Select one:

 

Which of the following is the solution set of this inequality?

 

2 − 4y > 14

 

Select one:

 

A right triangle and some of its measurements are shown in this diagram.

 

 

Based on the measurements shown in the diagram, what is t?


A. 6 mm
B. 4 mm
C. 6 mm
D. 8 mm

 

Select one:

 

This diagram shows a right square pyramid and some of its dimensions.

 

What is the volume of the pyramid?

 

Select one:

 

A travel agent surveyed people in two age groups about whether or not they like traveling. Which two-way table shows the possible results of the survey?

 

 

Select one:

 

Which of the following graphs does not represent y as a function of x?

 

 

Select one:

 

Consider square EFGH, shown on this coordinate plane.

 

 

Square EFGH will be reflected over the y-axis. Which graph correctly shows the image of square EFGH after the reflection?

 

 

Select one:

 

A parallelogram is shown on this coordinate plane.

 

 

What is the perimeter, in units, of the parallelogram?

 

Select one:

 

A sphere and one of its dimensions are shown in this diagram.

 

Which of the following is closest to the volume of the sphere?

 

Select one:

 

This table shows the values of the linear function f(x) for different values of x.

 

 

x f(x)
0 120
20 90
40 60
60 30

 

The function g(x) is represented by this equation.


g(x) = 10x + 40

 

Which statement correctly compares the rates of change and y-intercepts of f(x) and g(x)?


A. Function f(x) has a greater rate of change and a greater y-intercept than function g(x).
B. Function g(x) has a greater rate of change and a greater y-intercept than function f(x).
C. Function f(x) has a greater rate of change than function g(x), and function g(x) has a greater y-intercept than function f(x).
D. Function g(x) has a greater rate of change than function f(x), and function f(x) has a greater y-intercept than function g(x).

 

Select one:

 

A factory worker loaded some boxes onto a cart. Each box has the same weight.
This expression represents the total weight, in pounds, of the cart and n boxes.

 

10n + 25

 

Based on the expression, what is the weight, in pounds, of the cart?

 

Type your answer below as a number (example: 5, 3.1, 4 1/2, or 3/2):
Part A)

 

A student graphed ∆PQR on a coordinate plane, as shown.

 

 

A. The student reflected ∆PQR over the x-axis to create ∆EFG. What are the coordinates of vertex E? Show or explain how you got your answer.

 

Type your answer below:
Part B)

 

B. The student performed a different single transformation on ∆PQR to create ∆JKL. The coordinates of vertex K are (4, 1). What could be the single transformation the student performed?

 

Type your answer below:
Part C)

 

C. Describe a single transformation the student can perform on ∆PQR so that its image, ∆UVW, is similar to, but not congruent to, ∆PQR. Show or explain how you got your answer.

 

Type your answer below:
Part D)

#30 (G-CO.A.2)

 

 

D. What will be the coordinates of vertex W after the student performs the transformation described in Part C? Show or explain how you got your answer.

 

Type your answer below:

 

Marvin solved this equation.

 

4(x + 5) = 88

 

Marvin created a table showing each step he used to solve the equation. The table also showed the correct explanation for each step. Which of the following tables shows the correct explanation for each step in Marvin's solution?

 

 

Select one:

 

Each exterior angle of a regular polygon has a measure of 30°. What is the total number of sides of the polygon?

 

Select one:
Part A)

 

A. On a map, 1 inch equals 0.75 mile. The distance between a museum and a library on the map is 2 inches. What is the actual distance, in miles, between the museum and the library?

 

Type your answer below as a number (example: 5, 3.1, 4 1/2, or 3/2):
Part B)

#33 (N-Q.A.1)

 

B. On a map, 1 inch equals 0.75 mile. The actual distance between the library and a bus stop is 3 miles. What is the distance, in inches, between the library and the bus stop on the map?

 

Type your answer below as a number (example: 5, 3.1, 4 1/2, or 3/2):

 

Triangle LMN is similar to triangle XYZ. This diagram shows some of the dimensions, in units, of the triangles.

 

Based on the diagram, what is the length, in units, of XZ?

 

Select one:
Part A)

 

At the beginning of the year, Samantha deposits $1000 into a savings account that pays 2.5% interest. She does not deposit money into or withdraw money from the account for 1 year.


A. What is the interest rate expressed as a decimal?

 

Type your answer below as a number (example: 5, 3.1, 4 1/2, or 3/2):
Part B)

B. This formula can be used to calculate the total amount of money, including interest, in an account over time for a deposit of $1000.

 

What is the amount of money, in dollars, in Samantha's savings account at the end of 1 year if the interest is compounded annually (once per year)? Show or explain how you got your answer.

 

 

Type your answer below:
Part C)

C. Samantha deposits $1000 into a new savings account. The new savings account pays 3% interest, compounded semiannually (twice per year). She does not deposit money into or withdraw money from the account for 1 1/2 years. Write an equation that can be used to determine the amount of money, in dollars, in the new savings account at the end of 1 1/2 years. 

 

Write the equation using the "WIRIS editor" button 

 

Type your answer below:
Part D)

D. Use the equation you wrote in Part C to determine the amount of money, in dollars, in Samantha's new savings account at the end of 1 1/2 years. Show or explain how you got your answer. 

 

Type your answer below:

 

A storage rack has two wires that help support the sides of the rack. Each wire connects the top of one side to the base of the rack. The sides form right angles with the base of the rack. The rack and its interior dimensions are shown in this diagram.

 

 

Which of the following is closest to the length, in feet, of each wire?

 

Select one:
Part A)

 

A. This table shows the value of linear function f (x) for different values of x.

 

 

A student graphed the line that represents f (x) on a coordinate plane. Which statement about the graph of f (x) is true?


A. The slope of the line is negative, and the y-intercept of the line is negative.
B. The slope of the line is negative, and the y-intercept of the line is positive.
C. The slope of the line is positive, and the y-intercept of the line is negative.
D. The slope of the line is positive, and the y-intercept of the line is positive.

 

Select one:
Part B)

B. The student also graphed linear function g(x) on a coordinate plane, as shown.

 

Which of the following equations models g(x)?

 

Select one:

 

A student has two part-time jobs: babysitting and tutoring. The student earns an hourly wage at each job.


• On Monday, the student earned a total of $130 for 4 hours of babysitting and 2 hours of tutoring.


• On Tuesday, the student earned a total of $80 for 3 hours of babysitting and 1 hour of tutoring.


Which of the following systems of equations can be used to find x, the student’s hourly wage for babysitting, and y, the student’s hourly wage for tutoring?

 

Select one:

 

Figure R is shown on this coordinate plane.

 

 

Which of the following transformations would carry Figure R onto itself?


A. a reflection over the line y = 1
B. a reflection over the line x = 1
C. a 90° clockwise rotation about the point (1, 1)
D. a 180° clockwise rotation about the point (1, 1)

 

Select one:
Part A)

 

A. The population of each of four towns is predicted to increase or decrease at a constant rate. The equations shown in this table can be used to predict the population, P, of each town t years from today.

 

Based on the equations in the table, which statements about the populations of these towns are true? Select two true statements.


A. The population of Troy is decreasing.
B. The population of Pinehill is increasing.
C. The populations of Rye and Smithfield are each increasing.
D. The populations of Smithfield and Troy are each decreasing.
E. The populations of all four of the towns are each increasing.

 

Select all that apply:
Part B)

B. Which of the following lists the towns, based on their populations today, from least to greatest population?

 

Select one:

 

A student shaded part of circle V, as shown.

 

Which of the following is closest to the area of the shaded part of circle V?

 

Select one:

 

A student will draw the line of best fit for the set of data shown in this scatter plot.

 

Which of the following best describes how to draw the line of best fit for the set of data?


A. The line of best fit should pass through the origin.
B. The line of best fit should connect all of the data points.
C. The line of best fit should come as close as possible to every data point.
D. The line of best fit should contain the points with the highest and lowest y-values.

 

Select one: