10TH GRADE MATH PRACTICE WORKSHEET

Problem 1 :

Which of the following is equivalent to this expression?

−5x(−6x² + 1)

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

Solution

Problem 2 :

Consider this function.

f(x) = x(18 − x)

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

A) f(0) = −18 f(5) = 90 f(18) = −36

B) f(0) = 0 f(5) = 90 f(18) = −324

C) f(0) = 0 f(5) = 65 f(18) = 0

D) f(0) = 18 f(5) = −450 f(18) = −36

Solution

Problem 3 :

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?

A) 5π     B) 10π    C) 14π    D) 25π

Solution

Problem 4 :

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.

A) a translation 3 units up and 8 units to the right

B) a rotation of 270° counterclockwise about the origin

C) a dilation by a scale factor of 1 with respect to the origin

D) a dilation by a scale factor of 1.5 with respect to the origin

E) a dilation by a scale factor of −2 with respect to the origin

Solution

Problem 5 :

Consider this system of equations.

h + c = 2.25

h − c = 1.75

What value of h makes the system of equations true?

Solution

Problem 6 :

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)

Solution

Problem 7 :

Consider this inequality. y ≥ x − 4 Which of the following graphs represents the solution set of the inequality?

Solution

Problem 8 :

Line w is represented by this equation. y = 5x + 3 Which of the following equations represents a line that is perpendicular to line w?

A) y = − (1/5)x + 1     B) y = −5x + 1

C) y = 1/5x + 1       D) y = 5x + 1

Solution

Problem 9 :

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.

A. What is the value of y for the line when x = −4? Show or explain how you got your answer.

B. What is the value of y for the parabola when x = −4? Show or explain how you got your answer.

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. Show or explain how you got your answer.

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.

Solution

Problem 10 :

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.

Solution

Problem 11 :

Line segment KL is shown on this coordinate plane

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

A) (−1, 1/2 )    B) (−1/2 , 1)   C) (1/2 , −1)   D) (1, −1/2)

Solution

Problem 12 :

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.

Solution

Problem 13 :

What are the solutions of this equation?

x² + 7x + 12 = 0

A) x = −3; x = −4        B) x = −2; x = −6

C) x = 2; x = 6        D) x = 3; x = 4

Solution

Problem 14 :

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.

B. What is the median total number of minutes the athlete spent training each day? Show or explain how you got your answer.

C. What percent of the total number of minutes the athlete spent training for the 5 days was spent on strength training? Show or explain how you got your answer.

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.

Solution

Problem 15 :

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?

A) 2    B) 3    C) 8    D) 10

Solution

Problem 16 :

Four triangles and some of their angle measures are shown.

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

A) ΔFGE ~ ΔTUS         B) ΔGEF ~ ΔQPR

C) ΔLMN ~ ΔPQR        D) ΔNML ~ ΔTSU

Solution

Problem 17 :

These two triangles are similar.

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

A) ΔEFG ~ ΔZYX       B) ΔEGF ~ ΔXYZ   C) ΔFEG ~ ΔXZY

D) ΔFGE ~ ΔYZX       E) ΔGFE ~ ΔYXZ

Solution

Problem 18 :

Which of the following is equivalent to this expression?

x² + 5x − 84

A) (x + 6)(x − 14)      B) (x − 6)(x + 14)

C) (x + 7)(x − 12)      D) (x − 7)(x + 12)

Solution