Category focus

Expressions, Equations, and Relationships

Back to bank

Solve equations and inequalities and reason about geometric relationships and measurement.

Questions

125

Skill type

expressions and-equations

Study mode

Practice + review

Sample questions

Question

A student solved the equation x 2 = 132 to find the length of the diagonal of a square in centimeters. Which measurement is closest to x, the length of the diagonal of this square, in centimeters?

Open full-size question

Question

The table shows the dimensions of three cylinders. Cylinders Cylinder Radius (inches) Height (inches) W 3 9 X 4 2 Y 4.5 6 Which two cylinders have the same lateral surface area in square inches?

Open full-size question

Question

$Triangle HJK is graphed on the coordinate grid. Triangle HJK will be transformed using the rule (x, y ) → (− x, y ) to create triangle H′J′K′. y 9 8 7 J 6 5 4 3 H 2 1 K −9 −8 −7 −6 −5 −4 −3 −2 −1 x −1 1 2 3 4 5 6 7 8 9 −2 −3 −4 −5 −6 −7 −8 −9 Which graph represents triangle H′J′K′? y y 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 A x1 1 –9 –8 –7 –6 –5 –4 –3 –2 –1 C x–9 –8 –7 –6 –5 –4 –3 –2 –1 –1 1 2 3 4 5 6 7 8 9 –1 1 2 3 4 5 6 7 8 9 –2 –2 –3 –3 –4 –4 –5 –5 –6 –6 –7 –7 –8 –8 –9 –9 y y 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 B x1 D x1 –9 –8 –7 –6 –5 –4 –3 –2 –1 –1 1 2 3 4 5 6 7 8 9 –9 –8 –7 –6 –5 –4 –3 –2 –1 –1 1 2 3 4 5 6 7 8 9 –2 –2 –3 –3 –4 –4 –5 –5 –6 –6 –7 –7 –8 –8 –9 –9$ Open full-size question

A.
$Answer A: Answer A (see image)$
B.
$Answer B: Answer B (see image)$
C.
$Answer C: Answer C (see image)$
D.
$Answer D: Answer D (see image)$

Question

$The diagram shows a right triangle and the lengths of two of its sides in inches. 11.9 in. d 7.9 in. Which measurement is closest to the value of d in inches?$ Open full-size question

A.
$Answer A: 6.3 in.$
B.
$Answer B: 4.0 in.$
C.
$Answer C: 14.3 in.$
D.
$Answer D: 19.8 in.$

Question

$The perimeter of the triangle shown is 17x units. The dimensions of the triangle are given in units. 15 units 15 units 7x units Which equation can be used to find the value of x?$ Open full-size question

A.
$Answer A: 17x = 30 +7x$
B.
$Answer B: 17x = 15 +22 x$
C.
$Answer C: 17x = 7 +30 x$
D.
$Answer D: 17x = 22 +15 x$

Question

$A cylinder has a height of 5 feet and a diameter of 2 feet. Which measurement is closest to the volume of the cylinder in cubic feet?$ Open full-size question

A.
$Answer A: 62.8 ft 3$
B.
$Answer B: 15.7 ft 3$
C.
$Answer C: 78.5 ft 3$
D.
$Answer D: 157.1 ft 3$

Question

$A list of numbers ordered from least value to greatest value is shown. One number is missing. _18 _ 5 , 3.71, , √ 17 Which number could be the missing number?$ Open full-size question

A.
$Answer A: 4.5$
B.
$Answer B: 3.8%$
C.
$Answer C: 15 _57$
D.
$Answer D: (3.9) 2$

Question

$Rhonda’s job is to drive a car for a company. Each month she is paid the same salary. She is also paid extra money for the number of miles she drives the car each month. • In July Rhonda drove 640 miles and was paid a total of $3,502.00. • In August Rhonda drove 820 miles and was paid a total of $3,601.00. Which function can be used to find y, the total amount she is paid in a month if she drives x miles?$ Open full-size question

A.
$Answer A: y = 5.47x$
B.
$Answer B: y = 4.39x$
C.
$Answer C: y = 0.55x +3,150$
D.
$Answer D: y = 3,150x +0.55$

Question

$Fulgurites are pieces of glass in the shape of a cylinder produced when lightning strikes sand. A student found a fulgurite with a height of 21 inches and a diameter of 6 inches. Which equation can be used to find V, the volume of the fulgurite in cubic inches?$ Open full-size question

A.
$Answer A: V = π(6) 2(21)$
B.
$Answer B: V = π(3) 2(21)$
C.
$Answer C: V = π(6)(21)$
D.
$Answer D: V = π(3)(21)$

Question

$The coordinates of the vertices of a rectangle are A (5, 3), B (5, −9), C ( −1, −9), and D ( −1, 3). y 9 8 7 6 5 4 D 3 A 2 1 −9 −8 −7 −6 −5 −4 −3 −2 −1 x −1 1 2 3 4 5 6 7 8 9 −2 −3 −4 −5 −6 −7 −8 C − B9 Which measurement is closest to the distance between point B and point D in units?$ Open full-size question

A.
$Answer A: 5.8 units$
B.
$Answer B: 13.4 units$
C.
$Answer C: 10.4 units$
D.
$Answer D: 9.1 units$

Question

$Pentagon PQRST was graphed on a coordinate grid. Pentagon PQRST was rot ated 90° counterclockwise about the origin to form pentagon P′Q′R′S′T′. Which statement is true?$ Open full-size question

A.
$Answer A: The area of pentagon P′Q′R′S′T′ is not equal to the area of pentagon PQRST.$
B.
$Answer B: Pentagon P′Q′R′S′T′ is not congruent to pentagon PQRST.$
C.
$Answer C: The perimeter of pentagon P′Q′R′S′T′ is greater than the perimeter of pentagon PQRST.$
D.
$Answer D: The angle measures of pentagon P′Q′R′S′T′ are congruent to the corresponding angle measures of pentagon PQRST.$

Question

$Which measurements could represent the side lengths in feet of a right triangle?$ Open full-size question

A.
$Answer A: 10 ft, 24 ft, 26 ft$
B.
$Answer B: 14 ft, 14 ft, 14 ft$
C.
$Answer C: 3 ft, 3 ft, 18 ft$
D.
$Answer D: 2 ft, 3 ft, 5 ft$

Question

$The dimensions of a cylinder are shown in the diagram. 5.8 cm 7.6 cm Which measurement is closest to the lateral surface area in square centimeters of the cylinder?$ Open full-size question

A.
$Answer A: 164.9 cm 2$
B.
$Answer B: 277.0 cm2$
C.
$Answer C: 2138.5 cm$
D.
$Answer D: 191.3 cm 2$

Question

$The two lines graphed on the coordinate grid represent a system of equations. y 9 8 7 6 5 4 3 2 1 −9 −8 −7 −6 −5 −4 −3 −2 −1 x −1 1 2 3 4 5 6 7 8 9 −2 −3 −4 −5 −6 −7 −8 −9 What is the x-coordinate of the ordered pair that best represents a solution to both equations?$ Open full-size question

A.
$Answer A: 7 _1$
B.
$Answer B: 0$
C.
$Answer C: 5$
D.
$Answer D: 7$

Question

$A company is drilling a water well. The graph models the linear relationship between the depth of the well and the time spent drilling. Well Drilling y 50 40 30 20 10 0 1 2 3 4 5 x Time (hours) Which function best represents the relationship between y and x?$ Open full-size question

A.
$Answer A: y = 6x$
B.
$Answer B: y = 30x$
C.
$Answer C: y = 5x +30$
D.
$Answer D: y = 6x +30$

Question

$Mount Fuji in Japan can be modeled as a cone with a diameter of 25 miles and a height of 2.35 miles. Which measurement is closest to the volume of Mount Fuji in cubic miles?$ Open full-size question

A.
$Answer A: 1,154 mi 3$
B.
$Answer B: 385 mi 3$
C.
$Answer C: 1,538 mi 3$
D.
$Answer D: 72 mi 3$

Question

$Two student groups went to an amusement park on the same day. • Group 1 bought 9 tickets and received a $120 discount. • Group 2 bought 3 tickets and received a $30 discount. • Both groups spent the same total amount of money on tickets. • The price of each ticket was the same. What was the cost of each ticket?$ Open full-size question

A.
$Answer A: $25$
B.
$Answer B: $12.50$
C.
$Answer C: $15$
D.
$Answer D: $7.50$

Question

$The cost for electricity varies directly with the amount of kilowatt- hours of electricity used. The cost for using 1,079 kilowatt-hours of electricity was $129.48. What was the cost for using 908 kilowatt-hours of electricity?$ Open full-size question

A.
$Answer A: $41.52$
B.
$Answer B: $153.86$
C.
$Answer C: $75.67$
D.
$Answer D: $108.96$

Question

$The map shows five proposed routes and distances for a new state highway between Camden and U.S. Highway 99. Proposed Routes for State Highway 1001 Distances for Di˜erent Proposed Routes (km) US 99 675 Crestview 16 40 1001 1001 1001 1001 2, 111 1001 586 13 220 10 17 Camden Which list shows these distances from least to greatest? _ _ 586 _675 2$ Open full-size question

A.
$Answer A: 10 √ 17 , 40, _13 , 16 , √, 111 _ _ 675 _586 2$
B.
$Answer B: 40, 10 √ 17 , _16 , 13 , √, 111 _586 _675 _ _$
C.
$Answer C: 13 , 16 , 10 √ 17 , √ 2, 111 , 40 675 _586 2_ _$
D.
$Answer D: 40, _16 , 13 , √, 111 , 10 √ 17$

Question

$Which situation can be represented by this equation? 18x = 19 +12 x$ Open full-size question

A.
$Answer A: Krystal reads 12 pages per hour. Jondo reads 18 pages per hour. How many hours, x, would it take for Krystal and Jondo to read the same number of pages?$
B.
$Answer B: Krystal paid a deposit of $19 plus $18 per hour to rent a dining room at a restaurant. Jondo paid $12 per hour to rent a dining room at a restaurant. How many hours, x, would it take for Krystal and Jondo to pay the same amount of money?$
C.
$Answer C: Krystal installs 12 tiles per hour. Jondo installs 19 tiles per hour and started with 18 tiles already installed. How many hours, x, would it take for Krystal and Jondo to install the same number of tiles?$
D.
$Answer D: Krystal can make $18 per hour by tutoring. Jondo can make $12 per hour by tutoring. Jondo already has $19. How many hours, x, would Krystal and Jondo need to tutor for them to have the same amount of money?$