Middle School Math (5164) - Geometry and Measurement
Melissa records the amount of time she works by the hour, but can enter her time into her time card only to the nearest one-hundredth of an hour each day. Melissa works the following number of hours on consecutive days: 4.383 hr, 3.067 hr, 5.567 hr, and 2.217 hr. If the individual times are rounded to the nearest one-hundredth of an hour, which of the following is the best estimate of Melissa's total work time for the four days? (15.23 hr) (15.25 hr) (15.21 hr) (15.24 hr)
15.24 hr
A backyard farmer buys 160 linear feet of fencing material to build a rectangular pen for his new goat. If the width of the pen is 30 feet, what is its area? (320 ft²) (1950 ft²) (1500 ft²) (2400 ft²)
1500 ft²
What is the area of the figure graphed in the coordinate plane with vertices of: (0, 0), (4, 4), (0, 4), and (4, 0)? (20 units²) (4 units²) (8 units²) (16 units²)
16 units²
A rectangle has an area of 30 square units. If the length of the rectangle is increased by a factor of 3 and the width is increased by a factor of 2, what is the area of the new rectangle? (60) (90) (150) (180)
180
A right cylinder has a height of 10" and a base with a circumference of 12π". What is the surface area? (192π in²) (120 + 72π in²) (192 in²) (72π in²)
192π in²
Use the table to answer the question that follows. School Bell Schedule Class Period Start Time End Time 3rd 10:12 A.M. 10:58 A.M. 4th 11:03 A.M. 11:49 A.M. Lunch 11:54 A.M. 12:26 P.M. 5th 12:31 P.M. 1:17 P.M. 6th ???? 2:08 P.M. The portion of the school bell schedule shown lists the start and end times of the class period. Except for lunch, all class periods are the same length. What is the missing start time for 6th period? (1:21 P.M.) (1:22 P.M.) (1:27 P.M.) (1:31 P.M.)
1:22 P.M.
What is the slope of the line containing the points (2, 4) and (5, 10)? (4) (2) (5) (1/2)
2
A scientist received two separate reports of invasive beetle sightings. One observer estimates the length of the beetle to be similar to a lime and the other compares the length of the beetle to a house key. What is a good approximation for the size of the beetle? (1/12 foot) (2 inches) (10 centimeters) (30 millimeters)
2 inches
The ice cream shop in Longsville sold 3,042,213 ice-cream cones last year. The ice cream shop in Bertsville sold 841,928. Which of the following is the best estimate of how many more ice-cream cones were sold by the shop in Longsville than by the shop in Bertsville? (2,200,000) (22,000) (220,000) (2,200)
2,200,000
Which of the following is the least appropriate way to estimate 2,196,613 ÷ 311? (2,200,000 ÷ 300) ((2,100,000 ÷ 300) + (90,000 ÷ 300) + (6,000 ÷ 300) = 7,000 + 300 + 20) ((2,100,000 ÷ 300) + (96,000 ÷ 300) = 7,000 + 320) (2,100,000 ÷ 300)
2,200,000 ÷ 300
The coordinate points A (-4, 3), B (1, 3), C (4, 7), and D (-1, 7) form a parallelogram. Find the perimeter of the parallelogram. (10) (20) (18) (24)
20
Sara and Ben decided to fence a circular backyard garden with a 22-meter long piece of leftover flexible fencing. What is the maximum diameter of the circle that can be enclosed with this piece of fence? (22/π m) (11π m) (2√(22/π) m) (22π m)
22/π m
Two angles are complementary. If the measure of one of the angles is 68°, what is the measure of the other angle? (68° because complementary angles are congruent to each other.) (112° because the sum of the measures of complementary angles is 180°.) (292° because the sum of the measures of complementary angles is 360°.) (22° because the sum of the measures of complementary angles is 90°.)
22° because the sum of the measures of complementary angles is 90°.
What is the area of a geometric figure graphed on the coordinate plane bounded by the points (0,0), (0,5), (5,0), and (5,5)? (5 square units) (25 square units) (20 square units) (50 square units)
25 square units
Which of the following is a good estimate of the area of a circle with a circumference of 30 cm? (100π cm²) (25π cm²) (100 cm²) (25 cm²)
25π cm²
A ladder, 35 feet in length, leans against the side of a building. The base of the ladder is 21 feet from the base of the building. How far above the ground does the ladder touch the building? (14 feet) (17.5 feet) (28 feet) (40.8 feet)
28 feet
The time allowed for Elliot's lunch was 11:42 am to 12:10 pm. How many minutes was lunch? (28 minutes) (22 minutes) (32 minutes) (38 minutes)
28 minutes
What is the volume of a ball that is 12 cm in diameter? (216π cm³) (144π cm³) (288π cm³) (2304π cm³)
288π cm³
Which of the following is the best estimate for 6,189 × 485? (3,000,000) (30,000,000) (2,400,000) (24,000,000)
3,000,000
The coordinate points A (1, 0), B (6, 0), and C (1, 12) form a right triangle. Find the perimeter of the triangle. (21) (15) (13) (30)
30
Which of the following is the best estimate for the volume of a cup of coffee? (350 L) (350 cL) (350 dL) (350 mL)
350 mL
A neighborhood park has a large rectangular sandbox with an area of 80 square meters. The city parks department wants to replace the wooden border with new wood. If the sandbox is 10 meters long, how much wood does the parks department need to purchase? (32 meters) (36 meters) (40 meters) (20 meters)
36 meters
What is the volume of an ice cream cone that is 6cm wide at the top and 12cm tall? (36π cm³) (12π cm³) (108π cm³) (144π cm³)
36π cm³
Kaitlyn wants to call her best friend, Kirby, after Kirby finishes her work at 5:00 PM, but Kaitlyn is on a work trip in another time zone. If Kaitlyn's 4 ½ hour flight took off at 7:45 AM and she landed at 10:15 AM local time, at what local time can she call Kirby? (6:00 PM) (3:00 PM) (4:00 PM) (7:00 PM)
3:00 PM
12π ÷ 9 is approximately equivalent to: (4/3) (4π) (π) (4)
4
Becky arrived at her babysitting job Saturday morning at 9:15 am. She left at 1:30 pm. How many hours did she work? (4 hours, 15 minutes) (3 hours, 15 minutes) (4 hours, 45 minutes) (3 hours, 45 minutes)
4 hours, 15 minutes
Tom wants to mentally calculate a 20% tip on his bill of $40. Which of the following is best for Tom to use in the mental calculation of the tip? (40 X .02) (40 X .1 X 2) (40 X (200/1000)) (40 X (20/100))
40 X .1 X 2
Use the numbers below to answer the question below: 2828 3456 5678 922 8567 To estimate the sum of the numbers given above, Penelope rounds each number to the nearest hundred and then adds the rounded values. By how much will Penelope's estimate differ from the actual sum? (67) (28) (51) (49)
49
Hailey's mom wants to help her practice using fractions. They decide to make their famous chocolate chip cookie recipe, but it will need to be tripled so that she will have enough for all of the third-grade students. The original recipe calls for 2 ½ cups of flour and ¾ cup of sugar. How much more flour than sugar does she need to make enough cookies for her grade? (1 3/4 cups) (3 1/2 cups) (4 1/4 cups) (5 1/4 cups)
5 1/4 cups
Which of the following is the best estimate for the height of a one-story house? (5 m) (5 cm) (5 km) (5 mm)
5 m
Jim wants to walk to Bill's house. To get to Bill's house, Jim walks 3 miles south and then walks 4 miles east. Jim wants to know how many miles he would have walked if he just walked in a straight line. How many miles would Jim have walked if he walked in a straight line to Bill's house? (4 miles) (7 miles) (5 miles) (6 miles)
5 miles
A silo holding corn is in the shape of a cone. The silo has a diameter of 16 feet and a height of 24 feet. How much corn can the silo hold? (512π cubic feet) (2048π cubic feet) (266π cubic feet) (1536π cubic feet)
512π cubic feet
A trapezoid has an area of 600 mm². What is the area of the new trapezoid formed by dilating the original by a factor of 3? (500 mm²) (5400 mm²) (1800 mm²) (200 mm²)
5400 mm²
Danielle's third-period class began at 10:43 am and ended at 11:38 am. How long was the class? (1 hour, 21 minutes) (1 hour, 5 minutes) (55 minutes) (45 minutes)
55 minutes
On a given day, Mercury, Venus, and Earth all happen to align. That day, Venus is 26,028,957 miles from Earth. On the same day, Mercury is 30,975,143 miles from Venus. Which of the following is the best estimate of the distance from Earth to Mercury on that day? (57,000,000 miles) (5,000,000 miles) (4,000,000 miles) (56,000,000 miles)
57,000,000 miles
Which of the following is the closest estimate to the area of a football field? (6400 mi²) (6400 ft²) (6400 yd²) (6400 in²)
6400 yd²
Christopher had a basketball tournament on Saturday from 10:45 am to 6:15 pm. How long was tournament? (8 hours, 30 minutes) (4 hours, 30 minutes) (6 hours, 30 minutes) (7 hours, 30 minutes)
7 hours, 30 minutes
One leg of a right triangle is 17 inches less than the other leg. How long does the shorter leg need to be in order for the hypotenuse to be at least 25 inches? (-7 inches) (7 inches) (17 inches) (24 inches)
7 inches
A triangle has side lengths of 7, 14, and x. Which of the following could be the length of x? (22) (8) (6) (24)
8
Given a square with an area of 64 cm², what is the length of one side? (8) (32) (4) (16)
8
Which of the following measurements is a good estimate for the length of a bar of soap? (8 km) (8 mm) (8 cm) (8 m)
8 cm
In triangle XYZ, XY has length 5 and YZ has length 9. For which of the following possible lengths of XZ is XYZ an acute triangle? Select all answers that apply. (8) (9) (10) (11)
8, 9, 10
A class begins working on a mathematics project at 9:50 a.m. and stops working on the project at 11:10 a.m. How many minutes did the class work on the project? (60 minutes) (100 minutes) (20 minutes) (80 minutes)
80 minutes
Diego is making a tiled circular mosaic on the floor of a client's home and will install a thin border around the design. If the radius of the circular mosaic is 48 inches, what length of thin border material must Diego use around the outside edge of the mosaic? (8π ft) (12π ft) (4π ft) (16π ft)
8π ft
The Trout family just purchased a large table in the shape of a perfect circle. It is 600 cm across. John helps set one side of the table for dinner and walks exactly halfway around the table. Which of the following is closest to how far has he walked? (1,000 cm) (600 cm) (1,900 cm) (950 cm)
950 cm
Which of the following measurements would most likely be 15 centimeters? (a textbook spine) (a paperclip width) (a pencil length) (a school desk height)
A pencil length
There is a line AB defined by two points A and B. If Carly draws a point M that is not on line AB, which geometric figure is defined by the point M and the line? (a vertex) (an angle) (a plane) (two lines)
A plane
In the diagram, ΔABC is similar to ΔDEC. All but one of the following ratios are correct. Which one is incorrect? (AB/DE = BC/AC) (CE/DE = CB/AB) (BC/EC = AB/DE) (BC/AC = EC/DC)
AB/DE = BC/AC
If the lengths of two sides of a triangle are given as 5 cm and 11 cm, what statement is true of the third side? (The third side is greater than 6 cm but less than 11 cm.) (The third side is greater than 5 cm but less than 16 cm.) (The third side is greater than 5 cm but less than 11 cm.) (The third side is greater than 6 cm but less than 16 cm.)
The third side is greater than 6 cm but less than 16 cm.
Maria has drawn a triangle with sides 3" and 8". Which of the following is a true statement? (The third side must be less than 8" long.) (The third side must be greater than 5" long.) (The third side could be 12" long.) (The third side could be 4" long.)
The third side must be greater than 5" long.
The height of a rectangular prism has increased by a factor of 5. By how much has the volume of the prism increased? (The volume has increased by a factor of 5.) (The volume has increased by a factor of 5².) (The volume has increased by a factor of 5³.) (The change in volume cannot be determined by the information given.)
The volume has increased by a factor of 5.
A student is instructed to draw a four-pointed geometric shape on an xy-plane. After the shape is drawn, the student is instructed to add 5 to each x-coordinate and add 3 to each y-coordinate. Which of the following did the student perform? (rotation) (refraction) (translation) (reflection)
Translation
There exists a three-dimensional figure with 4 faces, 6 edges, and 4 vertices. Which of the following satisfies these criteria? (triangular prism) (triangular pyramid) (rectangular prism) (rectangular pyramid)
Triangular pyramid
A circle with diameter d has an area of 60. What is the value of d? (60/π) (4 3√(45/π)) (√(240/π)) (15/π)
√(240/π)
Tosha has 8 coins in her pocket. She has a mixture of pennies, nickels, dimes and quarters, but she has no more than 3 of any coin. What is the largest amount of money she could possibly have? ($1.21) ($1.23) ($1.11) ($1.07)
$1.11
Keisha earns $28 per day delivering newspapers. If her daily earnings are rounded to the nearest $5, which of the following is the best estimate of her weekly earnings, assuming she works 7 days per week? ($175) ($195) ($210) ($30)
$210
Use mental math to solve the problem below. James has saved $35.25. He wants to save his money to buy a bicycle that is listed as $85.00. If sales tax is 8%, about how much more must he save to purchase his bike, including tax? ($50) ($60) ($55) ($70)
$60
Triangle ABC lies on the xy-plane. The coordinates of the midpoint of line segment BC are (-2,-3). If the coordinates of point A are (-7,-6) and the coordinates of point B are (-3,-9), what are the coordinates of point C? ((3,9)) ((-3,-2)) ((2,0)) ((-1,3))
(-1,3)
Given the following glide reflection parameters, what are the coordinates of vertex C''? The vertices of △ABC are A (2, 3), B (3, 6), and C (7, 1). Translation: (x, y) → (x−11, y) Reflection: in the x-axis. ((4, -1)) ((-4, -1)) ((4, 1)) ((-4, 1))
(-4, -1)
Which of the following sets of three points is not collinear? ((0,0), (0,2), (0,4)) ((0,0), (3,0), (5,0)) ((0,0), (0,2), (3,0)) ((2,-2), (2,2), (2,3))
(0,0), (0,2), (3,0)
Quadrilateral LMNO has vertices L (-2, 0), M (-2, 4), N (4, 8), and O (10, 2). If LMNO is dilated with a scale factor of 1/2 and a center of dilation of D (6, 6), what are the coordinates of vertex M'? ((2, 5)) ((8, 4)) ((2, 3)) ((5, 7))
(2, 5)
Which of the following is not an appropriate way to estimate 384, 692 + 2164? ((3 × 100,000) + (8 × 10,000) + (6 × 1000) + (7 × 100)) ((38 + 10,000) × (6 + 1,000) × (7 + 100) × (15 + 10)) (380,000 + (4,000 + 2,000) + (600 + 100) + (90 + 60)) (385,000 + 2000)
(38 + 10,000) × (6 + 1,000) × (7 + 100) × (15 + 10)
A triangle has coordinate points A (-2, -1), B (-6, -1), and C (-4, 5). If it is rotated 90° clockwise about point A, what are the new coordinates of point C? ((-2, 3)) ((-2, -1)) ((-4, -5)) ((4, 1))
(4, 1)
A triangle with coordinates (2, -4), (3, 2), and (0, 0) is moved 3 units right and 3 units down. What are the coordinates of the new image? ((5, -7), (6, 5), (3, 3)) ((5, 7), (6, 5), (3, -3)) ((5, -7), (1, -7), (3, -3)) ((5, -7), (6, -1), (3, -3))
(5, -7), (6, -1), (3, -3)
Which of the following is the least appropriate way to estimate 86 X 9523? ((90 X 9000) + (90 X 500) + (90 X 20) = 810,000 + 45000 + 1800) ((80 X 9000) + (5 X 500) = 720,000 + 2500) (90 X 9000) (80 X 10000)
(80 X 9000) + (5 X 500) = 720,000 + 2500
Which of the following is the closest estimate to the mass of a paperclip? (1 kilogram) (1 gram) (1 tonne) (1 milligram)
1 gram
A patient has a circular rash on their skin. The doctor's assistant must calculate the area of the affected region in order to prescribe the correct amount of cream for the patch. If the diameter of the rash is 2.4 cm, what area is covered by the rash? (2.4π cm²) (5.76π cm²) (23.04π cm²) (1.44π cm²)
1.44π cm²
Rectangle LMOP has vertices at the following coordinates: (1,6); (25,6); (1,-4); (25,-4). It is has been transformed into rectangle L'M'O'P'. Each diagonal of rectangle L'M'O'P' has a length of 13. What is the scale factor used to transform rectangle LMOP into rectangle L'M'O'P'? (4) (1/2) (2) (1/4)
1/2
Use the expression to answer the prompt. 5902 + 2527 + 9864 If the result of the expression is estimated by rounding each number to the hundreds place, then by rounding each number to the tens place, by what value will the two estimates differ? (10) (700) (90) (7)
10
The volume of a rectangular box is 240 cm³. The length of the box is 12 cm and the width of the box is 2 cm. How tall is the box, in centimeters? (40 cm) (216 cm) (10 cm) (5 cm)
10 cm
Tia participates in marching band before school and plays volleyball after school. She arrived at school at 6:52am today and did not leave until 5:34pm. How many hours and minutes did she spend on the school campus? (11 hours 18 minutes) (11 hours 42 minutes) (10 hours 42 minutes) (10 hours 18 minutes)
10 hours 42 minutes
Aaron went to sleep at 8:35 pm Tuesday night. He woke up at 7:00 am. How much sleep did he get? (8 hours, 25 minutes) (10 hours, 35 minutes) (11 hours, 35 minutes) (10 hours, 25 minutes)
10 hours, 25 minutes
The area of a rectangular plot of ground is 100m². Which of the following is the correct length of one of the sides if the perimeter of the plot is 40 m? (2 m) (10 m) (3.5 m) (5 m)
10 m
After a lesson on rounding and estimation, a teacher tells students that the football concession stand has purchased 590 candy bars to sell for the 6 football home games this year. The teacher asks the students to estimate the average number of candy bars that will be sold at each home game. Which of the following would be the correct estimation? (105) (98.3) (100) (90)
100
The circumference of a circular garden is 20π meters. Determine the area of the garden. (10π m²) (100π m²) (400π m²) (2√5π m²)
100π m²
Of the following, which is most likely the distance from a classroom on the second floor to the playground outside at the end of the wing? (48 feet) (105 meters) (2,020 millimeters) (168 inches)
105 meters
Which of the following is the best estimate for the mass of a school bus? (11,000 mt) (11,000 g) (11,000 kg) (11,000 mg)
11,000 kg
Which of the following is the best estimate for the mass of a newborn kitten? (118 g) (118 kg) (118 mt) (118 mg)
118 g
Jamal went to bed at 9:38 pm and woke up at 10:15 am the next morning. How long did Jamal sleep? (12 hr 37 min) (12 hr 18 min) (10 hr 37 min) (11 hr 18 min)
12 hr 37 min
A triangle has side lengths of 5, 8 and x. Which of the following could be the value of x? Select all answers that apply. (13) (12) (3) (8)
12, 8
A rectangle has a length that is twice the size of its width. If the perimeter of the rectangle is 48 inches, what is the area of the rectangle in square inches? (576 in²) (128 in²) (72 in²) (64 in²)
128 in²
What is the approximate distance between A(-2, -8) and B(3, 6)? (5.4 units) (14.9 units) (13.1 units) (22.4 units)
14.9 units
The Johnson family intends to add a fence around a 1200 square foot section of their yard. If the area to be fenced is a rectangle with a width of 30 feet, what minimum length of fencing will be needed to surround the entire area? (40 ft) (120 ft) (300 ft) (140 ft)
140 ft
A farmer constructs a fence to make a circular pig pen. He uses 24 yards of fencing. What is the area of the pig pen? (144/π yards²) (12/π yards²) (12π yards²) (144π yards²)
144/π yards²
A large wheel has a diameter of 20 cm and can travel a set distance in 135 rotations. A small wheel must rotate 180 times to travel the same distance. What is the diameter of the small wheel? (16 cm) (15 cm) (18 cm) (17 cm)
15 cm
Jamie needs to measure the diagonal of his computer screen for a project he is working on. What is an appropriate unit of measure he could use? (kilometers) (yards) (centimeters) (grams)
Centimeters
To explain a mental math strategy, the teacher writes the following steps on a whiteboard: 63 + 86 63 - 3 = 60 60 + 86 = 146 146 + 3 = 149 Which of the following strategies is the topic of the lesson? (compensation) (estimation) (partitioning) (rounding)
Compensation
To explain a new estimation strategy, a teacher writes the following steps on a whiteboard: 51 ÷ 7 51 → 49 49 ÷ 7 = 7 51 ÷ 7 ≈ 7 She explains: "We want to estimate the quotient of 51 and 7. 51 is not a multiple of 7, but we can estimate the quotient by rounding 51 to a multiple of 7. 49 is equal to 7 times 7 and is very close to 51. Therefore, we know that 51 divided by 7 is approximately equal to 7." Which of the following strategies is the topic of the lesson? (dividing by partitioning) (estimating by rounding to the nearest whole number) (dividing by compensating) (estimating with benchmark numbers)
Estimating with benchmark numbers
Which is the most appropriate unit to measure the height of the average adult human? (millimeters) (inches) (miles) (kilometers)
Inches
Which is the most appropriate unit to measure length of the average football field? (miles) (meters) (inches) (millimeters)
Meters
A teacher draws the nets of a triangular prism and a square pyramid on the whiteboard. She is most likely beginning a discussion about which of the following concepts? (nets of 3D figures have the same formula for surface area) (nets of 3D figures with the same number of vertices) (nets of 3D figures with the same number of faces) (nets of 3D figures with the same number of edges)
Nets of 3D figures with the same number of faces
The following expression solution exemplifies which mental math strategy? 145 + 236 145 → 100 + 40 + 5 236 → 200 + 30 + 6 100 + 200 = 300 40 + 30 = 70 5 + 6 11 300 + 70 + 11 = 388 (partitioning) (benchmarking) (rounding) (compensation)
Partitioning
Which of the following is the most appropriate unit for expressing the volume of an average glass of milk? (pound) (pint) (gallon) (gram)
Pint
A quadrilateral has two sets of parallel sides and its diagonals are congruent but not perpendicular. What shape is this? (rectangle) (rhombus) (square) (trapezoid)
Rectangle
Which of the following geometric figures always contains congruent diagonals? (parallelogram) (rectangle) (rhombus) (trapezoid)
Rectangle
Which of the following does not have 8 vertices? (cube) (heptagonal pyramid) (rectangular pyramid) (rectangular prism)
Rectangular pyramid
Which of the following geometric figures possesses all of the following properties? I. At least one pair of opposite sides are parallel. II. Diagonals bisect each other. III. Diagonals bisect perpendicularly. (trapezoid) (rhombus) (rectangle) (triangle)
Rhombus
Nets are a useful tool for the early exploration of what mathematical concept(s)? Select all answers that apply. (slope) (surface area) (perimeter) (volume)
Surface area, Volume
Polygon ABCDE is dilated with a scale factor of 4/3. Which statement about polygon ABCDE and its image after dilation, A'B'C'D'E' is true? (The length of diagonal BE is equivalent to the length of B'E'.) (The measure of angle A and angle A' are in the ratio 4 : 3.) (The lengths of side CD and side C'D' are in the ratio 3 : 4.) (The length of side AB is equivalent to the length of side A'B'.)
The lengths of side CD and side C'D' are in the ratio 3 : 4.
Ellie is getting a new rug for her room. Her old rectangular rug is 5 ft by 7 ft. Her new rug is circular with a diameter of 7 ft. How is the size of the new rug related to the old one? (The new rug is about 4.5 ft² larger than the old one.) (The new rug is about 3.5 ft² smaller than the old one.) (The new rug is about 4.5 ft² smaller than the old one.) (The new rug is about 3.5 ft² larger than the old one.)
The new rug is about 3.5 ft² larger than the old one.
