Mrs. McHugh
7th Grade Math
2012 3rd Quarter EQT Review
COS 4: Express a pattern shown in a table, graph or chart as an algebraic expression: f(x) is the same as y=
x / y12 / 4
3 / 1
0 / 0
-6 / -2
1)
2)
3)
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4)
5)
6)
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COS 7: Determine transformations, including translations, reflections, or rotations, used to alter the position of a polygon on a coordinate plane.
1)
A C
B D
2)
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3)
4)
5) A figure is translated to the left 2 units and up 6 units. Write a rule to show how to find its image.
6) A figure is translated to the right 6 units and down 3 units. Write a rule to show how to find its image.
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7)
8)
A C
B D
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COS 8 – Recognize geometric relationships among two-dimensional and three-dimensional objects.
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2)
3)
4)
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8)
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COS 9 – Solve problems involving circumference and area of circles.
1) Brian is measuring one of his family’s round dinner plates so that he can buy more plates of the same size. He
found that it is 14 centimeters from the edge of the plate to the center of the plate. Which is closest to the circumference, in centimeters, of the plate?
A) 43.96 B) 87.92 C) 153.86 D) 615.44
2) Mr. Brown is building a circular patio in his yard. The diameter of the patio is 16 feet. Which is closest to the area, in square feet, of Mr. Brown’s patio?
A) 30 B) 50 C) 200 D) 800
3) GH is a diameter of circle O and measures 9 yards in length.
Which is closest to the circumference of the circle?
A) 14 yd B) 28 yd C) 57 yd D) 64 yd
4) Tyler drew a rectangle around three circles as shown below: Which is closest to the total area, in square inches, of the three circles? A) 19.63 B) 58.88 C) 78.50 D) 706.50
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5) The path of an amusement park ride is a circle with a diameter of 9.5 feet. Melanie is at the point marked on the path, as shown below.
Which is closest to the distance, in feet, Melanie will travel in one complete turn of the ride?
A) 14.92 B) 29.83 C) 59.66 D) 70.85
6) A hole punch cuts a circular hole with a diameter of 8 millimeters in a piece of paper. Which is closest to the area, in
square millimeters, of the hole?
A) 12.56 B) 25.12 C) 50.24 D) 200.96
7) Ray is putting a piece of material around the circular top of his drum. The radius of the top is 17.5 centimeters.
Which is closest to the circumference, in centimeters, of the top of the drum?
A) 54.95 B) 109.9 C) 219.8 D) 961.63
8) The radius of a coin is ½ inch. What is the area, in square inches, of the coin?
9) A circle has a circumference of 37.68 centimeters. What is the radius, in centimeters, of the circle?
10) The circumference of a circle equals 43.96 m, what is the diameter?
11) The area of a circle equals 379.94 cm, what is the radius?
12) The area of a circle equals 314 m, what is the diameter?
COS 10: Calculate the perimeter of polygons and the areas of triangles and trapezoids.
1) What is the perimeter, in centimeters, of the parallelogram shown below.
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2) Jill wanted to place rope around three sides of the playground. The sides measure 13.2 meters, 17.05 meters, and
10.8 meters as shown below.
3) What is the perimeter, in inches, of the square shown below?
4) Each side of a regular hexagon has a length of 8 inches. What is the perimeter, in inches, of the hexagon?
A) 32 B) 40 C) 48 D) 54
5) What is the area, in square meters, of the trapezoid shown below?
A) 42 B) 84 C) 132 D) 168
6) What is the area, in square inches, of the trapezoid shown below?
7) What is the perimeter, in centimeters, of the polygon shown below?
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8) What is the area, in square feet, of the figure shown below?
9) Each side of a regular pentagon has a length of 6.5 centimeters. What is the perimeter, in centimeters, of the pentagon?
10) Jorge plans to paint a bedroom wall that is shaped like a trapezoid. The bottom edge of the wall is 22.5 feet long, and the top edge of the wall is 9.5 feet long. If the wall is 8 feet tall, what is the area of the wall? Round your answer to the nearest hundredth if necessary.
COS 12: Determine the measures of central tendency (mean, median, mode) and range using a given set of data or graphs, including histograms, frequency tables, and stem and leaf plots.
1) The stem-and-leaf plot shows the number of fishing licenses purchased on different days last month. What is the median number of fishing licenses purchased?
A) 32 B) 35 C) 41 D) 45
2) The number of points Kyle’s basketball team scored in each of their last 6 games is shown below.
88, 70, 84, 93, 84, 97
Which is true about the number of points Kyle’s basketball team scored?
A) The mean is less than the mode. B) The median is less than the mode.
C) The mean and median are the same. D) The median and mode are the same.
3) The table below shows the number of students in attendance at Blanco Middle School for a one-week period. What is the mean number of students in attendance at Blanco Middle School for the one-week period?
4) The list below shows the number of collectible cards owned by Stefanie’s friends.
181, 256, 301, 72, 97, 412
What is the range of the number of collectible cards owned?
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5) The stem-and-leaf plot below shows the total caloric content of several main dishes.
Calculate the mean, median, mode and range.
6) The stem-and-leaf plot below shows the scores Leon received on each of his science quizzes. Use this data set to find the mode of all of Leon’s scores.
7) Carlos scored and 87, 95, 80 and 75 on his first four math tests. What must Carlos score on his fifth test if he wants to earn an 85% average?
ANSWER KEY:
COS 4: Express a pattern shown in a table, graph or chart as an algebraic expression: All linear equations are written in the form y = mx + b. The variable “m” represents the slope of the line (the slope represents the difference in y-values over the difference in x-values.) The “b” represents the “y-intercept” (this is the exact point where the line crosses the y-axis.)
x / y12 / 4
3 / 1
0 / 0
-6 / -2
1)
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Week(x) / Pieces of
Paper
(y)
1 / 165
3 / 95
4 / 60
5 / 25
2)
3)
4)
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5)
6)
COS 7: Determine transformations, including translations, reflections, or rotations, used to alter the position of a polygon on a coordinate plane.
Translations move on the coordinate plane horizontally and vertically.
Reflections are mirror images of the original polygon.
Rotations turn around a center point.
1) D – Be careful. C is also a reflection but it reflects across the y-axis, not the x-axis.
2) D – All translations can be represented by a rule. The rule for this translations is (x,y) →(x–5)
3) B
4) A – Be careful. Because the line is horizontal, students often choose x = 5. However; write the ordered pairs for the points on the line and you will notice the x is changing. It is the y that stays the same.
5) (x,y)→(x-2, y+6) It is x minus 2 because the figure is moving to the left which is a negative direction. It is y plus 6 because the figure is moving up which is a positive direction.
6) (x,y)→(x+6, y–3) It is x plus 6 because the figure is moving to the right which is a positive direction. It is y minus 3 because the figure is moving down which is a negative direction.
7) A – Be careful. Same as 4.
8) A
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COS 8 – Recognize geometric relationships among two-dimensional and three-dimensional objects.
1) C – The word exactly is very important. All the other figures have opposite sides that are parallel which really means they have 4 sides that are parallel. A trapezoid only has 1 set of parallel lines which means they only have 2 sides that are parallel.
2) D – The words not always are extremely important. Equilateral means all sides are equal to each other. Only a square has all sides equal. A rectangle has opposites sides equal. Therefore; that statement would not always be true if the congruent quadrilaterals (4-sided figure) were rectangles.
3) A – Be careful. A circle is not a polygon because it does not have sides.
4) A – Notice your side measurements and the right angle mark. If you turn the triangle on the right up and slide it over, both triangles will fit one on top of the other.
5) C – The word always is very important. A sphere is any type of ball. All types of balls are always similar in size.
6) B
7) C – Be careful. There is only 1 right triangle (the one on the left). The right angle mark on the inside of the triangle located on the right is only there to establish the height of the triangle.
8) B
COS 9 – Solve problems involving circumference and area of circles.
1) Since the measurement of the plate from the center to the edge represents a radius, use the formula (equation) for circumference that uses radius. C = π 2 r
C = 3.14 x 2 x 14
C = 87.92 cm (Choice B)
2) Use the area of a circle formula. Be careful!!!!! You can only use radius in this formula. The problem gives you diameter. Divide the diameter of 16 in half to get the radius of 8. Also, r2 means you multiply the radius times the radius, NOT the radius times 2. A = π r2
A = 3.14 x 8 x 8
A = 200.96 ft2 (Choice C because it is the closest)
3) Use the circumference formula (equation) that uses diameter. C = π d
C = 3.14 x 9
C = 28.26 yd (Choice B because it is the closest
4) Use the area of a circle formula. Be carefull!!!! You can only use radius in this formula. Use the width of the rectangle to get the diameter, then divide the diameter in half. The diameter is 5 inches. 5 ÷ 2 = 2.5
A = π r2
A = 3.14 x 2.5 x 2.5
A = 19.625 You have 3 circles so you have to multiply 19.625 x 3 = 58.88 (Choice B)
(5) This problem requires you to decide if you are computing the area or the circumference. The word around is extremely important. That word suggests that you are computing the circumference. Since they give you the diameter, use the formula (equation) that uses diameter. C = π d
C = 3.14 x 9.5
C = 29.83 ft. (Choice B)
6) Use area of a circle formula (equation). Again, you can only use the radius in this formula, therefore; you must divided the diameter of 8 in half to get 4. A = π r2
A = 3.14 x 4 x 4
A = 50.24mm (Choice C)
7) Use the formula (equation) for circumference of a circle with the radius. C = π 2 r
C = 3.14 x 2 x 17.5
C = 109.9 cm (Choice B)
8) You cannot put the fraction ½ in your calculator. Therefore; you have to use the decimal equivalent of 0.5. Use area of a circle formula (equation). A = π r2
A = 3.14 x 0.5 x 0.5
A = 0.785 in2 (Always round off to the hundredths place – the second decimal place. Look at the third decimal place to determine if you add one to the second decimal place. The third decimal place is 5, so add one to the 8 to equal 9. Final answer is 0.78 in2
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9) Always be prepared to find the radius or diameter if the problem gives you the circumference or area. Use the appropriate formula (equation). Fill in the numbers that you know. Then solve for the missing variable. Use the radius formula (equation) for circumference since the problem wants you to find the radius. Put the 37.68 under the C for circumference, bring down your 2 and replace π with 3.14.
C = 2 x π x r
37.68 = 2 x 3.14 x r
37.68 = 6.28r (draw your “river”) and divide both sides by 6.28
6.28 = 6.28
6 = r (Your radius is 6 cm)
10) Use the diameter formula (equation) for circumference since the problem wants you to find the circumference. Put 43.96 under the C for circumference, replace π with 3.14 and solve for the missing variable.
C = π d
43.96 = 3.14d (draw your “river”) and divided both sides by 3.14
3.14 3.14
14 = d (Your diameter is 14 m)
11) Use the area of a circle formula (equation). Put 379.94 under the A for area, replace π with 3.14 and solve for the missing variable.
A = π r2