Mrs. McHugh7th 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=

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Which equation is true for all pairs of values for x and y given in the table?

A) y = x B) –3y = x C) –x = y D) 3x = y 3 3

The table below shows the number of pieces of paper Eric has remaining after x weeks.

Week (x)

Pieces of Paper (y)

1 1653 954 605 25

Which equation represents the number of pieces of paper, y, Eric has remaining after x weeks?A) y = –5x + 170 B) x = –5y + 200 C) x = –35y + 200 D) y = –35x + 200

Which equation below best represents the total amount of water in the swimming pool at any given time as Jake emptied it?

A) y = 4800 – 30t B) y = – 30t C) y = t D) y = 30t – 600 30

x y12 43 10 0-6 -2

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Which equation below represents the distance completed for a given amount of time?

A) x = y ÷ 4 B) y = 4x C) x = 8y D) y = 8x

Which equation below best represents the total number of potatoes in a specified number of bags?

A) x = 15y B) x = 5 + 14y C) y = 15x D) y = 5 + 14x

A) c = 10 + t B) c = 10t C) t = 10 + c D) t = 10c

COS 7: Determine transformations, including translations, reflections, or rotations, used to alter the position of a polygon on a coordinate plane.

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A C

B D

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Which of the following diagrams shows the reflection of triangle MPN across the x-axis?

Using the diagram below which single transformation will move rectangle LONM to rectangle PSRQ?

A) Reflection across the x-axisB) Reflection across the y-axisC) Rotation of 90⁰ clockwise around (0,2)D) Translation of 5 units left

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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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Using the diagram below, which single transformation will move triangle IJK to triangle IGH?

A) A rotation of 270⁰ clockwise around point I.B) A rotation of 90⁰ clockwise around point I.C) A rotation of 180⁰ clockwise around point I.D) A rotation of 90⁰ counterclockwise around point I.

Using the diagram below, which transformation(s) will move polygon LMNOP to polygon FGHIJ?

A) Reflection across the line y = 5B) Reflection across the line x = 5C) Reflection across the line y = 7 and translation 3 units downD) Reflection across the line x = 5 and translation 3 units down

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A C

B D

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Using the diagram below, which single transformation will move quadrilateral PQRS to quadrilateral PTUV?

A) Reflection over the line y = –3B) Reflection over the line y = –5C) Rotation of 180⁰ clockwise about (–5, –3)D) Translation 6 units down

Triangle LMN becomes triangle XYZ after a translation of 7 units to the left and a reflection across the x-axis. Which of the following shows these transformations?

COS 8 – Recognize geometric relationships among two-dimensional and three-dimensional objects.

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Which of the following quadrilaterals has exactly two sides that are parallel?

A) Rhombus B) Rectangle C) Trapezoid D) Parallelogram

The quadrilaterals LMNO and HIJK are congruent. Which of the following statements about the quadrilaterals is not always true?

A) They have equal corresponding angles.B) They are both the same size.C) They are both the same shape.D) They are equilateral.

What do the three figures shown below have in common?

A) They all have lines of symmetryB) They are all equilateralC) They are all congruentD) They are all polygons

Which is true about the two triangles below?

A) They are congruent triangles.B) They are equilateral triangles.C) They are isosceles triangles.D) They are acute triangles.

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v b nx hdru0065

Page 7 of 19COS 9 – Solve problems involving circumference and area of circles.

Which of the following three-dimensional objects are always similar?

A) Square pyramids B) Rectangular pyramids C) Spheres D) Cylinders

Which term does not apply to the figure below?

A) Rhombus B) Square C) Quadrilateral D) Parallelogram

How are figures R and S the same?

A) Both are congruent polygonsB) Both are regular polygonsC) Both have acute anglesD) Both have obtuse angles

Which statement is true for the figures shown below?

A) Both figures have two sets of opposite angles that are congruent.B) Both figures have two obtuse angles.C) Both figures have two right angles.D) Both figures have two sets of opposite sides that are congruent.

1) Brian is measuring one of his family’s round dinner plates so that he can buy more plates of the same size. Hefound 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

Page 8 of 195) 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, insquare 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.

A) 4 B) 7 C) 11 D) 14

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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, and10.8 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?

What is the least amount of rope, in meters, she will need to place around the playground?A) 27.85 B) 30.25 C) 40.80 D) 41.05

A) 8 B) 16 C) 32 D) 64

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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, 97Which 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?

Page 11 of 195) 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.)

1) Step 1: Subtract the y-values. 4-1 = 3 (this is the numerator for the slope).Step 2: Subtract the x-values. 12 -3 = 9 (this is the denominator for the slope).The slope fraction is 3 Simplify to 1 9 3.Step 3: The y-intercept is the value of “y” when “x” = 0 (highlighted in yellow).Substitute the values into the linear equation y = mx + b y = 1 x + 0 3

x y12 43 10 0-6 -2

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Step 1: Subtract the y-values. 4-1 = 3 (this is the numerator for the slope).Step 2: Subtract the x-values. 12 -3 = 9 (this is the denominator for the slope).The slope fraction is 3 Simplify to 1 9 3.Step 3: The y-intercept is the value of “y” when “x” = 0 (highlighted in yellow).Substitute the values into the linear equation y = mx + b y = 1 x + 0 3

Step 1: Subtract the y-values. 165-95 = 70 (this is the numerator)Step 2: Subtract the x-values. 1- 3 = –2 (this is the denominator)The slope fraction is 70 Simplify to 35 or –35. This is the coefficient of “x” –2 –1Notice the values of “y” are decreasing by 35 each week, and the value of “x” is increasing by 1 each week. Therefore; to find the value of “y” when “x” equals 0, go backwards. Before week 1 you had week “0” or the beginning of the project. Since the “Pieces of Paper” are decreasing by 35 each week, if you add 35 + 165 = 200 you find out how many pieces of paper you had at the beginning. Therefore; when x = 0, y = 200. This is you “y-intercept” or the “b” part of the equation.Your equation then becomes y = –35x + 200 Choice D.Strategies: You can eliminate Choices B and C because they begin with “x” and not “y”. You then have to calculate the rest as described above to figure out which one of A or D is correct.

Look at the “y” and “x” axis to determine the intervals. The y-axis changes by 600 each time, the x-axis (written as t-axis in this problem) changes by 20 each time. Therefore; your fraction is 600 Simplify to 30 or 30. This is the 20 1coefficient of “x”. The line crosses the y-axis at 4800. This is your y-intercept or “b”. The graph shows you that the line is decreasing. Therefore; you equation is y = 4800 – 30x (Choice A).

Week (x)

Pieces of Paper (y)

1 1653 954 605 25

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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.

Translations move on the coordinate plane horizontally and vertically.

Step 1: Subtract the y-values 4–8 = –4 (this is the numerator)Step 2: Subtract the x-values 0.5–1.0 = –0.5 (this is the denominator)The slope of the fraction is – 4 Simplify (Remember, a fraction is a –0.5division problem. Therefore; if you put –4 ÷ –0.5 into your calculator, you will come out with 8. This is the coefficient of x. Your equation is y = 8x Choice D. Strategy: Eliminate A and C because they begin with x= instead of y=.

The y-axis increases by 75. The x-axis increases by 5. Therefore; your slope fraction becomes 75 Simplify to 15 or 15. This is the coefficient for x. 5 1If you look at the graph, when x = 0, y also = 0. Therefore; your equation isy = 15x + 0. Since we don’t need the plus 0, you can simplify to y = 15x (Choice A).Strategy: You can eliminate Choices A and B because they begin with x=.

They are using the variable “c” instead of “y” and “t” instead of “x”.The y-axis increases by 150. The x-axis increases by 15. Therefore; your slope fraction becomes 150 Simplify to 10 or 10. This is the coefficient for x. 15 1If you look at the graph, when x = 0, y also = 0. Therefore; your equation isc = 10t + 0. Since we don’t need the plus 0, you can simplify to c = 10t (Choice B).Strategy: You can eliminate Choices C and D because they begin with t=.

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) B4) 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

Page 14 of 19COS 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) B7) 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 closest4) 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 = 2.5A = 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

Page 15 199) 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 r37.68 = 2 x 3.14 x r37.68 = 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 d43.96 = 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

379.94 = 3.14 r2 (draw your “river) and divide both sides by 3.14 3.14 3.14 √121 = √r2 (NOTICE!!! This is r2 not r. You have to get the square root (√) of both sides to get the radius. 11cm = r

12) Use the area of a circle formula (equation). Put 314 under the A for area, replace π with 3.14 and solve for the missing variable.A = π r2

314 = 3.14r 2 (draw your “river” and divide both sides by 3.143.14 = 3.14

√100 = √r2 (NOTICE!!! This is r2 not r. You have to get the square root (√) of both sides to get the radius. 10m = r (This problem wants the diameter so you have to multiply 10 x 2 to get your final answer.)10 x 2 = 20 m This is the diameter.

COS 10: Calculate the perimeter of polygons and the areas of triangles and trapezoids.

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4) Choice C 48 in. You have to apply your knowledge of a regular polygon. A regular polygon means all sides are equal to each other and all angles are equal to each other. You also need to know how many sides are in a hexagon (remember, I told you to match the “x” in hexagon with the “x” in the number 6. Therefore; a hexagon is a six-sided figure. You must add 8 + 8 + 8 + 8 + 8 + 8 = 48.

5) Choice B 84 m2

To get the perimeter of the parallelogram, you have to complete the measurements of the sides. The side opposite 3 cm is also 3 cm. The side opposite 4 cm is also 4 cm. The total of the perimeter is 3 + 3 + 4 + 4 = 14 cm.Choice D

You have to determine if you are required to find the area or the perimeter. The word around suggests that it is the perimeter. Do not let the words least amount throw you off. It really means the exact amount. Add 13.2 + 17.05 + 10.8 = 41.05 m. Choice D

You have to apply your knowledge of a square (all sides are equal). To compute the perimeter, you must complete the measurements for the three remaining sides. Since all sides are equal, add 8 + 8 + 8 + 8 = 32. Choice C. Be careful!!!!. Notice your choices. Choice A assumes you will see the 8 listed by itself and choose that answer. Choice B assumes you will only fill in one side and add 8 + 8. Choice actually computes the area of the square. You must pay attention!!!!!

Use the formula (equation) for area of a trapezoid. It is very important that you get the correct height and bases. If you mix up the height with one of the bases, you will get the wrong answer. To assure that you get the correct height and bases, look at the right angle marks. The right angle mark on the left touches the 12 and the 9. The right angle mark on the right touches the 12 and the 5. Since both right angle marks touch the 12, that is your height. The 9 and the 5 are your bases. Use the formula (equation) A = .5 h (b1 + b2) A = .5 x 12 (9 + 5) Use order of operations. Solve the parentheses first. A = .5 x 12 x 14 A = 84 m 2

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9) Focus on the words regular pentagon. Remember, a regular pentagon has equal sides and equal angles. You must know that a pentagon is a 5 sided polygon. If each side measures 6.5 centimeters, then add 6.5 + 6.5 + 6.5 + 6.5 + 6.5= 32.5 cm.

10) If the wall is shaped like a trapezoid, use the area of a trapezoid formula (equation). The bases are the top (9.5 ft) and bottom (22.5 ft) of the wall. The word tall refers to the height (8 ft) of the wall. Complete the formula (equation).A = .5 h (b1 + b2)A = .5x 8 (9.5 + 22.5) Use order of operations and solve the parentheses first.A = .5 x 8 x 32A = 128 ft2

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.

Use the Area of a trapezoid formula (equation). Again, focus on the right angle mark. The one at the bottom touches the 3 in the middle and the 5 at the bottom. You can draw a right angle mark at the top. It will touch the 3 in the middle and the 3 at the top. Both right angle marks touch the 3 in the middle so that is your height. The 3 at the top and the 5 at the bottom are your bases.A = .5 h (b1 + b2)A = .5 x 3 (3 + 5) Use order of operations. Solve the parentheses first.A = .5 x 3 x 8A = 12 in2

Before you can find the perimeter, you must complete the measurements of the missing sides. Draw lines to make the figure look like a rectangle. You know the left side equals 18 cm. You also know the 8cm is the same length as the vertical line that you drew. If you subtract 18 – 8 = 10 cm, that is the measurement of the missing part. If you look at the horizontal line that you drew, its measurement matches the 12 cm. Imagine sliding that line down to the bottom and joining it with the 4 cm. This will give you the total of the missing measurement at the top ( 4 + 12 = 16). Now you can add all of your sides. 18 + 4 + 8 + 12 + 10 + 16 = 68 cm.

The shape is a triangle so you must use the area of a triangle formula (equation). A = .5bh. Slide the 6 ft dotted line at the left under the 6 ft dotted line at the right. Together, those two lines add up to 12 ft. Draw a right angle mark at the bottom of that line. The right angle mark touches the 12 and the 24. That is your height and base. Complete the formula. A = .5 b h A = .5 x 24 X 12 A = 144 ft 2

Mean is your average. To compute it, you add all of your numbers together and divide by the total pieces of data that you have.Median is your middle. Put your numbers in numerical order and eliminate a number from each end until you get to the middle. If you have an even set of data, there will be 2 numbers in the middle. Get the mean (average) of those 2 numbers (add the 2 numbers together and divide by 2). If you have an odd set of data, there will only be 1 number in the middle. That will be your median.Mode is the number that occurs (repeats itself) most often. It is possible to have more than one mode if you have more than one number that repeats itself the same amount of times. If you have no mode, be sure to write “none” or “no” mode. If you put 0 mode, it suggests that 0 is part of your data.Range is the difference (subtract) between the largest number and the smallest number.

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2) 88, 70, 84, 93, 84, 97

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4) To calculate the range, subtract the smallest number from the largest number in your data set. 412 – 72 = 340

181, 256, 301, 72, 97, 412

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The numbers are read as 14, 18, 19, 19, 20, 23, 26, 28, 28, 35, 35,37, 38, 39, 41, 41, 41, 46, 47, 52, 52, 53. To get the median, cross out the numbers beginning with the smallest number and largest number as shown. You have an even set of data, so you will have two numbers in the middle. Add 35 + 35 = 70 then divide by 2. 70 ÷ 2 = 35. 35 is you median.

You must compute the mean, median and mode and compare your results to the answer choices. Always put your numbers in numerical order from least to greatest. 70, 84, 84, 88, 93, 97Mean: 70 + 84 + 84+ 88 + 93+ 97 = 516 ÷ 6 = 86Median: This is an even set of data so you will have 2 numbers in the middle. Add 84 + 88 = 172 ÷ 2 = 86 This is your median.Mode: 84 repeats itself the most so it is your mode. Compare your answers to the choices. The correct response is C – The mean and the median are the same.

To calculate the mean, add the numbers and divide by 5 because you have 5 pieces of data. 788 + 872 + 1014 + 935 + 961 = 4570 ÷ 5 = 914.

Remember, the numbers are read as 116, 120, 127, 129, 182, 184, 184, 184, 189, 189, 218, 219. To find the mean, add all the numbers and divide by 12 because you have 12 pieces of data. 116 + 120 + 127 + 129 + 182 + 184 + 184 + 184 + 189 + 189 + 218 + 219 = 2041 ÷ 12 = 170.08333 (round off to the nearest hundredth – the second decimal place. Look at the third decimal place, it is 3. It is less than 5 so you don’t add anything to the 8. Drop everything else.Your Mean is 170.08Median – You have two numbers in the middle because you have an even set of data. Add the numbers and divide by 2. 184 + 184 = 368 ÷ 2 = 184Your Median is 184Mode – 184 repeats itself the most, so 184 is your mode.

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7) If Carlos wants to have an 85% average in his math class and he has a total of 5 tests, multiply 85 times 5 to get the total number of points Carlos must earn. 85 x 5 = 425. Now subtract the total points from all tests that Carlos has already taken. 87 + 95 + 80 + 75 = 337. Now subtract the 337 from the 425. 425 – 337 = 88. Carlos must score an 88% on his fifth test in order to have an 85% average in the class.

GOOD LUCK! STUDY HARD! HAVE A GREAT DAY!

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Remember, the numbers are read as 116, 120, 127, 129, 182, 184, 184, 184, 189, 189, 218, 219. To find the mean, add all the numbers and divide by 12 because you have 12 pieces of data. 116 + 120 + 127 + 129 + 182 + 184 + 184 + 184 + 189 + 189 + 218 + 219 = 2041 ÷ 12 = 170.08333 (round off to the nearest hundredth – the second decimal place. Look at the third decimal place, it is 3. It is less than 5 so you don’t add anything to the 8. Drop everything else.Your Mean is 170.08Median – You have two numbers in the middle because you have an even set of data. Add the numbers and divide by 2. 184 + 184 = 368 ÷ 2 = 184Your Median is 184Mode – 184 repeats itself the most, so 184 is your mode.

Remember, the numbers are read as 57, 63, 69, 70, 76, 82, 84, 84, 95, 96, 97. The number 84 repeats itself the most, so that is your mode.