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Grade Review for Math

Day 1

Question #1

 John’s test grades were: 76, 82, 95, 82, 78, 96, 91. His math teacher will allow John to choose the measure of central tendency to be used for his test grades. Which measure should John choose? Why?

 Mean because it is the highest value

Question #1 Explanation

 Calculate the mean, median, mode, and range to determine which has the highest value  Remember the mean is the average; add all of the numbers and divide by how many there are  Remember the median is the number in the middle (put them in order first)  Remember the mode is the number that is the most often  Remember the range is the highest minus the lowest

Question #2

 If y > 2x + 7 and y > 2x + 7 were each graphed a number line, explain the difference between the two graphs.

Day 2

 y > 2x + 7 will have an open circle, y > 2x + 7 will have a closed circle

Question #2 Explanation

 Graphing inequalities:  less than (<) and greater than (>) signs are an open circle because the number is

NOT

included in the solution set  less than or equal to (<) and greater than or equal to (>) are a closed circle because the number

IS

included in the solution set

Day 3

Question #3 and #4

  Name at least two 3-dimensional figures for which a circle could be the base.

Cone and Cylinder   Translate into an equation and solve: Eight more than a number is twenty seven.

n + 8 = 27 n = 19

Question #3 and #4 Explanation

Question #3:  The base of both a cone and a cylinder is a circle Question #4:  Replace the following words with the correct symbol  The words “more than” mean add   The words “a number” mean a variable The word “is” means equal  Re-write the statement using the numbers and symbols  Solve the equation by doing the inverse operation

Day 4

Question #5

 A basket of 25 peaches weighs 232 ounces. After 10 peaches are removed, the basket weighs 9 ½ pounds. How much does the basket weigh in ounces?

 152 ounces

Question #5 Explanation

 There are 16 ounces in a pound. Multiply the number of pounds that the basket weighs by 16. This will give you the number of ounces that the basket weighs.

 The 25 peaches weighing 232 ounces is extra information.

IGNORE IT!!

Day 5

Question #6

 In Pollville, records are kept on previous mayors. Here are the ages of the last 6 mayors when they were voted into office: 45, 88, 37, 42, 41, 44. How does the outlier affect the mean?

 The mean is 7.7 points higher with the outlier than without.

Question #6 Explanation

 First identify the outlier; the number that is a lot bigger or a lot smaller than the other numbers. In this case the outlier is 88.

  Cross out the outlier. Find the mean again without the outlier. Write that number down.

 Using all of the numbers find the mean (add all of the numbers and divide by how many there are). Write that number down.

Subtract the 2 means. That is the affect of the outlier.

Day 6

Question #7 and #8

    A triangle is graphed on a coordinate grid on which each unit is a centimeter. It has vertices at points (2, -8), (2, 5), and (-4, 5). Find its area.

39 centimeters squared Translate into an equation and solve: A number added to eight equals five.

8 + n = 5 n = -3

Question #7 and #8 Explanation

 Question #7:  Draw a coordinate plane and graph the triangle.

 Find the area of the triangle (1/2 base x height)  To find the base and the height, count the number of units across (base) and up (height).

    Question #8: Replace the following words with the correct symbol   The word “added” means add The words “a number” mean a variable Re-write the statement using the numbers and symbols Solve the equation by doing the inverse operation

Day 7

Question #9

  Mrs. Adams is building a miniature table for a dollhouse. The table will be a scale model of her dining room table. The top of her table measures 36 inches wide and 72 inches long. If the width of the miniature table will be 1.5 inches, what will be its length?

Length = 3

Question #9 Explanation

 Make a table:

Length Width Table

72 36

Model

1.5

  Write the information as a proportion.

Cross multiply and divide

Day 8

Question #10 and #11

    Unit Five starts on page 126 and ends on page 241. How many pages long is the unit?

115 pages long Translate into an equation and solve: The product of five hundredths and a number is 11 .05n = 11 n = 220

Question #10 and #11 Explanation

 Question #10  The words “how many long” mean subtract  Subtract the two numbers to find the length of the unit     Question #11 Replace the following words with the correct symbol  The words “product of” mean multiply   The words “a number” mean a variable The word “is” means equal Re-write the statement using the numbers and symbols Solve the equation by doing the inverse operation

Day 9

Question #12

 Write an algebraic expression to explain the pattern: 2, 5, 11, 23, ____. ____, ____  2x + 1

Question #12 Explanation

 Ask yourself: how am I getting from each number to the next?

 Make a list of all of the ways you can get to the next number  Are you adding, subtracting, multiplying, dividing or a combination of the operations?

 The answer is the one that works

EVERY

time!

Day 10

Question #13

 The lengths of the sides of a 5 m by 5 m square are increased by 3 m. The area of the square has increased by what percent?  156%

Question #13 Explanation

 This is a Percent of Change Question!

 Find the area of the square.

 Add three to each side.

 Find the area of the square again.

 Subtract the two areas; put that number as the numerator  Put the first area as the denominator  Convert the fraction to a percent  Divide bottom into top and move the decimal point 2 places to the right.

Day 11

Question #14

 The supply purchasing agent for Carowinds has a formula which tells her how much sugar to buy when she knows how much cotton candy will be sold: s = 40 + 0.125c

c = cotton candy sales s = pounds of sugar  On a day when 8,000 people purchase cotton candy, how much sugar should be purchased?

1040 pounds

Question #14 Explanation

  Write the formula that they give you Replace the variable with the given numbers  Solve the equation by doing the inverse operation

Day 12

Question #15 and #16

    Which is a better buy: a 14 ounce box of popcorn for $1.98 or a 36 ounce box of popcorn for $2.59? 36 ounces for $2.59

Translate the equation into words: 15x + 11 = 56 Eleven more than fifteen times a number is fifty six

Question #15 and #16 Explanation

    Question #15:  Find the unit price  Divide the price by the number of ounces  The lower price is the better buy Question #16: Replace the symbols with the correct words   When a number is right next to a variable it means multiply, so use a multiplication key word Use the words “a number” for the variable   Use an addition key word Use a key word for equals Re-write the equations using words

Day 13

Question #17 and #18

    A soccer ball is usually priced at $16. It is on sale for 25% off and a 6% sales tax must be added to the price. How much will the customer pay for the soccer ball?

$12.72

Write and solve the equation: The cost, c, of a CD is twice the cost of a $7 tape. What is the price of the CD?

c = 2($7) c = $14

Question #17 Explanation

  When an item is on sale:  Multiply the price and the percent off (remember to change the percent to a decimal by moving the decimal point 2 places to the left)  The answer will be the amount of money saved: subtract this number from the original price To find sales tax:  Multiply the price and the tax (change the percent to a decimal)  The answer will be the amount of tax: add it to the original price

Question #18 Explanation

   Replace the following words with the correct symbol   The “c” is the variable The word “twice” means 2 times Re-write the statement using the numbers and symbols Solve the equation

Day 14

Question #19 and #20

 A number has been decreased by 12. The result is –5. Find the original number.

  7 Mrs. Math asked her student, Molly, to tell which was greater: 80% or 4/5 or 0.8

Molly said that they were all equal. Explain why or why not Molly is correct.

 If you convert them to the same type of rational number they are equal

Question #19 and #20 Explanation

  Question #19:     The words “a number” means a variable The words “decreased by” means subtract Re-write the statement using the numbers and symbols Solve the equation by doing the inverse operation Question #20:  Convert each unit to the same unit: a fraction, a decimal, or a percent.

 Put them in numerical order and compare

Day 15

Question #21

  The scale on a map is 1 inch:30 miles. Westboro, Malden, and Oxbridge are all located on Route 2 and Malden is between Westboro and Oxbridge. On the map, the distance from Westboro to Malden is 2.5 inches and the distance fro Westboro to Oxbridge is 5.75 inches. How far, in miles, is Malden from Oxbridge?

247.5 miles

Question #21 Explanation

 This is a scale factor question!

 You are converting from a small unit to a large unit so you are going to divide:  Divide the distance between the two cities (in this case 8.25 inches; you have to add the two distances they give you) by the scale factor (in this case 1/30.

 Remember the scale factor is a fraction so you need to Keep Change Flip!

 This will give you the total distance in miles.

Day 16

Question #22

 A stadium seats 40,000 people. Tickets were $12 each and 24,000 seats were sold. What percent of the stadium was full? How much money was collected?

 60% full and $288,000 collected

Question #22 Explanation

 This is a ratio/percent question:  Write the number of seats as a ratio: Number of seats full : Total number of seats  Convert this ratio to a percent by dividing bottom into top and moving the decimal point 2 places to the right  To find the amount of money collected:  Multiply the number of full seats (24,000) by the cost of the ticket ($12)

Day 17

Question #23

    Investigate the Data

Ages of 24 Night Class Students

2 3 5 5 8 3 0 1 2 2 4 4 4 4 5 6 6 7 8 8 9 4 1 3 3 8 A) Find the mean, median, and mode of the data set.

B) Name the range, lower extreme, upper extreme, first quartile, and third quartile of the data.

C) What percent of the data is represented by the box in the box-and-whisker plot?

A) 34.6, 34, 34 B) 25, 23, 48, 31, 38 C) 56.5%

Question #23 Explanation

  A)  Calculate the mean by adding all of the numbers and dividing how many numbers there are  Find the median (the number in the middle) and the mode (the number that is most often) B)  Calculate the range by subtracting the biggest and smallest numbers  Find the lower extreme (the smallest number) and the upper extreme (the largest number)  Find the first quartile (the median of the bottom half of data, or the numbers before the median) and the third quartile (the median of the upper half of data, or the numbers after the median.

Question #23 Explanation Continued…

 C)  To find the percent of the data represented by the box in a box and whisker plot:  Count how many numbers there are from the first quartile to the third quartile; write this number as the numerator.

 Write the total number of values as the denominator  Convert the fraction to a percent by dividing bottom into top and moving the decimal point 2 places to the right.

Day 18

Question #24

  Tammy was paid $5 an hour for washing cars. She worked 3 hours on Friday, 9 hours on Saturday, and 5 hours on Sunday. Materials cost her $32.75. How much money did she make after expenses?

$52.25

Question #24 Explanation

 Calculate the total number of hours that Tammy worked  Add the number of hours for each day  Multiply the number of hours by the amount of money that she earns per hour  Subtract the amount of money needed for expenses from the amount of money she earned  This will be her earnings after expenses.

Day 19

Question #25

  Jason bought a car for $3,500. He sold his truck for $1,500 which he used as a down payment. The remaining amount was borrowed at 4.5% interest for 5 years. How much interest will he pay?

How much will his total repayment be?

$450 $2,450

Question #25 Explanation

 This is a Simple Interest Question:  First you have to find the Principle amount  Subtract the cost of the truck and his down payment  Write the formula: I = P x R x T  Replace the letters with the values from the question and do the math.

 This will be the interest  Add the interest to the principle to find the total amount he has to repay to the bank

Day 20

Question #26

  The surface area, SA, of a sphere is found using the formula: SA = 4  r² , where r is the radius of the sphere. Find the surface area of a sphere with a radius of 2.5 inches.

78.5 square inches

Question #26 Explanation

 On the EOG you will be given formulas that you are not familiar with…don’t worry, just replace the letters with the numbers they give you and do the math!

Day 21

Question #27

  Martha entered the elevator and went down seven floors, up ten floors, up two floors, then down five floors. She was then on the eleventh floor. On what floor did she enter the elevator?

Eleventh floor

Question #27 Explanation

 This is a Negative Numbers Question:  Re-write it as a number sentence and do the math (remember down is a negative number and up is a positive number): -7 + 10 + 2 – 5  This number sentence equals 0 so the elevator is still on the same floor!

Day 22

Question #28

 The Jones family rented a car for 3 days of their vacation. The rental charge was $21.95 per day plus $0.17 per mile. If the bill was $96.96 before taxes, write and solve an equation to find the number of miles, m, they drove  3(21.95) + 0.17m = 96.96 183 miles

Question #28 Explanation

   Replace the following words with the correct symbol   The word “per” means multiply The word “was” means equal Re-write the statement using the numbers and symbols Solve the equation using inverse operations

Day 23

Question #29

 A brownie pan has dimensions of 8 inches by 4 inches by 2 3/5 inches. Compute the volume of the pan. Express your answer in decimal form. If the batter is 1.75 inches deep, what percent of the pan is filled with brownie batter?  83.2 cubic inches 67.3% full

Question #29 Explanation

 First find the volume of the pan by using the formula: Bh (the area of the base x the height or length x width x height)  Next find the volume of the batter by multiplying the area of the base of the pan (length x width) by the height of the batter  Finally write a fraction using the volume of the batter as the numerator and the volume of the pan as the denominator  Convert the fraction to a percent by dividing bottom into top and moving the decimal point 2 places to the right.

Day 24

Question #30

  The Wiley family went to Pizza Place for dinner. They bought two pizzas for $12.95 (tax included) each. Mr. Wiley wanted to add a 20% tip to the bill. What was the total cost of the dinner?

$15.54

Question #30 Explanation

 To find the amount of a tip:  Multiply the cost of the meal and the percent (remember to change the percent to a decimal by moving the decimal point 2 places to the left)  To find the total cost of the meal add the cost of the meal and the tip

Day 25

Question #31 and #32

    A goat is tied to a corner of a 60 ft by 75 ft barn in the center of a grassy field. His rope is 50 ft long. Approximately how much area does he have to graze? 7,850 square feet Roger babysits 4 ¾ hours each Saturday and each Sunday. He plans to babysit for 3 ½ weekends next month. What is the total number of hours he will babysit next month?

33 ¼ hours

Question #31 Explanation

  Question #31: This is the area of a circle question:  Write the formula: 3.14 x radius x radius  Replace the words with the numbers and do the math  The size of the barn is extra information:

IGNORE IT!!

Question #32 Explanation

 A weekend it 2 days: Saturday and Sunday so a half of a weekend would be 2 day.

 Calculate the number of hours worked in a weekend by adding the number of hours for Saturday and Sunday.

 Multiply by 3 ½ to get the total number of hours for 3 ½ weeks

Day 26

Question #33

 Ali is going to paint her school’s basketball court. How many square feet of area does she need to paint if the court is 384 inches long and 108 inches wide?

408 square feet

Question #33 Explanation

 To find area of a rectangle: multiply length times width HOWEVER- the question wants the answer in feet so you have to divide each measurement by 12 first:    384/12 = 32 feet 108/12 = 15 feet After you have converted the measurements then multiply:  32 x 15 = 408 square feet

Day 27

Question #34

 The 7 th grade students were voting on locations for a class trip. Two-ninths voted to go to the zoo and four-sevenths voted to go to an amusement park. If there are 250 students: How many voted to go to the zoo?

56 How many voted to go to an amusement park?

143 How many students did not vote?

51

Question #34 Explanation

      To find fractional parts: multiply the total number of students by each fraction: 250 x 2/9 = 55.555 = about 56 students 250 x 4/7 = 142.857 = about 143 students So: 56 students voted for the zoo 143 students voted for an amusement park To find the number of students who have not voted: add 56 + 143 = 199 then subtract 199 from 250: 250 – 199 = 51 So 51 students did not vote

Day 28

Question #35

 Stan has just started a new job. In the first week he is paid $7 an hour plus a $50 bonus. How much money does he make in the first week if he works 32 hours?

$274

Question #35 Explanation

 Stan makes $7 an hour for each of the 32 hours so multiply the number of hours by the dollar amount:    32 x 7 = 224 Then add the bonus: 224 + 50 = 274 So Stan makes $274 the first week

Day 29

Question #36

 Monica makes 3 times as much money as George. If Monica make $5.52 an hour how much does George make. Write an equation to solve this problem.

$1.84

Question #36 Explanation

 Equation: 3g = $5.52

 Monica make 3 times George which is equal to $5.52  Solve the equation:  Divide both sides by 3 to get the g by itself  5.52/3 = 1.84

 So George makes $1.84

Day 30

Question #37

 A 52 foot light post casts a shadow that is 72 feet long. At the same time a lighthouse casts a shadow of 180 feet long. How tall is the lighthouse?

130 feet tall

Question #37

     Write a proportion: Height of lamp post = Height of lighthouse post shadow lighthouse shadow Plug in the numbers:  52 = ?

72 180 Cross multiply and divide:  180 x 52 =9360  9360/72 = 130 So the lighthouse is 130 feet tall