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Name: ________________________________ Date: ________________________

.…BLM 1–8.…1.1

For #1 to #5, choose the type of graph that best completes each sentence.

bar graph circle graph double bar graph line graph pictograph

1. Uses symbols to represent data ____________________

2. Compares one set of data using bars ____________________

3. Compares categories to the whole using percents ____________________

4. Compares two sets of data across categories ____________________

5. Shows changes in data over time ____________________

For #6 and #7, choose the type of graph you would recommend to represent each situation. Justify your choice.

a) Type b) Justification6. Ray wants to compare the percent of

students who go home for lunch to the percent of students who have lunch at school.

circle graph or bar graph

7. Ben’s mother has put marks on a wall to track his growth since he was three years old.

pictograph orline graph

8. The table shows Jessica’s pulse rate in 30-s intervals during exercise.

Time (s) 0 30 60 90 120Number of Beats 61 82 94 110 120

a) Which type of graph would best display these results? Explain why._____________________________________________________________

b) Draw the graph.c) If you recorded your pulse rate after exercise, could you add your results to

the graph you drew? Explain.__________________________________________________________________________________________________________________________

1.2 Copyright © McGraw-Hill Ryerson, 2008

Name: ________________________________ Date: ________________________

.…BLM 1–8.…(continued)

1. Describe two ways that the format of a graph can be misleading. a) ______________________________________________________________b) ______________________________________________________________

2. This graph shows the number of houses sold in one month by two real estate companies.a) According to the graph, how many houses did

each company sell? ____________________________________________________________

b) From the graph, which company appears to have sold many more houses? ____________________What part of the graph has been distorted to create this impression? __________________________________________________________________________________________________________________________

c) How should the graph be redrawn to represent the house sales more accurately? _____________________________________________________________

d) Write an accurate conclusion about the house sales. _____________________________________________________________

3. Christy and her friends like three different rock bands: The Stones, The Pebbles, and The Boulders. Christy surveys her classmates about their favourite one of these bands. She records the data.

Band VotesThe Stones 8The Pebbles 6The Boulders 5

a) Draw a graph to make it appear that The Stones are much more popular than the other two bands.

b) Explain how your graph distorts the data._____________________________________________________________

1.3

1. This graph shows how students get to school.

Copyright © McGraw-Hill Ryerson, 2008

Name: _________________________________ Date: ________________________


a) Is a pictograph effective to display the data about how students get to school? Explain.

b) Is the data represented accurately? Explain.c) What improvement(s) do you recommend for

representing the data?d) Is the graph informative? Make a suggestion

for making it more informative.e) Recommend another type of graph to represent the data. Give an

advantage of using this graph.

2. The school librarian wants to order books basedon the most popular genres. After recording the book loans for a period of two months, she presented the data in a circle graph. a) Is this graph an effective way to help the librarian

order books based on popular genres? Explain. b) If the librarian displayed the data on a bar graph,

what information would be communicated more easily?

3. Critique this graph using the three factors you learned about in this section. In your critique, suggest any improvements to the graph.

Use a table such as the one shown here to organize your answer.

Factor Critiquea) b) c)

2.1

1. Decide whether each of the following is true or false. If it is false, rewrite the statement to make it true.


Name: ________________________________ Date: ________________________


a) True/False A part-to-whole ratio compares different parts of a group to each other. ___________________________________________________________

b) True/False The ratio 3 : 1 can also be written as 1 to 3.___________________________________________________________

c) True/False A part-to-whole ratio can be written as a fraction, a decimal, and a percent.___________________________________________________________

d) True/False Two-term and three-term ratios compare quantities measured in different units.___________________________________________________________

2. Fill in the box to make an equivalent fraction.

a) b) c) d)

For #3 to #5, fill in the missing values in the table. a) Show the ratio in two ways. b) Show the fraction in lowest terms. c) Convert to a decimal. d) Convert to a percent.

a) Ratio b) Fraction c) Decimal d) Percent

Example: 6 to 30 or 6 : 30

0.2 = 0.20 = 20%

3. 10 to 15 or _____

4. _____ or _____

5. _____ or _____ 0.9 = 0.90 = 90%

2.2

1. Identify each of the following as a ratio, a rate, or a unit rate. Example: 110 km in 12 h rate


Name: _________________________________ Date: ________________________


a) 12 marks out of a total of 20 marks b) 25 cars sold in 5 daysc) 25 L of gas used to travel 390 km d) 8 m per min

2. Determine the unit rate in each situation.Example: There were 180 people on 3 buses. people per busa) 15 hours of TV in 3 days b) 282 tickets sold in 6 nights

For #3 and #4, do the following for each product: a) and b) Calculate the unit price of each brand. Show your work. c) Identify the best buy.

Itema) Unit Price

Brand Ab) Unit Price

Brand Bc) Best

Buy

Example: Salsa (425 mL)

2 for $6.49 = $3.25 3 for $8.99 = $3 Brand B

3. Plastic wrap (30 m) 8 rolls for $20 $29.40 for 12 rolls

4. Fruit juice (355 mL) 6 pack for $4.68 4 pack for $3

5. Calculate the fuel efficiency of each car. Show your work. For Step 1, calculate the litres of fuel used per kilometre. Give your answer

to the nearest ten-thousandth. For Step 2, multiply the unit rate by 100. Round to the nearest hundredth.

CarDistance

(km)Fuel Used

(L)Step 1: Unit Rate

(L/km)

Step 2: Fuel Efficiency (L/100

km)

Example: 248 20 0.0806 × 100 = 8.06 L/100 km

a) Car A 639 45

b) Car B 688 80

2.3 Provide answers for #1 and #2 in your notebook.1. Determine the unit rate. Include the units.


Name: ________________________________ Date: ________________________


a) It takes three hours to travel 240 km. b) Ten copies cost $1.20.c) Six classes have 168 students. d) The plant grew 108 mm in nine

days. 2. Write the operation and the number to use for solving the proportion.

Examples: Multiply the numerator and denominator by 4.

Divide the numerator and denominator by 5.

a) b) c) d)

3. Determine the value of each variable in #2.a) s = _____ b) r = _____ c) y = _____ d) x = _____

For #4 and #5: a) Set up a proportion using a variable (x).b) Determine the value of the variable.c) Write a concluding statement. Remember to include the units.

Item a) Proportion b) Value c) Statement Example: 5 T-shirts cost $62.50. How much will 15 T-shirts cost?

x = 187.5 Fifteen T-shirts will cost $187.50.

4. The ratio of boys to girls at a music concert was 3 to 5. If there were 140 girls at the concert, how many boys were there?

5. Three cups of flour are needed to make 48 pecan cookies. How many cookies will 5 cups of flour make?

3.1

1. If the underlined word is incorrect, write the correct word in the blank.a) The square of a number can be thought of as the area of a square.


Name: _________________________________ Date: ________________________


____________________b) In the prime factorization of a perfect square, there is an odd number of

each prime factor. ____________________c) The square of a number is the number divided by itself.

____________________d) The square root of a number can be thought of as the side length of a

rectangle. ____________________2. Follow the instructions for each number below.

a) Write the prime factorization.b) Determine whether the number is a perfect square and justify your answer.

Prime Factorization Perfect Square?

35

Circle one: YES NOJustify your answer:

64

Circle one: YES NOJustify your answer:

3. Complete the table.

Side Length of Square

Side Length Squared Area of Square

Example: 2 2 × 2 4a) ____ 4 × 4 16b) 7 _______________ 49


Name: ________________________________ Date: ________________________


c) 6 6 × 6 ____d) 10 _______________ ____

4. Determine the square roots. Hint: Look for patterns.a) ____ ____ ____b) ____ ____ ____c) ____ ____ ____d) ____ ____ ____

5. Find the area of the square, given its side length.a) 7 cm

____________________b) 11 mm

____________________c) 15 m

____________________

d) 22 cm ____________________

e) 40 m ____________________

f) 90 mm ____________________

6. Find the side length of the square, given its area.a) 100 cm2 ____________________b) 121 mm2 ____________________c) 169 m2 ____________________

d) 256 cm2 ____________________e) 529 mm2 ____________________f) 2500 m2 ____________________

3.2

1. Write down the words that fill in the blanks.In a ____________________ triangle, the sum of the areas of the ____________________ attached to the legs equals the area of the square attached to the ____________________.

2. a) Trace the right triangle below. Label the hypotenuse with t. Label the other legs of the triangle with r and s.


Name: _________________________________ Date: ________________________


b) Draw a square attached to each side of the triangle.c) Write the relationship of the areas of the

squares, using variables and symbols.

3. a) Calculate the areas of the three squares shown.

b) Is the triangle a right triangle? Explain.

4. Calculate the missing area of each square. Show your work.

5. Determine the area of the square that would be attached to the hypotenuse of each right triangle.


Name: ________________________________ Date: ________________________


3.3

1. Fill in the blanks. The first step in estimating the square root of a number that is not a perfect square is to think of the ____________________ ____________________ less than and greater than the number.

2. Complete the table.

Number

Perfect Square Less Than the

Number

Perfect Square Greater Than the Number

Perfect Square Number Is Closer To

33 25 36 36 11 47 6 70116

3. Estimate the square root of each number in #2. Then, check your answers with a calculator. Express your answers to one decimal place.

Estimate Checka) _____ _____b) _____ _____c) _____ _____d) _____ _____e) _____ _____f) _____ _____

4.Estimate the square root of each number. Then, check your answers with a calculator. Express your answers to one decimal place.


Name: _________________________________ Date: ________________________


Perfect Square Less

Thanthe Number

Perfect Square

Greater Thanthe Number

Perfect Square

Number IsCloser To Estimat

eCheck

a) _____ _____ _____ _____ _____b) _____ _____ _____ _____ _____c) _____ _____ _____ _____ _____d) _____ _____ _____ _____ _____

5. Identify all of the possible whole numbers with a square root greater than 3 and less than 4.______________________________________________________________

6. The square has an area of 10 cm2.

a) Use perfect squares to estimate the side length of the square, to one decimal place. Show your work.

b) Use a ruler to measure the side length of the square, to the nearest tenth of a centimetre. _______________

3.4 1. Fill in the blanks to find the length of the hypotenuse of the right triangle.

t 2 = r

2 + s2

t 2 = ____2 + ____2

t 2 = ____ + ____

t 2 = ____

t = t = ____

The length of the hypotenuse is ____ cm.2. Fill in the blanks to find the unknown leg length of the right triangle.


Name: ________________________________ Date: ________________________


e2 + f 2 = g2

e2 + ____2 = ____2

e2 + ____ = ____e2 + ____ – ____ = ____ – ____e2 = ____e = e = ____The length of leg e is ____ cm.

3. What is the length of the hypotenuse of each right triangle? Show your work. Give your answer to the nearest tenth of a centimetre.a) b)

4. Use the Pythagorean relationship to determine the unknown leg length of each right triangle. Give your answer to the nearest metre. Show your work.

3.5

1. Fill in the blanks to find the missing distance.d2 = 7002 + ____2

d2 = ____ + ____d2 = ____d = d = ____The hypotenuse is ____ m.


a) b)

Name: _________________________________ Date: ________________________


2. Fill in the blanks to determine if the triangle is a right triangle. Use the Pythagorean relationship, c

2 = a2 + b2.

Left Side132 = ____The area of the large square is ____ cm2.

Right Side52 + 122 = ____ + ____

= ____The sum of the areas of the two smaller squares is ____ cm2.

Is the triangle a right triangle? YES NOHow do you know? ____________________________________________________________________________________________________________________________

3. A rectangular field measures 20 m × 40 m. Stefan walked along the diagonal from one corner to its far corner. Megan walked along the two sides of the field.a) Draw a diagram to match this situation.

b) What is the distance Stefan walked? Give your answer to the nearest tenth of a metre.

c) What is the distance Megan walked?


Name: ________________________________ Date: ________________________


d) Which distance is shorter and by how much? Give your answer to the nearest tenth of a metre.

4. Before Larissa’s father builds the roof of a shed, he asks her to check if the walls meet at a right angle. She makes a mark at 150 cm from the corner on each wall. She measures the diagonal length as 220 cm. Do the walls meet at a right angle? Justify your response.

4.1

1. Fill in the blanks. a) Percent means out of ______.b) To represent a percent, you can shade squares on a

____________________ ____________________c) To represent a percent greater than 100%, shade

____________________ than one grid. d) A percent that includes a portion of a percent is a

____________________ percent. e) To represent on a hundred grid, divide one square into ____ sections

and shade ____ of the sections.

2. One completely shaded grid represents 100%. What percent does each diagram represent?


Name: _________________________________ Date: ________________________


a) b)

c) d)

For #3 and #4, use the grids that follow to answer the questions. Label the grid(s) you use.

3. Shade grids to represent each percent. a) 175% b) c) 0.2% d)

4. Shade grids to represent the percent in each statement.a) Attendance at the science fair decreased by 5.4% last year. b) 0.3% of Earth’s fresh water is found in lakes and rivers. c) The length of the St. Lawrence River is about 150% of the length of the

Columbia River.


Name: ________________________________ Date: ________________________


5. How many hundred grids are needed to show each percent?a) 235% ____ b) 789% ____ c) 1630% ____

4.2

1. Fill in the blanks.

a) Percent means out of 100, so .b) 0.19 means 19 ____________________, so 0.19 = ____%.

2. Fill in the blanks to convert each fraction to a percent.

a) = ____% b) = ____%

c) = ____% d) = 93 ÷ ____ = 0.____ = ____%


Name: _________________________________ Date: ________________________


3. Fill in the blanks to convert each percent to a fraction in lowest terms.

a) b) =

c) 12.5% = d) 0.66% = 0.____ = =

4. Complete the following table. The first row is completed for you.

Percent Fraction DecimalExample: 108% 1.08

a)

b) 0.082

c)

d) 0.78%

e) 3.36

5. Jeremy enlarged a picture. The length of the original picture is 8 cm and the width is 5 cm. The length of the enlarged picture is 10 cm and the width is 7 cm.a) What percent is the 10 cm length of the 8 cm length? Show your work.b) What is the area of each picture? By what percent is the area changed?

4.3

1.Use mental math to determine each percent. Show your thinking.a) 500% of 60 b) 0.2% of 600 c) 150% of 4000 d) of 80

2. Determine the percent of each number. Write the percent as a decimal. Give your answer to the nearest hundredth.


Name: ________________________________ Date: ________________________


Example: 110% of $30.50 As a decimal: 110 ÷ 100 = 1.1As a percent: 1.1 × 30.50 = $33.55

a) of 690 b) 385% of $210.60 c) 83 of 240

3. What is the percent of each number? Give your answer to the nearest hundredth.a) of 400 b) 325% of $89.95

c) of 715 d) 245% of $298.75

4. If the sales tax in a province is , what is the tax on a pair of shoes that cost $82? Show your work.

4.4

1. A backpack costs $29.99. PST is 6% and GST is 5%. You could use several different methods to find the total cost of the backpack. a) You could ____________________ the tax percents and then add the

cost of the ____________________. b) You could calculate the ____________________ separately and then

add the amounts to the cost of the ____________________. c) You could combine the cost and the ____________________ by using a

percent greater than ____ to find the total cost.

For #2 to #5, calculate the total cost for each item if GST is 5% and PST is 7%. a) Calculate the total tax. b) Calculate the total cost.

Item a) Total of GST and PST b) Total CostExample: DVD for $29.99

0.12 × 29.99 = 3.5988 = 3.6The total tax is $3.60.

29.99 + 3.6 = 33.59The total cost is $33.59.

2. 12-V drill for $39.99

3. Car radio for $89.99

4. Combination lock for $2.99

5. Soccer ball for $19.99


Name: _________________________________ Date: ________________________


6. An electronics store offered a 30% discount on MP3 players. The next week, the store offered a further discount of 15% on the already discounted price. The regular price was $45. What is the final sale price? Show your work.

7. Dan says that subtracting a 20% discount from the price of an item and then adding 12% for GST and PST taxes is the same as subtracting 8% from the price of the item. Is Dan correct? Explain your reasoning.

For #8 to #12, use the following information: A store is having a 20% off sale on each of the items in the table. Determine the total cost of each item including 5% GST and 7% PST. Show your work.

Item Regular

Pricea) Discount

Priceb) Sale Price

c) GST and PST

d) Total Cost

Example: Calculator at $15.49

0.20 × 26.49 = 3.098 Discount: $3.10

15.49 − 3.10 = 12.39Sale price: $12.39

0.12 × 12.39 = 1.4868Taxes: $1.49

12.39 + 1.49 = 13.88Total cost: $13.88

8. Camera at $129.96

9. Chair at $39.99

10. Pens at $4.99

11. Laptop at $849.96


Name: ________________________________ Date: ________________________


12. Phone at $17.95


Name: ________________________________ Date: ________________________

.…BLM 5–11.…

ANSWERS


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