Math 7 Final Exam Review Name:______________

General Information The Grade 7 Math final exam will be written on _____The exam has 45 multiple choice and 5 short answer questions. All answers will be placed on a scantron sheet. Simple calculators are allowed for this exam (no fractions buttons allowed). The final exam is worth 10% of your grade 7 math mark. The best way to prepare for an exam list this is practice, practice, practice … J Complete the following questions, on a separate sheet as required. Check with your teacher for the answers.

Chapter 1 – Coordinate Plane For #1 to #8, match letters on the coordinate grid to the descriptions. Each letter may be used more than once. 1. _____ x-axis 2. _____ quadrant I 3. _____ origin 4. _____ quadrant IV 5. _____ horizontal axis 6. _____ the possible location of a point with

signs (–, +) 7. _____ vertical axis 8. _____ the quadrant point M' would be in if

M(3, –4) is reflected in the y-axis 9. To plot the ordered pair (0, 5), you would move

A right 5 B up 5 C left 5 D down 5 10. Figure PQR is reflected in line n. What are the coordinates of Q'?

A (1, 0) B (-4, -1) C (0, 1) D (4, 1)

11. Look at the grid. What are the coordinates of each letter?

M __________________________

N __________________________

P __________________________

Q __________________________

R __________________________

12. a) On the grid, draw and label an x-axis and a y-axis from -5 to 5.

b) Plot and label each of the following points:

A (-3, 5), B (0, -4), C (4, -2), D (-4, -5), E (5, 0)

13. Use the coordinate grid shown to do the following: a) Rotate figure STV 90° in a clockwise

direction about centre of rotation T. b) Translate figure S'T'V' 4 units left and

1 unit down. c) What are the coordinates of V''? _______

Chapter 12 – Measures of Central Tendency Choose the term from the list on the right that best matches the description given on the left. Each term may be used more than once or not at all. 1. ____ A score that is much higher or lower than the rest of the scores. 2. ____ This is the middle number in a data set. 3. ____ This is the most frequent value in a data set. 4. ____ This is used to organize large sets of data. 5. ____ This is the difference between the lowest and highest scores.

A frequency table B mean C measure of central tendency D median E mode F outlier G range

6. Sara is a 100 m sprinter. Her times in the last seven races were (in seconds): 15.0, 14.5, 14.0, 15.0, 15.5, 13.8, 14.6. Find Sara’s median time.

A 15.5 B 15 C 14.63 D 14.6 Use the table below to answer #7 to #10. The table shows how many minutes Amelia spent doing homework each night over two weeks.

Sun Mon Tues Wed Thurs Fri Sat

30 0 75 70 70 35 25

40 15 85 75 75 45 30 7. What was the mean time that Amelia spent each night doing homework? A 47.9 min B 51.5 min C 75 min D 85 min 8. Which amount of time could Amelia consider as an outlier? A 0 min B 15 min C 75 min D 85 min

9. Which of the following is the most likely reason for the amount of time

Amelia spent doing homework on the two Monday nights? A On all of the other nights, she goes to clubs. B She does not spend much time doing homework on most days. C She has soccer practices on Monday nights that go quite late. D The teacher never assigns much homework.

10. What is the mode for the data set showing Amelia’s homework times? A 42.5 min B 47.9 min C 70 min D 75 min

11. Find the mode and mean of the set of data: 3, 5, 8, 12, 12, 14. 12. The tally chart shows the average

daily temperature and the number of days in the month with that temperature. Find the median temperature for the month and the range of the data.

13. A Grade 7 class

is surveyed. Each student is asked, “How many siblings (brothers and sisters) do you have?” The results are shown in the chart.

a) Determine the mean, the median, the mode, and the range. b) Are there any outliers in the data? If so, should the outlier be removed

from the data set? Explain your answer. 14. Students’ scores for a French test were 40, 42, 55, 56, 59, 68, 74, 76, 77, 78, 79, 81, 83, 87, 87, 87, 88, 93, 95, and 95. All scores are percents.

a) Determine the mean, the mode, and the median. b) Marco receives 76%. His mom asks him how he did on the test compared

to the rest of the class. Which of the mean, mode, or median should he tell his mom if he wants to make his results look good? Explain why.

Chapter 2 – Working with Decimals 1. Calculate the answer to 15.25 + 6.53 – 9.2.

A 30.92 B 20.86 C 17.31 D 12.58 2. Calculate the answer to 85.6 – 14.83.

A 71.73 B 71.23 C 70.87 D 70.77 3. Estimate the answer to 8.75 × 31.88 using front-end estimation.

A 240 B 270 C 2400 D 2700 4. Calculate the answer to 8.1 ÷ (0.65 + 3.3).

A 2.05 B 12.46 C 15.76 D 31.99

Average Temperature (°C)

Number of Days

12 llll 13 llll l 14 llll 15 llll ll 16 llll llll

Number of Siblings

0 1 2 3 4 5 6 7

Tallyllll l llll

llll l llll ll

llll l l

5. Marna cycles 38.4 km daily from Monday through Friday every week. What is the best estimate of the total distance she travels in 1 month?

A 500 km B 800 km C 1000 km D 1200 km

6. The sum of 84 hundredths and 3 tenths is ________. 7. When calculating 5 + 3 × (12 – 7) – 11, the operation of _________ is

performed first. 8. Without finding the answer, place the decimal point in the correct position.

Show your thinking. a) 0.697 + 0.21 + 0.5 = 1407 b) 38.24 – 27.65 = 1059 c) 5.8 ÷ 0.293 = 197952 d) 24 × 0.073 = 17520

9. What is the value of each expression?

a) 157.95 + 3.7 × 4 + 2 b) 14.6 – 5.25 × 2.3 10. Rewrite each statement using brackets to make a true statement.

a) 5.4 – 4 × 0.12 = 0.168 b) 7.1 + 6.8 × 3 ÷ 0.4 = 104.25 c) 6.7 ÷ 0.3 + 5.2 × 3.9 = 4.75 d) 9.3 – 5.5 × 2.7 + 0.6 = 12.54

11. Four friends form a landscaping company. In one week, they have 5 clients

that pay the following amounts: $270, $315, $295, $425, and $330. If the friends share the money equally, determine how much each person

receives from the work. Show your calculations. 12. Margie’s company manufactures pens. An empty box costs $0.12. Each pen

costs $0.15. One full box holds 8 pens. Calculate the cost of manufacturing 100 boxes of pens. Show your work.

13. Terry pays $18 per year to purchase music at reduced prices. Last year, she

paid $17.30 each for 3 CDs and $24.65 each for 4 DVDs. a) Terry’s sister, Jana, wrote the following expression to calculate how much

Terry spent on music last year. 18 + 17.30 ÷ 3 + 24.65 ÷ 4 Evaluate Jana’s expression. b) Terry estimates that she spent $165 in total. How does Terry’s estimate

compare with the calculation according to Jana? If the answers are not close, who do you think is correct? What mistake did the other girl make?

c) Calculate the actual amount Terry spent on music last year. d) Was Terry’s estimate in part b) an underestimate or an overestimate?

Chapter 4 – Fractions, Decimals and Percents For #1 to #6, choose the letter representing the term that best matches each description. Each letter may be used more than once or not at all. 1. ____ 3.452 2. ____ 24.89898989 3. ____ about two thirds

4. ____ 45

5. ____ 43.8 6. ____ 1400

A terminating decimal B repeating decimal C 80 percent D 65% E 50%

7. Convert 1120

to decimal form.

A 0.45 B 0.55 C 0.6 D 1.818181... 8. Write 0.78 as a percent.

A 0.78% B 7.8% C 78% D 780% 9. Find 58% of 250.

A 431 B 145 C 4.31 D 0.232 10. What percent does the shaded region below represent?

A 48% B 58% C 60% D 62%

11. What percent of the disks shown are white?

12. A radio is on sale at 35% off the regular price of $35.99. How much is the

discount?

13. In a grade seven class, 18 students have pets and 12 do not. What percent of the class has a pet?

14. Arrange the numbers 0.55, 23 , and 60% in ascending order.

15. a) Calculate 45% of 60, 28% of 120, 65% of 80, and 25% of 200. b) Arrange your answers in descending order. 16. A plumber charges $45 to come and unplug a drain. If GST is 6%, estimate

and then calculate the total cost for the plumber. 17. Fifty-eight women and 32 men belong to the wellness club at Metco

Manufacturing. Thirty-five women and 25 men plan to go on the ski trip. What percent of the club is going skiing?

18. Sarah is buying some entertainment equipment for her apartment.

Item Regular Price Discount Television $895 15% off DVD video recorder $225 20% off Stereo receiver $310 25% off

Calculate the cost of Sarah's purchases before tax. 19. Amir owns and operates a clothing store. He sells a shirt for $59.95. He

originally bought the shirt for $40.50. What is the buying price as a percent of his selling price?

20. Tara is shopping for a cruise vacation. A–1 Travel has a $1400 cruise at

15% off. Cruise Deluxe has almost the identical package for $1510 at 20% off. Which company is offering the better price? Justify your answer.

21. Your calculator display shows a decimal value of 0.52525252525. Write the exact decimal value of the number. Explain your thinking. 22. Describe a simple way to estimate 30% of $139.95.

Chapter 6 – Adding/Subtracting Fractions For #1 to #6, choose a term from the list on the right that best matches each description on the left. Each letter may be used more than once or not at all. 1. _____ The part of the fraction that tells how

many parts out of the whole you have 2. _____ When a number can be divided by

another number, with no remainder 3. _____ A number that will divide into another

number, with no remainder 4. _____ The part of the fraction that tells into

how many parts the whole has been cut 5. _____ 12 ÷ 0

6. _____ 6 38 4=

A numerator B not possible C factor D divisible E denominator F written in lowest terms G multiple

7. Adding all of the digits in a whole number and then checking if the sum is

divisible by 9 is the rule for A divisibility by 9 B divisibility by 6 C divisibility by 4 D divisibility by 3

8. ABCDE represents a five-digit whole number. You are told that ABCDE is

divisible by 5. Which of the following must be true? A E must be 0, 2, 4, 6, or 8. B E must be 0, 2, 4, or 6. C E must be 0. D E must be 0 or 5.

9. 32 81 is a five-digit whole number. You are told that 32 81 is divisible

by 3. Which one of the following could be true?

A = 2 B = 3 C = 4 D = 5

10. Add or subtract. Write your answers in lowest terms.

a) 8 1+15 15= ______________ b) -3 1

8 8 = _______________

11. In the illustration, the large rectangle is one whole. How much of the whole is made when the pieces are subtracted as shown? Write your answer in lowest terms.

__________________________

12.A large number of people were at an international meeting. Out of all the people, 4

15 were from Canada, 4

15 were from the United States, 2

15 from China,

215

from Korea, and the rest were from different countries in Europe. What

fraction of the people were from Europe? Show your work. 13. a) Make a diagram on the grid that

shows how to add the following:

5 3+12 12

In your diagram, show 5 3+12 12

as well as the final answer. b) Write the final answer in fraction

form. ______ Chapter 7 – Adding/Subtracting fractions with unlike denominators

1. 6, 12, 18, and 24 are each a(n) ____________ of 6. 2. If one hexagon is one whole, then shows

a(n) ____________.

3. For the fractions 38 and 56 , the number 24 is a(n)

____________.

4. 125

is an example of a(n) ____________.

5. 295 is an example of a(n) ____________.

A common denominator

B multiple C mixed number D improper fraction

6. Which number is a common denominator for 15 and 14 ?

A 1 B 10 C 20 D 30 7. What is the sum of the shaded parts in the diagram?

A 23 B 58 C 611

D 914

8. Which subtraction statement best describes the diagram.

A 1 34 12- B 141

122- C 1

23 141- D 123 1

4-

9.James is making a salad dressing using 12 cup olive oil and 13 cup vinegar.

He pours the oil and vinegar into a jar. In total, how many cups of dressing does James have?

10. Write a mathematical statement for each diagram. Then, solve. Write each

answer in lowest terms.

a) b)

11.Add or subtract. Write each answer in lowest terms.

a) 5 16 3+ b) 2 3

3 4+ c) 1 27 72 + 4 d) 3 1

10 24 + 7

e) 4 35 51 - f) 34 1

3- g) 3 4

10 52 - h) 4 35 73 1-

12. Leanne is learning a new dance routine. On Saturday, she rehearsed for

231 h. On Sunday, she rehearsed for 1

42 h. How long did Leanne spend

rehearsing this weekend? 13. After 2

52 h, a baseball game was almost over when the score became tied.

The extra innings extended the total playing time to 144 h. How long did the

extra innings take? 14. Gerry and Raj operate cement-mixing trucks. On Monday morning, they

each had a full truck of cement. By lunch time, Gerry had poured 716

of his truck’s cement, and Raj had poured 58 of his truck’s cement.

a) Did they pour more or less than a total of one full truck of cement before stopping for lunch?

b) How much cement did each person have in his truck at lunch time?

Chapter 9 Test - Integers 1. Which addition does the diagram represent?

A (–5) + (+8) B (+5) + (–8) C (–8) + (+5) D (+5) + (+8) 2. Which diagram best represents two negative integers being added together?

A B

C D

3. What is the final value?

A +2 B –2 C +14 D –14

4. Which shows the correct changes to find the answer for (-7) - (-12)?

A (+7) + (–12) B (–7) + (–12) C (–7) + (+12) D (+7) – (+12) 5. Tracey uses integer chips to represent (–3) – (–5). She starts with three

negative chips and then adds more chips to prepare for the subtraction. Which one of the following represents this step? A B

C D

6. A bird flies above the water at a height of 35 m. A fish swimming directly underneath the bird is 9 m below the surface of the water. Calculate the distance between the bird and the fish. Show all your work.

7. At noon, Jake checked the temperature and found that it was –7°C. By the late afternoon, the temperature had dropped 8°C. What is the temperature in the late afternoon? Show all your work.

8. What is each sum or difference?

a) (–12) + (+7) d) (–6) + (–9) b) (+5) – (–8) e) (+8) – (+15) c) (–4) – (+9) f) (+12) + (–10)

9. Determine the perimeter and area of the figure with vertices at (–11, +7), (–11, –4), (+6, +7), and (+6, –4). Show all of your work.

Chapter 3 - Geometry For #1 to #5, choose the letter representing the term that best matches each illustration. Each letter may be used once or not at all. 1.

2.

A parallel B perpendicular C area D height E angle bisector F base G vertex H perpendicular bisector

3. 4. 5.

6. The edges of the paper that meet in the corner of your test paper are best described as being:

A acute B obtuse C parallel D perpendicular 7. What is the relationship between line segments AB and RS?

A parallel B perpendicular C intersecting D base 8. Chan took a piece of paper and carefully folded it twice as shown below.

When he unfolds the paper, how would the fold lines appear on the paper?

A parallel B perpendicular C bisecting D obtuse 9. a) Construct an angle of 36° and label it PQR. b) Draw an angle bisector and label it QT. 10. Calculate the area of the figure shown below.

11. Copy line segment JK.

a) Draw a perpendicular bisector that passes through JK at point M and

label it. b) Draw a line segment PT so that it is parallel to JK and label it.

12. A sandbox is a parallelogram with a height of 4 m and a base of 5 m. You need to make a lid for the sandbox. a) What area do you need to cover? b) If material for the cover costs $12 per square metre, how much will it

cost to cover the sandbox? 13. Jared’s apartment has a living room in the shape of a rectangle. He wants to

install some flooring in a triangular shape as shown. Point A bisects side PS. a) What is the area of the triangular surface? b) If the floor tile costs $12.50 per square metre, what is the total cost

before tax?

Chapter 8 - Circles

For #1 to #6, choose the letter representing the term that best matches each illustration or description. Each letter may be used more than once or not at all.

1. ____

2. ____ approximately 3.14:

3. ____

4. ____

5. ____ the distance around a circle:

6. ____

A central angle B diameter C radius D pi E semi-circle F sector G circumference

7. Marcel stands and swings his straightened arm around in a large circle. As he traces out a circle shape, which of the following would be approximately the centre? A his hand B his elbow C his arm D his shoulder

8. What is the formula for calculating p?

A =p radiuscircumference

B = 2×p radius

C =p diametercircumference

D =p circumferencediameter

9. What is the formula for calculating the area of a circle?

A Area = 2 × p × r B Area = p × r

2

C Area = 2 × p × r

2 D Area = (p × r)2

10. On a survey, 420 people were asked for their

favourite gum from five different brands. The results are shown in the circle graph.

Which shows the ranking from least to most preferred brand of gum?

A C, E, B, A, D B C, B, A, E, D

C C, E, A, B, D D C, E, B, D, A

For #11 to #14, answer to the nearest tenth unless otherwise indicated.

11. What is the circumference of the circle? Round the answer to the nearest tenth.

12. Jana is preparing the area for a circular helicopter-

landing zone. The circular zone measures 15 m across. Find the area of the landing zone. Show your work.

13. A school posts the following grades and numbers of students. a) Complete the following table. b) Complete the circle graph.

Grade Number of Students

Sector Angle

8 300 83° 9 220 60.9° 10 280 11 300 83° 12 200 Totals: 1300

14. You get hired to enclose a circular ice rink with fencing. The diameter of the rink is 20 m. You ask two companies for an estimate. Show all your work. a) “Ice Rinks R Us” estimates $75 per metre. Calculate the total cost. b) “Rink Builders” estimates $84 per metre. Calculate the total cost. c) What is the difference in cost? d) Putting ice in a rink costs $80 per square metre. Calculate the total cost.

Chapter 10 – Patterns and Relations

1. ____ x in the expression 4 + 7x 2. ____ 2 in the expression 2a 3. ____ 3 14-p is an example of one 4. ____ 15 in the expression +15m

A table of values B expression C constant D numerical coefficient E variable

5. Which one of the following is equal to 79 ?

A 0.7 B 0.797979 C 0.0777… D 0.777… 6. Determine the value of 4x when = 8x . A 2 B 12 C 32 D 48 7. Using the relationship =2 5,-y x which of the ordered pairs is not correct? A (3, 1) B (4, 3) C (5, 5) D (6, 6) 8. Which graph represents the linear

relation shown in the table of values?

A B

C

9. Look at the following pattern: 1 2 3 4= 0.3, = 0.6, = 1, = 1.3,...3 3 3 3

What is 73 as a decimal number? ____

x 2 3 4 5

y 1 3 5 7

10. a) The Pizza Shack charges $8 for each pizza. No matter how many pizzas you order, they charge $5 for delivery. Using p for the number of pizzas, what is an expression for the cost to have pizzas delivered to your home?

__________________________________________________________ b) What is the cost of five pizzas? Write your answer as a sentence.

__________________________________________________________ 11. The diagram shows that a cabin with one room has two doors, a cabin with two rooms has five doors, and a cabin with three rooms has eight doors.

a) If the pattern continues, how many doors does a cabin with five rooms have? Write your answer as a sentence.

__________________________________________________________

b) What is an expression for the pattern? Tell what your variable represents.

__________________________________________________________ 12. a) For the linear relationship y = 2x - 1 complete the following table of values. b) Graph the values in the table onto the coordinate grid provided. c) Describe a pattern in real life that the linear relation y = 2x - 1 could represent. Make sure you explain what both x and y represent.

Chapter 11 – Solving Equations For #1 to #6, write EQ beside each item that is an equation or EX beside each item that is an expression.

1. 4x - 9 = 11 ____ 2. 15 + 6x ____ 3. 8c ____

4. -24 = x - 17 ____ 5. = 75m ____ 6. 15 + 5x - 9 ____

x y 2 3 4 5

7. Which one of the following does the illustration represent?

A 3x + 5 = 8 B 3x + 2 + 8 C 3x = 6 D 3x + 2 = 5 8. Which of the following shows the correct set of opposite operations?

A + and – × and ÷ B + and ÷ × and – C + and × ÷ and – D + and ÷ × and +

9. Connie’s age is three more than twice her brother Anthony’s age. If a represents Anthony’s age, write the equation that represents Connie’s age.

10. Mark is checking to see if n = 3 is a solution to the equation 9 = 5n – 6. His

work is shown below:

Mark concludes that since the two sides are not equal, 3 is not a solution to

the equation. Is Mark correct? Explain why or why not. 11. Solve each equation. Show all of your work.

a) 7m = 42 b) a + 11 = 17 c) = 36c

d) 19 = x + 6 e) k – 6 = 8 f) 30= 2w

12. Solve each equation and check your answer. a) 4x + 11 = 27 b) 12 = 7 + 5x c) 6n + 5 = 47 13. Write an algebraic expression for each word statement. a) five more than a number b) three times a number, less eight c) eight more than two times a number d) six times a number, less 3

14. Draw a picture to represent 4x – 3 = 5. 15. Evan is sewing trim on a pair of shorts. He needs four equal length pieces of

trim to put two stripes down each side of the shorts. The teacher gives him a piece of black trim that is 185 cm long. He measures and cuts 4 equal lengths. He ends up with a small piece of leftover trim that is 13 cm long. How long is each piece of trim?

a) Write an equation to represent this situation. b) Solve the equation and check your answer. 16. a) What equation does this balance represent?

b) Solve the equation. Explain your steps. c) Draw a diagram to represent the equation 4x + 3 = 15. d) Solve the equation in part c). Explain your steps.

Chapter 5 - Probability

For questions #1 to #6, choose the letter representing the term that best matches each statement. Each letter may be used more than once or not at all.

1. ____ A die is tossed 5 times and a six shows up twice giving a probability of 25 .

2. ____ These are the successful results in a probability experiment.

3. ____ Tossing a coin and spinning a spinner at the same time are examples.

4. ____ These are all the possible results in a probability experiment.

5. ____ When tossing a coin, heads is expected to have a probability of 12 .

6. ____ In a lottery, every outcome has an equal chance of occurring.

A outcomes B probability C favourable outcomes D independent events E sample space F random G theoretical

probability H experimental

probability

7. A basket contains 4 yellow, 3 red, and 3 blue slips of paper. Without looking, Navida reaches in to pull out one slip. What is the probability that it is red?

A 34 B 35 C 37 D 310

8. Which of the following gives the correct way to calculate the probability of an event?

A number of favourable eventsProbability =

all possible events B all possible events

Probability =number of favourable events

C number of favourable events

Probability =independent events

D theoretical events

Probability =experimental events

9. The probability of an accident occurring is P(accident) = 0.28. What is the probability that an accident does not occur? A 0.14 B 0.56 C 0.28 D 0.72

10. A student rolls a six-sided die three times in a row. The first roll results in a 6 and the second roll also results in a 6. What is the probability that the third roll will result in a 6?

A 16 B 13 C 26 D 23

11. Jorge tosses a coin and then rolls a four-sided die. Draw a tree diagram to

show the sample space. 12. If you pick one letter at random from the word possibilities, what is the

chance that it will be a vowel? Show your answer as a fraction and a percent.

13. Kirsten has a spinner and 4 balls as shown below. She spins the spinner and

selects one ball at random.

a) Use a table to show all of the possible outcomes. b) How many outcomes will result in Q and an even

numbered ball? c) What is P(Q, even numbered ball) as a decimal

and a percent? 14. Dominic and Tony are playing a board game with a pair of six-sided dice. If

Dominic can roll a total of five using the two dice, he will win the game. a) What are all of the possible sums Dominic can roll using the pair of dice? b) Circle the outcomes that could win the game for Dominic.

c) What is the probability that Dominic will win the game on this roll? Show your answer as a fraction and a percent.