MPM1D Exam Review #1: Polynomials & Exponents 1) Write in expanded form, then evaluate.

a) 35 b) (−4)2 c) −(4)2 d) − (

4

5)

3

e) (−2

6)

4

2) Evaluate.

a) 5(−2)3 b) −4(−5) − (−3)3 c) [−2(−1)3]6 d) (−2)2−22

−32 e) 33+3(7)

−24 +3(−5)2

−15

f) −7

16(1

1

3) g) 6

1

4 ÷ 2

1

2 h) 1

1

6− (−2

1

9) − 3

3

4 i) − (−

2

3)

4

j) 49

(4)3(4)2

k) (62)

3

(62)2 l) (−6)0(−6) m) (43)(52) n)

((57)(56))4

(52)10 o) (92)

25(975)

9(920)6

3) Assume 𝑏 and 𝑛 are positive integers. For each situation below, decide whether each of the following is positive, negative, or zero. Explain your reasoning

a) −𝑏𝑛 and 𝑛 is odd b) −𝑏𝑛 and 𝑛 is even

c) (−𝑏)𝑛 and 𝑛 is odd d) (−𝑏)𝑛 and 𝑛 is even

4) Write each as a single power, then evaluate.

a) 33 × 3 × 35 b) 65

63

c) (2𝑥𝑦3)4 when 𝑥 = 2 and 𝑦 = −1 d) 5(25)4 5) Classify the following polynomials by the number of terms.

a) 4𝑦 − 5𝑧2 b) 2𝑎2𝑏 + 5𝑎𝑏2 − 3𝑎2𝑏2

6) Identify the like terms in each of the following: a) 3𝑥, 3𝑥𝑦, 3𝑥𝑦2, 8𝑥𝑦2, 5𝑥2𝑦, 2𝑦𝑥2 b) 2𝑏3, 2𝑏2, 2𝑏, 2

7) Simplify the following: a) (3𝑥 + 4𝑦) + (2𝑥 − 5𝑦) b) (2𝑎 − 3𝑏) + (7𝑏 + 5𝑎) + (3𝑎 − 𝑏) c) (2𝑥 + 5𝑦) − (7𝑥 − 3𝑦)

d) (6𝑝 − 𝑞 + 3𝑟) − (7𝑞 − 2𝑟 + 5𝑝) e) (5𝑥 + 3) + (6𝑥 − 4) f) (4𝑦 − 3) − (5𝑦 − 2) 8) Use the distributive property to expand and simplify:

a) 3(5𝑦 − 2) b) 7𝑎(𝑎2 + 2) c) 3[2 + 5(4𝑝 − 3)]

d) 3(2𝑥 − 4) e) 2(𝑥 + 4) f) −3(2𝑥 + 4)

g) −7(3𝑥2 − 4𝑥 + 3) h) 8(2𝑥2 − 3𝑥 + 5) i) 230(56𝑥2 + 3𝑥)

j) (4𝑚2 − 3𝑚𝑛 − 2𝑛2) − (𝑚𝑛 + 𝑚2 − 5𝑛2)

9) Simplify by collecting like terms.

a) 5𝑥 + 6 + 3𝑥 b) 3𝑥 − 𝑥 + 2 c) 2𝑥2 − 6 + 𝑥2 + 3

d) −5 + 𝑥 + 3 − 2𝑥 e) 𝑥 − 4 + 6 − 5𝑥 f) 3𝑥3 − 𝑥 + 2𝑥3 + 3𝑥

g) 4𝑥2 + 3𝑥 + 5 − 5𝑥2 − 2𝑥 − 7 h) 3𝑥 + 5𝑦 + 4𝑥 + 6𝑦 i) 6𝑎3 − 4𝑎𝑏 + 5𝑏2 − 3 + 5𝑎3 − 3𝑎𝑏

j) 3𝑤2 + 2𝑤𝑦 − 𝑦2 − 2𝑤2 − 2𝑤𝑦 + 4𝑦2 k) 5𝑑 + 3𝑚 − 4𝑑 − 5𝑚

10) Simplify each of the following.

a) (𝑎5𝑏4) × (𝑎3𝑏2) b) 𝑑6𝑑5

𝑑7 c) (𝑦6)

3

(𝑦5)2

11) Expand and simplify. a) 3(𝑥2 + 2𝑥 − 5) + 4(𝑥2 − 6𝑥 + 2) b) 5(𝑥2 − 2𝑥 + 6) − 3(2𝑥2 − 6𝑥 + 2)

c) 4(2𝑥 + 3𝑦) − 5(3𝑥 − 6𝑦) d) 2𝑎[3𝑎(𝑎 + 4)] − 𝑎(2𝑎 − 3)

12) Simplify.

a) (4

9𝑎3) (−

3

4𝑎) b) (3𝑎2𝑏3)(2𝑎𝑏2) c) (−4𝑥𝑦3)5

d) (2𝑥2𝑦)(𝑥2𝑦2)3 e) (𝑎4𝑏3)(−2𝑎𝑏)3(3𝑎2𝑏)2 f)

(2𝑥2)3

(3𝑥)2

(−4𝑥)3

g) (3𝑎2𝑏5𝑐7

9𝑎𝑏3𝑐7 )3

h) (3𝑥2𝑦3)

2(2𝑥2𝑦2)

2

2𝑥𝑦 i)

(3𝑑4𝑚3)(8𝑑3𝑚5)

(3𝑑2𝑚2)2

13) a) Determine an expression for the volume of a cube with side length 𝑥.

b) Suppose we doubled the side length of the cube. Determine a new expression for the volume of the cube, in terms of 𝑥. c) How many times greater is the larger cube than the smaller cube? Determine how many times bigger the following cube is than the first: d) If the sides were tripled. e) If the sides were made four times longer.

14) Determine a simplified expression for the Perimeter and Area of the following:

15) a) Determine a simplified expression for the area of the shaded region below.

b) Determine an expression for the total edging (both inside and outside). 16) Matt is building a dock at his cottage. The length of the dock is 3 metres longer than twice the width.

a) Draw a diagram of the dock and label the width and length with algebraic expressions. b) Find simplified expressions for both the Area and Perimeter of the dock. c) Find the Perimeter and Area of the dock if the width is 2 metres.

Exam Review #1 – Solutions

1) a) 243 b) 16 c) −16 d) 64

125 e)

1

81 2) a) −40 b) 47 c) 64 d) 2 e) −8 f) −

7

12 g)

5

2 h) −

17

36

i) −16

81 j) 256 k) 36 l) −6 m) 1600 n) 532 o) 6561 3) a) Negative b) Negative

c) Negative d) Positive 4) a) 19683 b) 36 c) 256 d) 1953125 5) a) Binomial b) Trinomial 6) a) 3𝑥𝑦2 and 8𝑥𝑦2, 5𝑥2𝑦 and 2𝑦𝑥2 b) None 7) a) 5𝑥 − 𝑦 b) 10𝑎 + 3𝑏 c) −5𝑥 + 8𝑦 d) 𝑝 − 8𝑞 + 5𝑟 e) 11𝑥 − 1 f) −𝑦 − 1 8) a) 15𝑦 − 6 b) 7𝑎3 + 14𝑎 c) 60𝑝 − 39 d) 6𝑥 − 12 e) 2𝑥 + 8 f) −6𝑥 + 12 g) −21𝑥2 + 28𝑥 − 21 h) 16𝑥2 − 24𝑥 + 40 i) 12880𝑥2 + 690𝑥 j) 3𝑚2 − 4𝑚𝑛 + 3𝑛2 9) a) 8𝑥 + 6 b) 2𝑥 + 2 c) 3𝑥2 − 3 d) −𝑥 − 2 e) −4𝑥 + 2 f) 5𝑥3 + 2𝑥 g) −𝑥2 + 𝑥 − 2 h) 7𝑥 + 11𝑦 i) 11𝑎3 − 7𝑎𝑏 + 5𝑏2 − 3 j) 𝑤2 + 3𝑦2 k) 𝑑 − 2𝑚 10) a) 𝑎8𝑏6 b) 𝑑4 c) 𝑦8 11) a) 7𝑥2 − 18𝑥 − 7 b) −𝑥2 + 8𝑥 + 24

c) −7𝑥 + 42𝑦 d) 4𝑎3 + 22𝑎2 + 3𝑎 12) a) −1

3𝑎4 b) 6𝑎3𝑏5 c) −1024𝑥5𝑦15 d) 2𝑥8𝑦7

e) −72𝑎11𝑏8 f) −9

8𝑥5 g)

1

27𝑎3𝑏6 h) 9𝑥7𝑦9 i)

8

3𝑑3𝑚4 13) a) 𝑉 = 𝑥3 b) 𝑉 = 8𝑥3 c) 8 times

d) 27 times e) 64 times 14) 𝑃 = 10𝑥 + 2; 𝐴 = 4𝑥2 + 3𝑥 15) a 𝐴 = 9𝑥) b) 𝑃 = 12𝑥 + 12

16) a) b) 𝐴 = 2𝑥2 + 3𝑥; 𝑃 = 6𝑥 + 6 c) 𝐴 = 14 𝑚2; 𝑃 = 18 𝑚

MPM1D Exam Review #2 – Equations 1) Solve. a) 2𝑥 + 5 = 11 b) −3𝑦 − 5 = −8 c) 10 + 4𝑓 = −32 d) −6 + 4𝑦 = −3

e) 11 = −4𝑝 + 8 f) 5𝑥 + 4 = 2𝑥 + 13 g) −3𝑟 + 7 = −5𝑟 + 3 h) 5

3𝑛 + 8 = 8𝑛 − 10

i) 4𝑎 − 2 − 𝑎 = 6𝑎 + 3 − 7𝑎 j) −7𝑑 + 3 = −3𝑑 + 11 k) 3

2(𝑥 + 6) =

7

3+ 1 l)

𝑏−5

7= 3

m) 4 − 3(2𝑥 + 1) = −2(𝑥 − 5) + 11 n) 6 =2

3𝑚 − 1 o)

1

3(𝑝 + 5) = 2𝑝 − 3 p)

𝑥−5

3=

2𝑥+1

5

q) 3

5(𝑣 + 2) =

1

2(𝑣 − 3) r)

𝑥+1

7− 2 =

3−4𝑥

4 s)

𝑦

3−

5𝑦

6= −

1

2 t)

𝑥

2−

2𝑥

3= 4 −

𝑥

10

u) 3𝑦+1

2= 5 v)

𝑥+2

2+

𝑥−2

5= 2 w)

𝑥+1

3−

2−3𝑥

2= −1 x)

3𝑥+2

2−

𝑥+1

3= 𝑥

y) 3𝑥 +2𝑥−1

3−

7−𝑥

4=

3𝑥+1

6− 2 +

𝑥−2

2

**Complete formal checks for f), h), and q).**

2) Isolate the indicated variable. a) 𝐹 = 𝑚𝑎 for 𝐹 b) 𝐴 = 𝜋𝑟2 for 𝑟 c) 𝑃 = 2(𝑙 + 𝑤) for 𝑤

d) 𝑦 = 𝑚𝑥 + 𝑏 for 𝑚 e) 𝑑 = 𝑣𝑡 +𝑎𝑡2

2 for 𝑎 f) 𝐸 =

𝑚𝑣2

2 for 𝑚

g) 𝑑 =1

2(𝑢 + 𝑣)𝑡 for 𝑢 h)

𝑢+𝑣

𝑎= 𝑡 for 𝑣

Please provide complete algebraic solutions. This includes writing proper let statements, concluding statements, and showing your work. 3) A safe contains 120 coins, the value of which is $10. If the coins consist of nickels and dimes, how many of each kind are in it? 4) In a triangle, the largest angle is twelve times larger than the smallest angle, while the smallest angle is three times smaller than the middle angle. Find the measure of the angles.

5) The sum of three consecutive integers is 24. Find the three integers. 6) Best Banquet Halls charges $225 to rent hall plus $45 per person attending. Good Times Banquet Hall, it costs $1450 to rent the hall plus $38 per person attending. For how many people do the two Banquet Hall cost the same amount? 7) The sum of three consecutive odd integers is -33. Find the three integers. 8) One number is three more than four times another. If the sum of the two numbers is 23, then find both numbers. 9) One number is six more than six times another. If you subtract the larger number from the smaller number the result is -41. What are the two numbers? 10) The total age of three cousins is 20. Suresh is half as old as Hakima and four years older than Saad. How old are the cousins? 11) Two friends are collecting pop tabs for charity. Chris has 250 more pop tabs than Jeremy. Together they have collected 880

pop tabs. How many tabs has each person collected? 12) Jacob, Garrett, and Liam are raising money for a marathon. Jacob raises twice as much as Liam, while Liam raises $50 less than

twice as much as Garrett. Together, they raised $2475. How much did each person raise? 13) The length of a banquet hall is double its width. The perimeter of the banquet hall is 192m.

a) Find the length and width of the banquet hall. b) How much shorter would it be to walk across the diagonal of the banquet hall instead of around the perimeter?

14) The formula 𝐶 =5

9(𝐹 − 32) is used to convert Fahrenheit temperatures to Celsius.

a) Determine the Celsius temperature when 𝐹 = 90. b) Solve for F in terms of C. c) Determine the Fahrenheit temperature when 𝐶 = 25.

15. When you multiply a number, 𝑥, by 𝑘, add 𝑛, and divide by 𝑟, the result is 𝑤. a) Write an equation that represents this relation. b) Solve the relation for 𝑥.

16. Write each of the following in standard form.

17. Solve each of the following proportions. Use proportions to solve each of the following problems.

18. What is 15% of 40? 19. 45% of what number is 36? 20. What percent is 26 of 250? 21. What is 300% of 154?

22. In an exam, Ashley secured 332 marks. If she secured 83% makes, find the maximum marks. 23. In a basket of apples, 12% of them are rotten and 66 are in good condition. Find the total number of apples in the basket. 24. While mining, John found a large metal bar that weighed 25 grams. John was also able to determine that the bar had 13 grams of silver. What percent of the weight of the bar was silver? 25. Miguel decided to raise all the prices in his store by 15%. What would be the new price of an $24.95 item after the price increase? What is the final cost after HST? (Solve using proportions)

Exam Review #2 – Solutions

1) a) 𝑥 = 3 b) 𝑦 = 1 c) 𝑓 = −21

2 d) 𝑦 =

3

4 e) 𝑝 = −

3

4 f) 𝑥 = 3 g) 𝑟 = −2 h) 𝑛 =

54

19

i) 𝑎 =5

4 j) 𝑑 = −2 k) 𝑥 = −

34

9 l) 𝑏 = 26 m) 𝑥 = −5 n) 𝑚 =

21

2 o) 𝑝 = 14/5 p) 𝑥 = −28

q) 𝑣 = −27 r) 𝑥 =73

32 s) 𝑦 = 1 t) 𝑥 = −60 u) 𝑦 = 3 v) 𝑥 = 2 w) 𝑥 = −

2

11 x) 𝑥 = −4

y) 𝑥 =13

35

2) a) 𝑚 =𝐹

𝑎 b) 𝑟 = √

𝐴

𝜋 c) 𝑤 =

𝑃

2− 𝑙 d) 𝑚 =

𝑦−𝑏

𝑥 e) 𝑎 =

2(𝑑−𝑣𝑡)

𝑡2 f) 𝑚 =2𝐸

𝑣2 g) 𝑢 =2𝑑

𝑡− 𝑣

h) 𝑣 = 𝑡𝑎 − 𝑢 3) a) 40 nickels and 80 dimes 4) 10°, 50°, 120° 5) 7, 8, 9 6) It would cost the same for 175 people. 7) −13, −11, −9 8) 4, 19 9) 7, 48 10) 4, 8, 16 11) 315, 565

12) $375, $700, $1400 13) a) 64m, 32m b) 24.4m 14) a) 32.2 b) 𝐹 =9

5𝐶+ 32 c) 77

15) a) 𝑤 =𝑘𝑥+𝑛

𝑟 b) 𝑥 =

𝑤𝑟−𝑛

𝑘

16) a) 3𝑥 − 4𝑦 − 8 = 0 b) 7𝑎 + 12𝑏 − 12 = 0 c) 9𝑥 − 5𝑦 + 4 = 0

17) a) 𝑥 =14

5 b) 𝑥 =

36

7 , 𝑦 =

47

7 c) 𝑥 =

63

5

18) 6 19) 80 20) 10.4% 21) 462 22) 400 marks.

23) 75 apples 24) 52% 25) increase price = $28.69 and after tax = $32.43

a) −3𝑥 + 4𝑦 = 8 b) −1

3(7𝑎 + 12) = 4(𝑏 + 2) c) 𝑦 =

9

5𝑥 + 4

a) 𝑥: 7 = 6: 15 b) 4: 5: 7 = 𝑥: 𝑦: 9 c) 5

9=

7

𝑥

MPM1D Exam Review #3 – Measurement

1. Find the measures of the unknown sides in the triangles below: a) b)

2. A rectangular lot measures 150 m by 200 m. Instead of walking along the outside of the lot, Alexei

hops a fence and walks along the diagonal of the lot. How much distance does he save? 3. Find the area of the following triangles.

a) b)

4. Zach is planning to repaint the two gables on his house. One of

the gables is shown. A can of paint covers 10 m2. How many cans of paint does he need?

5. A school field has the dimensions shown.

a) Calculate the length of one lap of the track. b) If Loreena ran 625 metres, how many laps did she run? c) Calculate the area of the field.

6. An engine seal is circular in shape, with a square cut-out to fit over a

shaft, as shown to the right. a) Calculate the area of rubber required to make the seal. b) The inside and outside edges of the seal have a steel wire embedded inside to add strength. How much wire is needed?

p

15 cm

8 cm

9 cm

q

25 cm

7. Determine an expression for the shaded area of each figure. a) b) c)

8. A DVD player came packaged in the box pictured to the right.

a) Find the volume and surface area of the box. b) Determine the box’s volume if all dimensions are doubled.

9. Matt made the ramp to the right to test his new Slinky.

Find the volume and surface area of the ramp. 10. A spherical storage tank has a diameter of 16m.

a) Find the surface area of the tank. b) A can of paint costs $30 and covers 20m2. How much will it cost to paint the tank? c) A new tank will be built with a surface area of 2000m2. What radius will be required?

11. Chris is organizing a track meet, and he’s rented the pyramid-shaped changing

tent on the right for the athletes. Find the tent’s volume, as well as the amount of fabric used to make the tent.

12. A dozen tennis balls, each with a radius of 3.2 cm, are placed in a box so that

they just barely fit. The balls form a single layer that measures 3 balls by 4 balls. How much empty space is left in the box?

13. Sawdust from a woodworking lab is blown into a conical container for recycling into other products.

The container has a radius of 1.5m and a height of 2m. a) Find the area of aluminium needed to make the sides and top of the container. b) How much sawdust can the container hold?

14. A cone is truncated to make a paper cup as shown in the diagram to the right. Calculate the amount of paper needed to make the cup, as well as the amount of water this cup can hold.

15. A square-based pyramid has a volume of 100 m3 and a base area of

40 m2. What is its height?

16. A pyramid and a prism, both with the same height,

each have a base area of 64 m2. How do their volumes compare? 17. A triangular piece of cheese has a volume of 146.4 cm3.

Find the thickness, t, of the cheese.

Exam Review #3 – Solutions 1a) 17cm b) 23.3cm 2) 100m 3a) 120m2 b) 12cm2 4) 6 5a) 170m b) 3.7 c) 1530.04m2 6a) 42.27cm2 b) 37.1cm 7a) 𝐴 = 𝜋𝑅2 − 𝜋𝑟2 b) 𝐴 = 4𝑟2 − 𝜋𝑟2 c) 𝐴 = 4𝑟2 − 𝜋𝑟2 8a) 24000cm3, 5200cm2 b) 192000cm3 9) 9600cm3, 5040cm2 10a) 804.25m2 b) $1230 c) 12.6m 11a) 1.50m3, 8.68m2 12) 1498.61cm3 13a) 18.85m2 b) 4.71m3 14a) 147.59cm2, 147.78cm3 15) 2.5m 16) volume of prism is 3 times larger 17) 3.2cm

MPM1D Exam Review #4 – Relationships

1. Jacob did a science experiment to test Beer’s Law, which states that as the concentration of a solution increases, the absorption of light increases as well. The data he collected is shown to the right.

a) Identify the independent and dependent variables. b) Create a scatter plot to represent the relationship between concentration and light absorption. c) How does the value of the dependent variable change as the independent variable increases? d) Identify any outliers in the data. 2. Data was collected to study whether students’ test marks were related to the number of hours of

television they watched the night before the test. Data was collected for 10 students. a) Make a scatter plot of the data. b) Describe any trends in the data. c) Draw a line of best fit on your scatter plot. d) Determine the equation of your line of best fit. e) Using the line of best fit, predict the test score for a student that watched 6 hours of television. f) Using the line of best fit, predict the amount of TV watched by a student that scored 70%.

Concentration (µM/L)

Absorption (%)

0 0

20 4.7

40 9.6

60 13.5

80 18.2

100 21.4

120 27.3

140 39.7

160 34.2

180 37.9

200 42.6

TV Watched (h) 2 4 0 3 2 2 1 3 1 2

Test Mark (%) 82 64 84 70 74 76 85 73 94 90

3. A driver leaves home at 8:00 AM and drives 120km by 9:30 AM. From then until 10:30 AM, she travels another 50km. She drives an additional 200km by 12:30 PM. She then stops for 30 minutes, before driving back home. She arrives home at 5:30 PM. She travels at a constant speed during each period of time. a) Draw the distance-time graph that represents this trip. b) Determine the driver’s speed over each section of the trip.

4. Justin takes a bus from his house to the mall. Use the

distance-time graph to the right to describe Justin’s trip.

Exam Review #4 - Solutions 1) a) Ind: Concentration, Dep: Absorption b) See below c) As the concentration increases the absorption increases d) (140, 39.7) 2) a) See graph below b) As the number of hours of watching TV increases, the test mark decreases.

c) See graph below d) 𝑀 = −19

3ℎ + 92 e) (6, 54), 54% on the test.

f)(3.47, 70), approximately 3.47 hours 3) a) See graph below. 3b) Section Time (h) Distance (km) Speed (km/h) 8:00 – 9:30 1.5 120 40 9:30 – 10:30 1 50 50 10:30 – 12:30 2 200 100 12:30 – 5:30 5 370 82.22

4) Section Time (min) Distance (m) Direction Speed (m/min) a 3 250 Away 83.33 b 4 100 Towards 25 c 5 0 None 0 d 7 150 Towards 21.43

Question 1 Question 2

Question 3

i) iv) iii)

ii)

MPM1D Exam Review #5 – Linear Relations

1. Match each linear equation with the graph that best suits it. a) 𝑦 = −3𝑥 + 5 b) 𝑦 = 7𝑥 − 4 c) 𝑦 =

5

8𝑥

d) 𝑦 = −1

4𝑥 − 4 e) 𝑥 = 5 f) 𝑦 = 3

2. Identify the slope and y-intercept for each of the relations

shown below. Then, write the equation of each line.

3. Convert the following to slope-intercept form. Identify the slope and y-intercept.

a) 0852 =−+ yx b) 1937 =− yx c) ( )15

23 +−=− xy

4. Convert the following into standard form.

a) 73 +−= xy b) 2

11

5

3−= xy c) ( )4

3

27 −=− xy

5. Determine the x-intercepts, y-intercepts, and slope of each of the following.

a) 142

5−−= xy b) 6045 −=− yx c) 03367 =−− yx

6. Graph the following lines on the same grid.

a) 8−=y b) 7=x c) 15

4+= xy d) 1243 =− yx e) 4)6(3 ++−= xy

7. Determine whether the points A(2, -6), B(-3, 10) and C(-1, 1) are on the line 024 =−+ yx .

8. Alexei works during the weekends at a restaurant, earning $10.50 per hour. His pay varies directly with the time, in hours.

a. Choose appropriate letters for variables and make a table of values showing Alexei’s pay for 0h, 1h, 2h, 3h, and 4h. b. Graph the relationship. c. Write an equation to represent this relationship.

9. Matt bikes 50km to a friend’s home. The distance, d, in kilometres, varies directly with the time, t, in hours. a. Find an equation relating distance and time if it takes 1.5 hours to travel 24 kilometres. b. What does the rate of change represent in this problem? c. Use the equation to determine how long it will take Matt to reach his friend’s house.

10. Loreena has $50 in her piggy bank, but withdraws $2.50 each day to buy a chocolate milk and muffin at the cafeteria. Create a table of values, a graph, and an equation to represent the amount of money remaining in her piggy bank each day.

D E F

H

B

A

C

G

11. The amount of juice varies directly with the amount of water used to prepare it. Tommy used 2L of water to make 2.5L of juice. a. Explain why it makes sense for this relation to be a direct variation. b. Write an equation relating the amount of juice made to the amount of water needed.

12. Identify each of the following as direct variation, partial variation, or neither.

a) 25 += xy b) dC = c) xy −= 1 d) 52 −= xy e) 6

1

3

2+−= xy

13. a) Complete the table of values on the right, given that y varies partially with respect to x.

b) Identify the initial value and rate from the table, and use them to write an equation in the form

bmxy += .

14. A company is having business cards printed. The cost to design the cards is $25. There s an additional

charge of $0.04 per business card printed. a) Identify the fixed cost and variable cost. b) Write an equation representing this relationship. c) Use your equation to determine the total cost of 500 business cards. d) Use your equation to determine the number of business cards that can be purchased for $225.

15. Calculate the slope of each line segment on the graph

below.

16. Calculate the slope of the line through each pair of points. a) (-2, 5) and (4, -8) b) (-7, 8) and (4, 8) c) (32, 630) and (58, 1020)

17. Dalton was biking towards his home at a constant speed.

After two hours of cycling he was 55km from home. After 4.5 hours of cycling he was 17.5 km from home. How fast is he cycling?

18. For safety reasons, an extension ladder should have a slope between 6.3 and 9.5 when it is placed against a wall. Determine if

the following ladders are within the safe range. a) A ladder reaches 4m up the wall, while the foot of the ladder is 0.5m from the wall. b) A ladder reaches 3m up the wall, while the foot of the ladder is 0.6m from the wall.

19. Determine whether each relation is linear or non-linear. If the relation is linear, determine an equation to represent the

relation.

a) x y b) x y c) x y d) x y

0 5 0 14 0 21 3 -15

1 11 1 8 3 13 4 -12

2 17 2 3 6 5 5 -9

3 23 3 -1 9 -3 6 -6

4 29 4 -4 12 -11 7 -3

20. The distance-time graph to the right shows two cyclists that are travelling at the same time. a) Calculate the speed of each cyclist.

b) What does the point of intersection of the two lines represent?

x y

0 5

1 9

2

3 17

4

37

21. Find the equation of the line (in slope-intercept form) with a slope of 3

4− that passes through the point (5, 7).

22. Find the equation of the line of the line that has a slope of 8

9 and passes through the point (9, 10).

23. Determine the equation of the line that is perpendicular to the line 01106 =−+ yx and has the same y-intercept as

13 =+ yx .

24. Find the equation of the line that is parallel to the line 012 =−− yx and passes through (8, -7).

25. Find the equation of the line perpendicular to 01234 =+− yx that has the same x-intercept as 01893 =+− xy .

26. Find the equation of the line the passes through:

a) (3, -3) and (-3, 5) b) (5, 2) and (5, -3) c) (8, -5) and (2, 7)

27. Holly downloads music from a site called MyTunes, which chargers a monthly membership fee plus an amount for each song downloaded. A 3-month record of her site activity is shown below. a) Use two points from the table to determine an equation relating Holly’s monthly

bill the number of songs she downloaded. b) Verify that the third point in the table satisfies your equation.

28. Solve the following linear systems graphically. Check your solution.

a) 52 −= xy and 53 +−= xy b) 04 =−+ yx and 022 =+− yx

29. Majida needs to park her car downtown while she takes a course. She can buy a monthly pass for $82, or she can register for

$10 and then pay $6 each day to park. Under which conditions should Majida buy the monthly pass? When should she go with the second plan?

Exam Review #5 – Solutions

1) (a) -> (iii), (b) -> (vi), (c) -> (iv), (d) -> (ii), (e) -> (i), (f) -> (v) 2i) slope: 2, y-int: 3, 32 += xy ii) slope: 5

4− , y-int: -2, 2

5

4−−= xy

iii) slope: 0, y-int: 8, 8=y iv) slope: undefined, y-int: none, 6−=x

3a) 5

8

5

2+−= xy , slope:

5

2− , y-int:

5

8 b)

3

19

3

7−= xy , slope:

3

7, y-int:

3

19− c)

5

13

5

2+−= xy , slope:

5

2− , y-int:

5

13

4a) 073 =−+ yx b) 055106 =−− yx c) 01332 =+− yx

5a) x-int: 5

28− , y-int: -14, slope:

2

5− b) x-int: -12, y-int: 15, slope:

4

5

c) x-int: 7

33, y-int:

2

11− , slope:

6

7

6) on graph above 7) A: yes, B: no, C: no 8) a) 0, $10.50, $21.00, $31.50, $42.00 c) y=10.50x 9) a) d=16t b) speed c) 3.125 hours

10) Equation: 5050.2 +−= dA

11) a) (0,0) is part of the relation, meaning that 0L of water will make 0L of juice b) WJ 25.1=

12) a) partial b) direct c) partial d) neither e) partial

13) a) (2, 13), (4, 21), (8, 37) b) initial value: 5, rate: 4, equation: 54 += xy

14a) fixed cost: $25, variable cost: $0.04 per card b) 2504.0 += nC c) $45 d) 5000

Month # of songs Monthly Bill January 54 $26.90

February 38 $25.30 March 21 $23.60

15) AB: 2

3 CD:

4

1− EF: 0 GH: undefined 16a)

6

13− b) 0 c) 15 17) 15 km/h 18a) safe b) unsafe

19a) linear, 56 += xy b) non-linear c) linear, 213

8+−= xy d) linear, 243 −= xy

20a) A: 10km/h B: 20km/h b) The point where cyclist B passes cyclist A.

21) 3

41

3

4+−= xy 22) 𝑦 =

8

9𝑥 + 2 23) 1

3

5+= xy 24) 𝑦 = 2𝑥 − 23

25) 2

3

4

3+−= xy 26 a) 𝑦 = −

4

3𝑥 + 1 b) 5=x c) 𝑦 = −2𝑥 + 11

27a) 50.2110.0 += nC 28 a) (2, -1) b) (2, 2) 16) If she is going to park more than 12 times,

she should buy the monthly pass. If she parks fewer than 12 times, she should go with the second plan. If she parks exactly 12 times, then it doesn’t matter which plan she choose

MPM1D Exam Review #6 - Angle Geometry

1. Identify a pair of the following angles in the diagram: a) Corresponding Angles (F-Pattern) b) Co-Interior Angles (C-Pattern) c) Alternate Angles (Z-Pattern) d) Opposite Angles (X-Pattern) e) Supplementary Angles

2. a) Find the measures of the exterior angles of ΔPQR.

b) Find the measure of ‹ABD. a) b)

3. Find the measures of the unknown angles in the diagrams below.

a) b) c)

4. For the diagram below, find the value of ( )ba + . Give your answer as a number of degrees.

5. Determine the measure of ‹EGA in the diagram to the right. 6. The interior angle in a certain parallelogram is four

times larger than the exterior angle adjacent to it. Determine the measure of each interior angle.

7. In triangle ABC, ‹C is 1° more than five times the measure of ‹A,

while ‹B is 21° less than four times the measure of ‹A. Find the measure of all interior and exterior angles.

a b

d c

e f

g h

P

Q

R

S

T

U

30°

85°

A

B CD

25° 75°

x105°

75° 85°

92°

97°

55°

y

50° z

y x

5x 4x

a

b

3x

C

F

H

x + 20

G

? B A

E

D

8. The formula for calculating the sum of the interior

angles for an n-sided polygon is ( ) 1802 −n .

a) Explain why 2 is subtracted from n. b) Explain why (n - 2) is multiplied by 180°.

9. Determine the measures of each interior and exterior angle for the following figures.

a) A regular 12-gon b) A regular 15-gon c) A regular 25-gon 10. The sum of the interior angles of a polygon is 2160°. Find the number of sides. 11. Madison designed a tabletop in the shape of a regular pentagon. Mr. Toms suggested that she redesign it in the shape of a

regular hexagon. By how much would each interior angle change? 12. Determine the value of x in the diagram to the right.

13. Determine the values of a, b, c, d, and e

in the diagram below.

14. In triangle QTU, QU = 6 cm, TU = 8cm, and QT = 10 cm.

What is the perimeter of triangle QRS?

Exam Review #6 - Solutions 1a) a & e b) c & f c) d & f d) e & h e) b & c 2a) P = 95°, Q = 150°, R = 115° b) 155° 3a) x = 95° b) 116° c) y = 50°, x = z = 130° 4) 20° 5) 120° 6) 144°, 144°, 36°, 36° 7) At A: Int. = 20°, Ext. = 160° At B: Int. = 59°, Ext. = 121° At C: Int. = 101°, Ext. = 79° 8) Check your notes 9a) Int. = 150°, Ext. = 30° b) Int. = 156°, Ext. = 24° c) Int. = 165.6°, Ext. = 14.4° 10) 14 11) 12° 12) 107 13) a = 90°, b = 60°, c = 60°, d = 210°, e = 60° 14) 12 cm

x + 4

x - 5

x + 3 x + 10

x - 7

e d

c

b

a

S R

T U

Q