MPM 1D
Final Exam Review
Name: _________________________
Final Exam Review
Review the terminology presented throughout the course.
Unit 1 – Number Sets and Numeracy
1. Complete the chart:
N
W
0.34
̅̅̅̅
0. 34
√6
√36
𝜋
2. Simplify. Make sure to show all of your work.
3
55
2
1
a) 2 4 ÷ 12 − 3 × 1 8
b) 3 − 4(12 ÷ (−3) + 6 × (−1))
3. Substitute, then evaluate for 𝑥 = 3 and𝑦 = −4
a)
2𝑥−3𝑦
3𝑥𝑦
b)
𝑥 2 −𝑥𝑦
𝑥−𝑦
I
Q
̅
𝐐
R
MPM 1D
Final Exam Review
4. Complete the chart.
Decimal
0.063
Name: _________________________
Fraction
Percent
7
5
42%
Unit 2 – Relationships
1. Set up a table of values and graph each relation (one graph per grid).
1
a) 𝑦 = −2𝑥 + 4
b) 𝑦 = 3 𝑥 − 5
c)𝑦 = 2𝑥 2 + 1
2. Complete a difference table, state whether the relation is linear or non linear and why.
x
-2
-1
0
1
2
y
-1
2
5
8
11
x
-2
-1
0
1
2
y
-2
1
2
1
-2
MPM 1D
Name: _________________________
Final Exam Review
Time (days)
3. The table below shows the heights of several plants after various growing times.
1
3
a) Plot the data on a scatter plot.
2
3
b) What type of correlation is there between the variables?
4
2
1
c) Calculate the mean point. Draw the mean line of best fit.
2
Height (mm)
6
13
11
14
15
10
4
7
d) Describe the relationship between the number of days that have elapsed and a plant’s height.
4. Jess is planning an anniversary celebration for her parents. The caterer is charging a hall rental fee of $120 and $15
per person attending the dinner. Let 𝐶, in dollars ($), be the total cost of the dinner and 𝑛 be the number of people
attending the dinner.
𝒏
a) Write an equation to represent the situation.
0
b) Is this partial or direct variation?
25
c) Create a table of values for n = 0, 25, 50, 75, 100
50
d) Draw the graph of the relation.
e) What is the total cost if 65 people attend the celebration? Did
you interpolate or extrapolate?
75
100
f) How many people are attending if the total cost is $1920? Did
you interpolate or extrapolate?
5. Describe the correlation in each graph (positive, negative, weak, strong, none)
a)
b)
𝑪 =
(𝒏, 𝑪)
MPM 1D
Final Exam Review
Unit 3 – Slope, Ratio and Proportion
Name: _________________________
1. State the slope of each line.
𝑚𝑙1 =
𝑚𝑙2 =
𝑚𝑙3 =
𝑚𝑙4 =
2. Using the graph to the right:
a) What does the slope represent?
b) Determine the slope of each section of the graph.
c) Write a short story that describes the graph, with reference to the distance, speed and time.
MPM 1D
Name: _________________________
Final Exam Review
3. State the slope, y-intercept and the equation of each line from the graph.
4. Graph each of the following lines on separate grids:
2
a) P (3, 4) lies on the line, with slope − 3
b) 𝑦 = 3𝑥 + 4
c) A (-3, 2) lies on the line, with a slope that is undefined
d) B (4, -1) lies on the line, with a slope of zero
5. Use the slope formula to find the slope of the line passing through the given points.
a) A (3, -5) and B (-6, 4)
b) X (7, 3) and Y (7, 5)
6. Determine whether the relations are linear or nonlinear by completing a finite difference table for each.
x
-4
-2
0
2
4
y
-7
-4
-1
2
5
MPM 1D
Final Exam Review
x
-2
-1
0
1
2
Name: _________________________
y
10
7
4
1
-2
7. Given the following linear equations:
i) 𝑦 = 2𝑥 + 4
3
iv) 𝑦 = 2 𝑥 + 1
2
ii) 𝑦 = − 3 𝑥 − 5
iii) 𝑦 = −6
v) 𝑥 = 2
vi) 𝑦 = −2 + 2𝑥
Write the appropriate equations in the space provided.
a) Two lines that are parallel
_________________________ _________________________
b) A vertical line
_________________________
c) Two lines are perpendicular
_________________________ _________________________
d) A horizontal line
_________________________
8. Define the following terms:
a) ratio:
b) proportion:
9. Find the value of 𝑥 in each of the following proportions:
a) 5 : 13 = 𝑥 : 26
b) 11 : 4 = 21 : 𝑥
c) 𝑥 : 12 = 17 : 13
10. One brand of chain saw requires a gasoline mixture of 32 : 1.
a) If you have 125 mL of oil, how much gas must you have to complete the proper oil mixture?
MPM 1D
Name: _________________________
Final Exam Review
b) The fuel tank on this chain saw holds 1000 mL. How much gasoline and oil do you need to fill this tank?
11. One can of concentrated orange juice is mixed with three cans of water.
a) How much orange juice can you make with one 250 mL can of concentrate?
b) How many 250 mL cans of concentrate and needed to make 5L of juice?
Unit 4 – Powers
1. Simplify using Power Laws
a. 𝑥 2 (𝑥 3 )
b. 𝑦10 ÷ 𝑦 7
c. (𝑚𝑛)2
f. (3𝑥 2 )4
g. 𝑥 5 (𝑥 2 )
h. 𝑥 4 𝑦1
𝑥 2𝑦3
𝑥 5
2𝑤 4
)
𝑧
d. (𝑦)
e. (
2
i.
(−5𝑥𝑦 3 )
(𝑥 4 𝑦 2 )3
2. Simplify using power laws, and then evaluate. Do not use decimals!
4
a) 30 ÷ 4−2
b.
7−2 (73 )
(75 )2
c. 2−3 − 3−2
2
j.
(4𝑥 3 𝑦 2 ) (8𝑥 5 𝑦 8 )
(2𝑥 4 𝑦 2 )3
MPM 1D
Final Exam Review
3. Determine the value of x.
Name: _________________________
a)
7cm
x
9 cm
b)
18 cm
x
6 cm
5. a) Find the volume of the cylinder
c) Determine the area of the shaded region
b) Determine the perimeter of the figure
MPM 1D
Final Exam Review
Unit 5 – Polynomials
Name: _________________________
1. Complete the chart:
Polynomial
Number of
Terms
Degree of the
Polynomial
Coefficient of
𝒙
7𝑥 2 − 3𝑥 + 7
4𝑥 − 2𝑥 2 + 11𝑥 − 13
2𝑥 11 − 3𝑥 8 + 6𝑥 7 − 11𝑥 2 − 4𝑥 + 8
−4𝑥 4 − 7𝑥 3 + 13𝑥 2 + 𝑥
5𝑥 10 − 3𝑥 3 + 4𝑥 − 9
12
4𝑥 + 3
3
2. Page 387 #12, 13
3. Simplify:
a) 4𝑥 2 𝑦 7 − 3𝑥𝑦 4 + 𝑥 2 𝑦 7 + 2𝑥𝑦 4
b) (3𝑥 2 − 4𝑥 − 7) − (−4𝑥 2 + 2𝑥 − 8)
c) 5 − 3(2𝑥 − (3𝑥 + 4))
4. Simplify.
a) (6𝑥𝑦 3 )(−2𝑥 4 𝑦 2 )
b) 𝑥 5 ÷ 𝑥 3
Coefficient of
𝒙𝟐
Constant
Term
MPM 1D
Final Exam Review
c)
Name: _________________________
(4𝑥 2 𝑦 11 )(−5𝑥 3 𝑦 5 )
(−2𝑥 2 𝑦)(−5𝑥𝑦9 )
5. Expand and simplify where needed.
a) 2(𝑎 + 4)
b) −3(𝑥 − 7)
c) 2𝑥 2 𝑦 5 (−3𝑥𝑦 5 + 7𝑥 2 𝑦 − 5𝑥 3 𝑦 4 )
6. Expand and simplify.
a) 3(𝑥 + 2𝑦) − 4(2𝑥 − 3𝑦)
c) 4𝑥(3𝑥 − 4𝑥𝑦) + 2𝑦(𝑥 2 − 𝑦) − 3(𝑥 2 − 𝑦 2 )
b. 𝑥(𝑥 + 𝑦) + 𝑦(𝑥 − 𝑦)
MPM 1D
Name: _________________________
Final Exam Review
7. Determine an expression for the missing side of the triangle, given that the Perimeter is modeled by the expression
𝑃 = 9𝑥 2 − 6𝑥 + 5
8. a) Write an expression for the area of the shaded region. Make sure to simplify fully.
b) Evaluate when 𝑥 = 4
i)
ii)
Unit 6 – Equations
1. Page 253 # 3, 4, 5, 6, 8; Page 298 # 8, 9, 10; Page 301 #15
2. Solve:
a) 6 + 3𝑥 = 27
b) 2 − 3𝑦 = 11
MPM 1D
Final Exam Review
c) 3𝑥 − 7 = −25
e)
3𝑥−1
4
Name: _________________________
d)
=2
2
3
2𝑥−1
6
=
=6
f) 5𝑘 − 2 = 4𝑘 + 2
g) 9𝑤 = 7𝑤 − (20 = 4𝑤)
i) +
𝑥−3
2
3𝑥−2
3
−
5
6
3. Solve and check.
3(2𝑛 − 4) = 4(𝑛 + 3) − 6
h) 4(𝑥 − 1) = 17 − 3𝑥
MPM 1D
Final Exam Review
4. Solve the following word problems:
Name: _________________________
a) Six more than three times a number is 36. Find the number.
b) The sum of three consecutive numbers is 84. Find the numbers.
c) Kyle is eight years older than Pat. In four years the sum of their ages will be 36. How old is Pat?
d) Sarah has 45 coins made up of quarters and nickels. If she has $7.25, how many nickels does she have?
MPM 1D
Name: _________________________
Final Exam Review
e) The length of a rectangle is 3 m greater than the width. Find the dimensions if the perimeter is 26m.
Unit 7 – The Line
1. Page 387 #15
2. Use a table of values to graph 𝑦 = −3𝑥 + 2
3
3. Graph 𝑦 = − 7 𝑥 − 4 using slope and y-intercept.
4. Graph the line 2𝑥 − 5𝑦 + 10 = 0 using x and y –intercepts.
MPM 1D
Final Exam Review
5. Complete the following table:
Equation
Slope
Name: _________________________
y-intercept
Corresponding
point
Direction of
the line
Slope of a line
parallel
Slope of a line
perpendicular
𝑦 = −7𝑥 − 5
𝑦 = −4
0 = 3𝑥 − 5𝑦 + 15
𝑦 = 6𝑥
𝑥=3
6. Find the slope of the line passing through the following points, and state the direction of the line.
a) A (1, 4) and B (3, 8)
b) C (-3, 8) and D (-3, 3)
d) G (-4, 9) and H (8, 9)
e) J (7, 11) and K (4, 2)
7. Rewrite the following equations into the form 𝑦 = 𝑚𝑥 + 𝑏
a) 5𝑥 − 2𝑦 + 9 = 0
b) 2𝑥 − 𝑦 + 5 = 0
8a) Find the equation of the line with a slope of -5 and y-intercept of -8.
b) Find the equation of the line with slope of 5 and passing through the point (7, 4)
c) E (0, -6) and F (1, -8)
MPM 1D
Name: _________________________
Final Exam Review
1
c) Find the equation of the line with slope of 2 and passing through the point (-3, -2)
d) Find the equation of the line passing through the points A (3, -2) and B (4, 5).
9. Solve the following systems graphically, use the method indicated:
a) 𝑥 + 𝑦 = 5 and 𝑥 + 5𝑦 = −7, using a table of values
b) 2𝑥 + 𝑦 = 8 and 4𝑥 − 5𝑦 = 30 using x and y-intercepts.
MPM 1D
Final Exam Review
c) 𝑦 = 2𝑥 and 𝑦 = 12 − 2𝑥
Name: _________________________
11. The cost, C in ($) to rent a banquet room is given by the equation 𝐶 = 125 + 10𝑛
a) Complete a table of values for n=0, 50, 100, 150 and 200
b) Draw the graph using an appropriate scale.
Use the graph to answer the following questions:
c) How many people will attend the banquet if the cost is $425? Did you interpolate or extrapolate?
d) What is the cost if 250 people attend the banquet? Did you interpolate or extrapolate?
e) What does the C-intercept represent?
f) What does the slope represent?
Unit 8 – Geometry
Find the missing angle measures.
1.
2.
MPM 1D
Final Exam Review
3.
5.
Name: _________________________
4.
6.
7.
9.
8.
10.
MPM 1D
Final Exam Review
11.
Name: _________________________
12.
13.
14.
Unit 9 – Measurement
1. The perimeter of each figure is given. Find the missing dimensions.
a)
b)
MPM 1D
Final Exam Review
2a) Calculate the area of the field shown in the diagram.
Name: _________________________
30 m
80.6 m
b) How much would it cost to fertilize the field if 1kg of fertilizer is needed for 10 m2 of field and fertilizer costs
$3.50/kg?
3a) Calculate the area of the flower bed.
30 m
20 m
b) Calculate the perimeter of the flower bed.
c) How much would it cost to fence the bed at a cost of $1.43/m2
4. A swimming pool cabana is made out of cloth. It consists of a rectangular prism (2m wide by 2m deep by 2m high)with
a square based pyramid on top (height of 2m).
a) Sketch the cabana.
b) What is the total area of material needed for the cabana.
MPM 1D
Final Exam Review
Name: _________________________
MPM 1D
Final Exam Review
Name: _________________________