MPM 1D
Final Exam Review
Name: _________________________
Final Exam Review Answers
Unit 1 – Number Sets and Numeracy
1. Complete the chart:
N
0.34
̅̅̅̅
0. 34
√6
√36
𝜋
2 a)
3
− 20
W
I
̅
𝐐
Q
x
x
x
x
x
x
x
x
b) 43
3a)
1
−2
b) 3
4. Complete the chart.
Decimal
0.063
1.4
0.42
Unit 2 – Relationships
1a)
Fraction
Percent
6.3%
7
5
21/50
140%
63/1000
42%
R
x
x
x
x
x
MPM 1D
Final Exam Review
b)
Name: _________________________
c)
2a) Since the first differences are constant (at 3), therefore the relation is linear
b) Since the first differences are not constant, therefore the relation is non-linear
3a)
b) Strong, positive correlation
c) (2.25, 10)
d) The more time (days) that pass, the taller the
plants height
MPM 1D
Final Exam Review
4a) C = 15n +120
Name: _________________________
b) Partial
d)
e) $1095, interpolation
f) 120, extrapolation
5a) Strong positive
b) No correlation
Unit 3 – Slope, Ratio and Proportion
1. 𝑚𝑙1 =
−4
3
𝑚𝑙2 = undefined
3
𝑚𝑙3 = 2
2a) The slope represents the rate speed (distance per hour)
b) AB = 10, BC = 0, CD = 20, DE = -20
3a) m=2, b = -3, y = 2x-3
b) m= 0, b=3, y = 3
c) m=undefined, b = none, equation x=4
4a)
𝑚𝑙4 = 0
MPM 1D
Final Exam Review
b)
Name: _________________________
c)
d)
5a) 𝑚𝐴𝐵 = −1
b) 𝑚𝐴𝐵 = undefined
MPM 1D
Final Exam Review
6a) First differences are 3. Therefore, the relation is linear
Name: _________________________
b) The first differences are constant, therefore the relation is linear.
a) Two lines that are parallel
𝑦 = 2𝑥 + 4 and 𝑦 = −2 + 2𝑥
b) A vertical line
𝑥=2
c) Two lines are perpendicular
𝑦 = 2 𝑥 + 1 and 𝑦 = − 3 𝑥 − 5
d) A horizontal line
𝑦 = −6
3
2
8a) Ratio: a comparison of two quantities
b) Proportion: an equation stating that two ratios are equal
9a) x = 10
b) approximately 7.6
c) approximately 15.69
10a) 4000 mL of gas
b)1 L or 1000 mL
c) 5 cans
Unit 4 – Powers
1a) 𝑥 5
b) 𝑦 3
c) 𝑚2 𝑛2
h) 𝑥 −2 𝑦 2
i)25𝑥 −10
j) 16𝑥 −1 𝑦 6
17
b) 70 = 1
c) 72
2a) 16
3a) 11.4 cm
b) 17.0 cm
4a) 87.96 cm3
b) 25 cm
d)
𝑥5
𝑦5
16𝑤 4
𝑧4
f) 81𝑧 8
Degree of the
Polynomial
2
3
11
14
10
0
1
Coefficient of
𝒙
-3
11
-4
1
4
0
4
e)
g) 𝑥 7
1
c) 229.47 cm2
Unit 5 – Polynomials
1. Complete the chart:
Polynomial
7𝑥 2 − 3𝑥 + 7
4𝑥 3 − 2𝑥 2 + 11𝑥 − 13
11
2𝑥 − 3𝑥 8 + 6𝑥 7 − 11𝑥 2 − 4𝑥 + 8
−4𝑥 4 − 7𝑥 3 + 13𝑥 2 + 𝑥
5𝑥 10 − 3𝑥 3 + 4𝑥 − 9
12
4𝑥 + 3
2. See textbook for answers
Number of
Terms
3
4
6
4
4
1
2
3a) 5𝑥 2 𝑦 7 − 𝑥𝑦 4
b) 7𝑥 2 − 6𝑥 + 1
c) 3𝑥 + 17
4a) −12𝑥 5 𝑦 5
b) 𝑥 2
c) −2𝑥 2 𝑦 6
Coefficient of
𝒙𝟐
7
-2
-11
13
0
0
0
Constant
Term
7
-13
8
0
-9
12
3
MPM 1D
Final Exam Review
5a) 2𝑎 + 8
Name: _________________________
b) −3𝑥 + 21
c) −6𝑥 3 𝑦10 + 14𝑥 14 𝑦 6 − 10𝑥 5 𝑦 9
6a) −5𝑥 + 18𝑦
b) 𝑥 2 + 2𝑥𝑦 − 𝑦 2
c) 9𝑥 2 − 14𝑥 2 𝑦 + 𝑦 2
7. 5𝑥 2 − 9𝑥 + 14 units
8 i) 𝐴 = 5𝑥 2 + 7𝑥 units2, when 𝑥 = 4, A = 108 units2
ii) 𝐴 = 6𝑥 2 − 𝜋𝑥 2 + 4𝑥 units2, when 𝑥 = 4, A = 61.73 units2
Unit 6 – Equations
1. Check answers in textbook
2a) x = 7
b) y = -3
h) x = 3
i) x = 3
c) x = - 6
d) x = 15
e) x = 3
f) k = 4
g) a = 10
3. n = 9
4a) 10
b) 27, 28, 29
Unit 7 – The Line
1. Check answers in textbook
2.
3.
c) 10 years old
d) 20 nickels
e) 8 m by 5 m
MPM 1D
Final Exam Review
4.
Name: _________________________
5.
Equation
Slope
𝑦 = −7𝑥 − 5
-7
-5
(0, -5)
Corresponding
point
Negative
𝑦 = −4
0
-4
(0, -4)
Horizontal
0
0
= 3𝑥 − 5𝑦
+ 15
𝑦 = 6𝑥
3
5
3
(0, 3)
Positive
3
5
6
0
(0, 0)
Positive
6
𝑥=3
Undefined
None
None
Vertical
Undefined
6 a) 𝑚𝐴𝐵 = 2
7a) 𝑦 =
5
𝑥
2
y-intercept
b) 𝑚𝐶𝐷 = undefined
9
+2
c) 𝑚𝐸𝐹 = −2
Direction of
the line
-7
d) 𝑚𝐽𝐾 = 3
b) 𝑦 = 2𝑥 + 5
−1
𝑥
2
8a) 𝑦 = −5𝑥 − 8
b) 𝑦 = 5𝑥 − 31
c) 𝑦 =
10a) (8, -3)
b) (5, -2)
c) (3, 6)
7
−2
Slope of a
Slope of a line
line parallel perpendicular
1
7
undefined
d) 𝑦 = 7𝑥 − 23
−
5
3
1
6
zero
−
MPM 1D
Final Exam Review
11b)
Name: _________________________
c) 30 people, interpolate
d) $2625, extrapolate
e) C-intercept is the fixed cost of renting the banquet hall, it is $125
f) The slope represents the cost per person that attends the banquet. In this case, the cost per person is $10.
Unit 8 – Geometry
1. 70°
2. 50°
3. 60°
4. 110°
5. 130°
6. 75°
7. 30°
8. 82°
9. 60°
10. 110°
11. 90°
12. 53°
13. 88°
14. 107°
2a) 2418m2
b)$846.30
3a) 600m2
b)100 m
c) $858.00
Unit 9 – Measurement
1a) 24 cm
4b) 32m2
b) 5.6 m