Download Math11_TR_Ch08W_p457-534.indd

Name
Date
REVIEW OF TERMS AND CONNECTIONS
WORDS You Need to Communicate Effectively
1. Match each term with the example that most closely represents it.
a) ratio
d) expression
g) cube root
b) square root
e) equation
h) linear function
c) origin
f) rate
i) reciprocals
i) (0, 0)
iv)
2_3
,
3 2
ii)
iii) A(t)
504t
3
27
v) 2m + 3
vi) 7 km/h
vii) 2m + 3 − 1
viii) 6 : 5
ix)
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CONNECTIONS You Need for Success
Determining Slope
Slope is the change in the value of y (the dependent variable) divided by the
change in the value of x (the independent variable), or the rate of change.
The slope of a line can be determined by dividing the rise by the run.
2. Determine the slope of the line that passes through each pair of points.
a) C(5, 0), D(1, 1)
c) X(6, − 4), Y(0, 0)
b) P(3, − 7), Q(− 2, − 4)
d) S(4, − 3), T(− 8, − 6)
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Foundations of Mathematics 11: Chapter 8: Proportional Reasoning
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Date
Calculating Surface Area and Volume
Surface Area of a Right Rectangular Prism
Surface area sum of areas of faces
SA 2(area of top + area of front + area of side)
SA 2(lw + lh + wh)
SA 2[(10 cm)(6 cm) + (10 cm)(4 cm) + (6 cm)(4 cm)]
SA 248 cm2
The surface area of the right rectangular prism is 248 cm2.
10 cm
- cm
4 cm
6 cm
10 cm
4 cm
Volume of a Right Rectangular Prism
Volume = area of base X height OR length X width X height
V = lwh
V = (10 cm)(6 cm)(4 cm)
V = 240 cm3
The volume of the right rectangular prism is 240 cm3.
Copyright © 2011 by Nelson Education Ltd.
Surface Area of a Right Cylinder
Surface area = 2(area of base) + area of curved surface
SA = 2mr 2 + 2πrh
SA = 2m(4.0 in.)2 + 2π (4.0in.)(12.0 in.)
SA = 402.123… sq in.
The surface area of the right cylinder is about 402.1 sq in.
4.0 in.
4.0 in.
12.0 in.
12.0 in.
πd
Volume of a Right Cylinder
Volume = area of base × height
V = πr2h
V = m(4.0 in.)2(12.0 in.)
V = 603.185… cu in.
The volume of the right cylinder is about 603.2 cu in.
3. Determine the surface area and volume of each 3-D object.
a) a rectangular prism with side lengths of 5 ft, 6 ft, and 2 ft
b) a cylinder with a height of 8.0 cm and a radius of 5.0 cm
c) a rectangular prism with side lengths of 8 m, 2 m, and 1 m
d) a cylinder with a height of 7.0 yd and a diameter of 6.0 yd
e) a cube with side lengths of 9 cm
PRACTISING
4. Identify the greatest common factor for each set of numbers.
a) 3, 15, 21
b) 12, 8, 20
c) 100, 1000, 75
d) 27, 18, 36
5. Express each percent or ratio as a decimal.
a) 25%
b) 14 : 5
c) 140%
d) 3 : 8
Review of Terms and Connections
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Name
Date
6. Express each measurement in the unit indicated.
a) 7.9 km, in metres
c) 1 h 25 min, in minutes
b) 36 in., in feet
d) 215 cm, in metres
7. Expand each expression.
a) 2(x + 5)
b) 4(k2 + 2k)
c) 3(5t + t2 + 1)
8. Write the reciprocal of each fraction.
9
5
c) 7
d) _
b) 1
a)
8
4
5
9. Simplify each expression.
4
x9
7 5
a) x 2 x 3
b) x__
c)
d)
(x
)
6
8
x
x
10. Determine the square root of each number. Express your answers to the
nearest hundredth, if necessary.
a) 36
b) 14
c) 100
d) 82
11. Determine the cube root of each number. Express your answers to the
nearest hundredth, if necessary.
a) 64
b) 8
c) 120
d) 92
12. Solve each equation. Express your answers to the nearest tenth, if
necessary.
_
x 34
64 t
a)
c)


4 5
5 6
21 8
b) y 71
d)


9 k
3 8
13. These 2-D shapes are similar. Identify the corresponding sides.
Copyright © 2011 by Nelson Education Ltd.
E
B
C
F
A
D
H
∠ABC + ∠BCD + ∠CDA + ∠DAB = 360o
∠ABC 124o
∠GHE 124 o
o
∠BCD 76
∠HEF 760o
o
∠CDA 110
∠EFG 110 o
o
∠DAB 51
∠FGH 51o
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Foundations of Mathematics 11: Chapter 8: Proportional Reasoning
G
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14. a) A right triangle has a hypotenuse that is 26 cm and one side that is
10 cm. What is the length of the other side?
b) A right triangle has two sides that are 4.0 in. What is the length of
the hypotenuse to the nearest tenth of an inch?
Copyright © 2011 by Nelson Education Ltd.
15. Copy and complete this chart to show what you know about rates.
Review of Terms and Connections
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