11 Interest: Investing Money
Relating Units of Time 1. Becky has been working at a fl ower shop for 2.15 yr.
a) How long is this in weeks? Round up.
2.15 yr 3 wk/yr is about wk
b) How long is this in days? Round up.
2.15 yr 3 d/yr is about d
2. Write each length of time as a fraction of the unit given.
a) 6 d 5 365
yr c) 18 wk 5 yr
b) 35 d 5 yr d) 8 d 5 mo
Working with PercentsPercent means “out of 100.”1% is the same as 1 hundredth, or 1
100, or 0.01.
32% is the same as 32 hundredths, or 32100, or 0.32.
32.5% is between 32% and 33%. So, it is between 0.32 and 0.33.
Ones Tenths Hundredths Thousandths
0 3 2 5 32.5% 5 0.325
3. Write each percent as a decimal.
a) 9% 5 d) 4.8% 5
b) 25% 5 e) 11.9% 5
c) 79% 5 f ) 0.8% 5
4. Write each decimal as a percent.
a) 0.02 5 % d) 0.269 5 %
b) 0.58 5 % e) 0.005 5 %
c) 0.45 5 % f ) 0.152 5 %
The whole number part of the percent ends with the number of hundredths in the decimal.
Hint
To write a decimal as a percent, write the number of hundredths. 0.75 5 75%0.399 5 39.9%
Hint
Use1 yr (year) 5 365 d (days)
5 52 wk (weeks) 5 12 mo (months)
1 mo 5 30 d
Hint
1NEL Chapter 1 Interest: Investing Money
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5. Calculate each percent.
a) 10% of 280 5 c) 7.5% of 200 5
b) 6% of 275.5 5 d) 0.8% of 620 5
Multiplying Decimals and Fractions 6. Multiply.
a) 1.64 3 34
5 c) 1.98 3 7
52 5
b) 0.05 3 60
365 5 d) 4.453 3
512
5
Solving Equations 7. Solve for each variable.
a) 3s 1 11 5 35
3s 1 11 2 11 5 35 2 11
3s 5
s 5
c) 2 5 t5
2 4
b) 1.1d 5 44 d) 0.85 5 6.12
n
Calculating with ExponentsAn exponent shows how many times a number is multiplied by itself.
5(2)2 5 5 3 2 3 25 5 3 4
5(2)3 3 2 5 5(2)6
5 5 3 2 3 2 3 2 3 2 3 2 3 25 5 3 64
5(0.1 1 0.5)3 5 5 3 0.6 3 0.6 3 0.65 5 3 0.216
8. Calculate.
a) 5(3)2 5 d) 4(5)3 3 2 5
b) 8(2.3)5 5 e) 4.25(0.8)4 3 2 5
c) 2.8(1.8)4 5 f ) 7.62(1 1 0.1)5 5
10% of 280 means the same as 10% 3 280, or 0.1 3 280.
Hint
Multiplying a Decimal by a FractionTo multiply5.2 3 45, enter 5.2 3 4 4 5 5
Tech Tip
Square Key (x2)To calculate 5(2)2, enter 5 3 2 x2 5
Tech Tip
Exponent Key (yx)Use the exponent key for exponents other than 2. For 5(2)6, enter5 3 2 yx 6 5
Tech Tip
2NEL Apprenticeship and Workplace 11: Review of Essential Skills
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22 Working with Graphs
Graphing Data 1. Shade bars on the bar graph to show the monthly ticket
sales. The fi rst bar is done for you.
Month
Number of Tickets Sold
Num
ber
so
ld
Jan. Feb. Mar. Apr.
200
400
600
800
0 May
Number of Tickets Sold
Month Number sold
January 750
February 500
March 400
April 650
May 325
2. Plot points on the grid to show the total amount of money raised for a school trip. The fi rst point is plotted for you.Join the points.
0
Amount of Money Raisedfor School Trip
Tota
l am
oun
t ra
ised
Week
400
800
1200
1600
1 2 3 4 5 6 7 8 9 10
Amount of Money Raised for a School Trip
WeekTotal amount
raised ($)
1 200
2 400
3 500
4 600
5 900
6 1000
7 1100
8 1200
9 1200
10 1400
3NEL Chapter 2 Working with Graphs
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Reading Graphs 3. Matt counted the number of customers
in a store each hour, from opening time until closing time.
a) About how many customers were in the store at 10 a.m.?
b) About how many customers were in the store at 1 p.m.?
c) At what time were there about 45 customers in the store?
d) At what time were the most customers in the store?
4. Anna, Ben, Candace, and Dan ran for student-council president. The graph shows the election results.• Use the graph to estimate what
percent of the students voted for each person.
• Record your estimates in the chart below.
• Check to make sure that your total is 100%.
• Explain how you used a fraction to estimate each percent.
Anna Ben Candace Dan
Estimated percent % % % %
How I estimated
10 a.
m.
12 p
.m.
2 p.m
.
4 p.m
.
6 p.m
.
8 p.m
.
10 p
.m.
Customers in a Store
Num
ber
of
cust
om
ers
Time
20
0
40
60
80
Dan
Candace
Ben
Anna
Percent of Votes inSchool Election
To estimate percents on a circle graph, compare the parts with benchmark fractions or decimals. Examples of benchmarks are 12 or 50%,14 or 25%, and13 or about 33%.
Hint
4NEL Apprenticeship and Workplace 11: Review of Essential Skills
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Units of Measurement 1. Match each object to the amount of space it could cover.
beach towel about 1 sq ft
ruler about 2 m2
tablecloth about 15 cm2
bathroom scale about 12 sq in.
pen about 1 sq yd
Working with Polygons 2. The area of a polygon is the number of square units of space
that it covers. Name each polygon, and determine its area.
a) 6 m
3 m
Name of polygon:
Area 5 m 3 m
5 m2
c) 2.1 ft
4.2 ft
4.7 ft
Name of polygon:
Area 5
5
b)
7 in.14 in.
Name of polygon:
Area 5
5
d) 12 cm
5 cm
5 cm
Name of polygon:
Area 5
5
Surface Area
Units of Measurem1 Match each objec
S33Suppose you cut apart this square and then put the pieces together to make a new shape. The new shape would still cover 1 sq ft.
1 ft
1 ft
Hint
areas of polygons rectangle
A 5 (length)(width) 5 lw
w
l
triangle
A 5 12
(base)(height)
5 12
bh
h
b
parallelogram
A 5 bh
h
b
trapezoid
A 5 12
(b 1 B)h
h
B
b
5NEL Chapter 3 Surface Area
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Working with Circles 3. Use the formulas at the right. If your calculator does not have
a key for p, use 3.14 as an estimate for p.
a) Determine the circumference, to the nearest whole unit.
4.5 m
diameter 5 m
C 5 3 m
5 m,
or about m
b) Determine the area, to the nearest whole unit.
10 in.
radius 5 in.
A 5 3 ( in.)2
5 sq in.,
or about sq in.
Using the Pythagorean TheoremThe Pythagorean theorem can be used for right triangles.
Pythagorean theorem: Suppose you drew a square on each side of a right triangle. You could exactly cover the square on the longest side by combining the areas of the squares on the two shorter sides.
Suppose you knew the lengths of two sides of a right triangle. You could use this formula to calculate the length of the third side.
4. Use the Pythagorean theorem to calculate the unknown side length. Label each length on the diagram, to one decimal place.
(6 m)2 1 (8 m)2 5 c2
m2 1 m2 5 c2
m2 5 c2
" m2 5 "c2
m 5 c
a2 � b2 � c2
a c
b
c
6 m
8 m
circle formulas
radius
diameter
circumference
C 5 p 3 (diameter)or C 5 2p 3 (radius)
area
A 5 p 3 (radius)2
The square root of a number is the side length of a square whose area is the number. For example: !9 5 3 because a square with an area of 9 square units has sides that are 3 units long (3 3 3 5 9).
Hint
6NEL Apprenticeship and Workplace 11: Review of Essential Skills
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Units of Measurement 1. Draw a line to match each volume to an object.
5 cu ft semi-trailer for a truck
60 m3 suitcase
12 cu yd softball
30 cu in. full tube of toothpaste
120 cm3 load of dirt in a dump truck
2. Draw a line to match each capacity to a container.
10 gal soup bowl
80 L hot-water tank
15 mL cooking pot
2 c aquarium
1 qt spoon
Calculating Volume 3. Calculate the volume.
a)
6 ft 3 ft
2 ft
b)
6.4 cm
7 cm
V 5 (Abase)(h) V 5 (Abase)(h)
5 ( ft 3 ft)( ft) 5 pr2(h)
5 cu ft 5 p( cm)2( cm)
5 cm3
Volume and Capacity
Units of Measurem1. Draw a line to ma
V44
Volume measures the space that an object occupies.
Hint
Capacity measures the amount that a container can hold.
Hint
For prisms and cylinders: Volume 5 (area of base)(height)
Hint
7NEL Chapter 4 Volume and Capacity
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Multiplying with Fractions 4. Multiply.
a) 12
(2.8 cm)(3.5 cm)(2 cm) 5 12
( cm3)
5 cm3
b) a34
ydb a23
ydb 5 3 3 24 3 3
sq yd
5
sq yd
5
sq yd
c) 78
mi 334
mi 5 3
3 sq mi
5
sq mi
d) a23
ftb a612
ftb 5 3
3 sq ft
5
sq ft
5
sq ft
Working with Capacity 5. Complete each sentence.
a) You can pour pt into a 1 gal container.
b) You can pour mL into a 1 L container.
c) You can pour c into a 1 qt container.
d) You can pour c into a 2 gal container.
Multiplying by 12 gives the same result as dividing by 2.
Hint
To multiply two fractions, multiply the numerators and multiply the denominators.45
356
54 3 55 3 6
52030
523
To multiply by a mixed number, write the mixed number as an improper fraction.
412
334
592
334
59 3 32 3 4
5278
5 338
Hint
Use the charts inside the back cover of the Workbook.
Hint
8NEL Apprenticeship and Workplace 11: Review of Essential Skills
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Interest: Borrowing Money
Working with Money 1. Use mental math to estimate each amount, to the nearest
dollar.
a) 12 of $19.99 is about $ .
b) 13 of $30.25 is about $ .
c) 23 of $30.25 is about $ .
d) 14 of $99.50 is about $ .
e) 34 of $99.50 is about $ .
2. Use mental math to estimate each amount, to the nearest dollar.
a) 10% of $69.99 is about $ .
b) 25% of $79.98 is about $ .
c) 75% of $79.98 is about $ .
d) 33% of $2100 is about $ .
e) 20% of $2510 is about $ .
3. Evaluate to the nearest cent. Estimate to check that your answers make sense.
a) 18.5% 3 $2200 5
b) 17.6% 3 $20 000 5
c) 12.8% 3 $11 500 5
d) 9.25% 3 $42 000 5
e) 24.85% 3 $10 375 5
f) 32.75% 3 $59 729 5
4. Evaluate.
a) $1000 1 (6% of $1000) 5 $1000 1
5
b) $7500 1 (12% of $7500) 5 $7500 1
5
In
Working with Mon1 Use mental math
55
To calculate 14 of a number, divide by 4.To calculate 34 of a number, divide by 4 and multiply by 3.
Hint
10% 5 10100 or 1
10
20% 5 20100 or 15
25% 5 25100 or 14
33% 5 33100 or about 13
50% 5 50100 or 12
75% 5 75100 or 34
Hint
Multiplying with PercentsTo calculate 18.5% of $2200, enter18.5 % 3 2200 5 ,
or0.185 3 2200 5
Tech Tip
When working with money, round to the nearest cent after you have made the fi nal calculation.
Hint
9NEL Chapter 5 Interest: Borrowing Money
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c) $3000 1 (16.2% of $3000) 5 $3000 1
5
Calculating with Exponents 5. Calculate. Round to the nearest hundredth.
a) 3.15 5 c) 5(1 1 0.08)4 5
b) (1 1 0.3)3 5 d) 3a1 10.0712
b10
5
Using Interest FormulasSimple interest: To calculate the amount of simple interest, I, earned on an investment, use
I 5 Prt
where P is the principal, r is the yearly interest rate, and t is the time in years.
6. Sophie invested $1000 in a guaranteed investment certifi cate for 3 yr. The interest rate is 1.8% per year. How much interest will Sophie earn?
I 5 Prt
5 $ 3 0.018/yr 3 3 yr
5 $
Sophie will earn $ in interest.
Compound interest: To calculate the value of an investment amount, A, earning compound interest, use
A 5 P(1 1 i)n
where A is the total value of the investment with interest, P is the principal, i is the interest per compounding period, and n is the number of compounding periods.
7. Max invested $1200 in a savings account. The account earns 2.3%/yr, compounded monthly. How much will Max’s investment be worth in 3 yr?
A 5 $1200a1 10.023
12b3312
5 $1200 ( )36
5 $
Max’s investment will be worth $ in 3 yr.
Multiplying Expressions in BracketsUse 3 to multiply expressions in brackets. For example, for 5(1 1 0.08)4, enter5 3 ( 1 1 0.08 ) yx 4 5
Tech Tip
10NEL Apprenticeship and Workplace 11: Review of Essential Skills
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Relating Decimals, Percents, and Fractions 1. Complete each row in the chart by expressing the same
number in different ways.
Decimal PercentFraction in
lowest terms
0.75 75%
75100
575 4 25
100 4 25
534
0.4
60%
18
Writing Ratios in Lowest TermsA ratio compares two numbers. A ratio is in lowest terms if the numbers have no common factors.
14 : 35 is not in lowest terms because 7 is a factor of both numbers.14 4 7 5 2 and 35 4 7 5 5 14 : 35 5 2 : 5, in lowest terms
2. Write each ratio in lowest terms.
a) 20 : 15 5 4 : d) 12 : 36 5
b) 3 : 18 5 e) 16 : 40 5
c) 50 : 40 5 f ) 42 : 24 5
Converting Measurements 3. a) 2.5 h 5 min c) 8 yd 5 ft
b) 2.1 km 5 m d) 0.2 L 5 mL
Slope and Rates
Relating Decimals1. Complete each ro
S6 6
To write a fraction in lowest terms, divide the numerator and the denominator by their greatest common factor.
Hint
Writing a ratio as a fraction can help you write it in lowest terms.
14 : 35 5 1435
5 25
5 2 : 5
Hint
Use the charts inside the back cover of the Workbook.
Hint
11NEL Chapter 6 Slope and Rates
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Working with Integers
• Sometimes, it helps to think about what the operation means.3 3 (24) means “3 groups of (24).” 3 3 (24) 5 212
• Sometimes, it helps to think about opposites. 10 4 5 5 2, so 10 4 (25) must be the opposite. 10 4 (25) 5 22
• Sometimes, it helps to think about the related operation. For 214 4 (22), think about the related multiplication. 7 3 (22) 5 214, so 214 4 (22) 5 7
4. Multiply or divide.
a) 6 3 (23) 5 d) 224 4 8 5
b) 24 3 8 5 e) 30 4 (25) 5
c) 26 3 (27) 5 f ) 227 4 (23) 5
Think of a number line to subtract with integers.
When you multiply or divide two integers with the same sign, the result is positive.
3 3 4 5 1223 3 (24) 5 12
12 4 4 5 3212 4 (24) 5 3
Hint
tan A° 5oppositeadjacent
Hint
opp
osite
∠A
adjacent to ∠A
hypotenuse
A°
Move right to subtracta negative number.
Move left to subtracta positive number.
6543210�1�2�3�4�5�6
0 � 4 � �4 0 � (�4) � 4
5. Subtract.
a) 12 2 8 5 d) 4 2 (23) 5
b) 3 2 6 5 e) 210 2 (26) 5
c) 25 2 8 5 f ) 212 2 (215) 5
Calculating Tangents 6. Calculate the tangent for each angle of elevation.
a)
35 ft
x°
20 ft
b)
8 mt°
6 m
tan x° 5 tan t° 5
12NEL Apprenticeship and Workplace 11: Review of Essential Skills
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Using Equivalent RatiosA ratio compares two numbers. For example, 5 to 26, or 5 : 26, is the ratio of vowels to total letters in the alphabet.
Equivalent ratios describe the same relationship. Suppose that you wrote the alphabet twice. The ratio of vowels to total letters would be 10 : 52. The two ratios, 5 : 26 and 10 : 52, are equivalent ratios.
32 42
526
51052
5
265
1052
You get an equivalent ratio when you multiply or divide both terms in a ratio by the same number.
32 42
Sometimes, one number in a pair of equivalent ratios is missing.
16 : 40 5 ? : 10
To calculate the missing number, determine the factor that the numbers in one ratio are multiplied or divided by to get the other ratio.
44 34
1640
54
10 or
1640
54
10
44 34
1. Calculate the missing terms.
3 4
a) 6
24 5
12
b)5
40 5
8
3 4
Drawing Objects and Shapes
Using Equivalent A ratio compares two
D77
Use the given numbers to determine the multiplication or division factor.
Hint
13NEL Chapter 7 Drawing Objects and Shapes
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2. Calculate the missing term.
a) 3 : 5 5 : 25 c)8
36 5
2
b) 1260
5 20
d) 12 : 15 5 : 5
Comparing Similar Shapes 3. Rectangle ABCD was enlarged to make
rectangle EFGH. The angles did not change.
All the side lengths of rectangle ABCD were multiplied by 2.
a) How long is HE?
b) How long is EF?
c) How long is GH?
d) The ratio of length : width for rectangle ABCD is 5 : 3. What is the ratio of length : width for rectangle EFGH? :
e) What is the ratio from Part d) in lowest terms?
:
Multiplying Mixed Numbers by Whole Numbers
Method 1: Multiply the whole numbers. Then multiply the fraction parts.
4 3 314
in. 5 (4 3 3 in.) 1 a4 314
in.b 5 12 in. 1 1 in. 5 13 in.
Method 2: Change the mixed number to a fraction.
4 3 314
in. 5 41
3 134
in.
54 3 131 3 4
in.
5524
in.
5 13 in.
3 m
A
B
? m
E
F
D
C
H
G
? m
5 m
314 is a mixed
number.
314 5 3 wholes
and 14
3 wholes 5 124 ,
so 314 5 12
4 1 14
5 134
134 is the fraction name for 31
4.
Hint
4. Multiply.
a) 5 3 218
in. 5 b) 2 3 612
ft 5
5 5
5 5
14NEL Apprenticeship and Workplace 11: Review of Essential Skills
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Adding and Subtracting with MoneyWhen you add or subtract money amounts on paper, line up the dollars and cents.
$126.75 14.001 7.60$148.35
1. Farida shares an apartment with a roommate. This chart shows the bills that she pays each month.
a) How much does Farida pay for her cellphone plus the Internet?
b) What are Farida’s total monthly expenses?
c) Farida earns $2500.00 per month. How much money is left after she pays her monthly expenses?
d) How could Farida use the money she has left after expenses? Estimate the cost for each item. Include an amount for monthly saving.
If there are no cents, write zeros after the decimal point. This keeps the numbers in line.
Managing Money
Adding and SubtraWhen you add or sub
M88
Dollars and CentsWhen you enter money numbers in a calculator, you do not need to enter “.00” if there are no cents.
Tech Tip
Monthly Expenses
rent $485.00
utilities $75.43
cellphone $45.00
Internet $35.26
food $375.00
bus pass $55.00
Farida’s Spending Plan
savings
Total
15NEL Chapter 8 Managing Money
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Relating Percents to Decimals 2. Write each percent as a decimal.
a) 6% 5 c) 15% 5
b) 90% 5 d) 12.5% 5
3. Write each decimal as a percent.
a) 0.01 5 % c) 0.7 5 %
b) 0.45 5 % d) 0.152 5 %
Calculating Percents 4. Calculate.
a) 22% of $375 5 c) 2% of $1500 5
b) 63% of $1200 5 d) 37.5% of $92 5
To write a percent as a decimal, write the number of hundredths.9% 5 9 hundredths, or 0.0980% 5 80 hundredths, or 0.80, or 0.811.5% 5 11 hundredths 5 thousandths, or 0.115
Hint
Another way to calculate the percent of a number is to calculate 1% of the number. Then multiply by the percent you are determining. To calculate 11% of $150:
1% of $150 5 $150 4 100 5 $1.5011% of $150 5 11 3 $1.50 5 $16.50
Hint
Percents of Money AmountsCalculate 25% of $350. If your calculator has a % key, enter
350 3 25 % 5 , or 350 3 25 2nd % 5
If your calculator does not have a % key, enter
350 3 0.25, or 350 3 25 4 100 5
Tech Tip
5. The sale price of an electric guitar is 85% of $400. What is the sale price?
Calculating with Exponents An exponent shows how many times a number is multiplied by itself.
6(4)2 5 6(4)(4) 3(0.1 1 0.2)2 5 3(0.3)(0.3) 5 6(16) 5 3(0.09) 5 96 5 0.27
6. Calculate.
a) 2(7)2 5 c) 5(0.8)4 5
b) 7.2(1.1)5 5 d) 8.3(1 1 0.1)4 5
16NEL Apprenticeship and Workplace 11: Review of Essential Skills
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Using the Pythagorean TheoremIf you know the lengths of two sides of a right triangle, you can use the Pythagorean theorem to determine the length of the third side.
1. Use the Pythagorean theorem. Calculate the unknown side length. Label each length, to one decimal place.
a)
9 m
5 m
(9 m)2 1 (5 m)2 5 c2
m2 1 m2 5 c2
m2 5 c2
" m2 5 "c2
m 5 c
c)
3 in.
6 in.
(3 in.)2 1 (6 in.)2 5 c2
sq in. 1 sq in. 5 c2
sq in. 5 c2
" sq in. 5 "c2
in. 5 c
b) (4 cm)2 1 b2 5 (11 cm)2
16 cm2 1 b2 5 121 cm2
b2 5 121 cm2 2 cm2
b2 5 cm2
"b2 5 " cm2
b 5 cm
c
b
a
4 cm11 cm
Solving Right Triangle Problems
Using the PythagoIf you know the length
S99
Suppose that you know the lengths of a and c, but not the length of b. You can use b2 5 c2 2 a2.
Hint
a2 1 b2 5 c2
17NEL Chapter 9 Solving Right Triangle Problems
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Using Trigonometric RatiosTrigonometric ratios work for right triangles. You can use trigonometric ratios to calculate side lengths and angle measures.
opp
osite
to
∠A
adjacent to ∠A
hypotenuse
25°A C
B
• In the triangle above, /A is 25°.• /B must be 65° since 25° 1 90° 1 65° 5 180°. • Every right triangle with a 25° angle has the same angles. • Triangles with the same angles are similar.• Similar triangles have the same side : side ratios.
2. a) Use side lengths to calculate each ratio in the chart below for the triangle at the right. Answer to four decimal places.
b) Calculate each ratio using the trig function keys on a calculator. Do your answers match?
Ratio a) Using side lengths b) Using a calculator
sin 35° 5opposite
hypotenuse7.0
12.2 ft 5 ft sin 35° 5
cos 35° 5adjacent
hypotenuse
tan 35° 5oppositeadjacent
3. a) Use a calculator. Enter the tangent of 35° that you calculated for Question 2. Then press tan21. What does your calculator show, to the nearest whole number?
b) What does this number tell you about the triangle?
12.2 ft7.0 ft
10.0 ft
Y
ZX35°
The three trigonometric ratios for ∠A are
sin A
5opposite
hypotenuse
cos A
5adjacent
hypotenuse
tan A
5oppositeadjacent
Hint
Inverse Trig FunctionsThe sin21, cos21, and tan21 keys are called inverse trig functions.
Tech Tip
18NEL Apprenticeship and Workplace 11: Review of Essential Skills
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Identifying and Extending Patterns 1. Describe each pattern.
a) 15, 18, 21, 24 …
The pattern starts with .
Each number is the number before it.
b) 92, 87, 82, 77 …
The pattern starts with .
Each number is the number before it.
c) 2, 4, 8, 16 …
The pattern starts with .
Each number is the number before it.
2. Write the next two terms in each pattern.
a) 40, 43, 46, 49, ,
b) 95, 91, 87, 83, ,
c) 6, 18, 54, 162, ,
d) 226, 201, 176, 151, ,
Making a Table of ValuesA table of values shows how two variables are related. Here, the amount of money earned increases by $15 for each hour worked.The following equation shows this relationship:
money earned 5 hours 3 $15
3. Complete the table of values for each relation.
a) y 5 x 1 4
x 0 1 2 3 4
y 4
c) y 5 2x 2 3
x 0 1 2 3 4
y
b) y 5 x 2 6
x 0 1 2 3 4
y 26
d) y 5 4x 1 3
x 0 3 6 9 12
y
Linear Relations
Identifying and Exten1 Describe each patter
Lin1010
Hours worked 0 1 2 3 4
Money earned $0 $15 $30 $45 $60
19NEL Chapter 10 Linear Relations
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Plotting Patterns on a Coordinate GridAn ordered pair is a pair of numbers that describes a point on a coordinate grid. An example is (3, 22).
• The fi rst number describes the distance along the horizontal axis, or x-axis.
• The second number describes the distance along the vertical axis, or y-axis.
You can plot points on a coordinate grid to show a number pattern.
• If the pattern increases or decreases by the same amount each time, the points form a straight line.
• A pattern that makes a straight line is called a linear pattern.
4. Plot each pattern on the coordinate grid below. Join the points to form a line. Use a different colour for each pattern.
20 4 6�4�6 �2
x
y4
2
�2
�4
�8
�6
a) The fi rst point is (0, 22).
x 0 1 2 3 4
y 22 21 0 1 2
b) The fi rst point is (24, 26).
x 24 23 22 21 0
y 26 24 22 0 2
5. Which pattern in Question 4 is growing faster? How do you know?
2 4�2�4 0
�2
2
4y
(3,�2)
�4
x
20NEL Apprenticeship and Workplace 11: Review of Essential Skills
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