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End of Year Revision Packet Mathematics – Level I Page 1 of 30

SABIS® Proprietary

SABIS® School Network Mathematics

Level I

End of Year Revision Packet

Highlights:

Test for divisibility.

Apply prime factorization to find the GCF and LCM of two or more numbers.

Compare, add, subtract, multiply, and divide fractions, mixed numbers, and whole numbers.

Represent repeating and terminating decimals as ratios of integers.

Add, subtract, multiply, and divide decimals.

Simplify numeric and algebraic expressions.

Compare positive and negative numbers.

Define and recognize rational, natural numbers, whole numbers, and integers.

Contrast the decimal representation of rational numbers with those of irrational numbers.

Apply the axioms of real numbers to simplify expressions.

Provide counterexamples to show that subtraction & division are neither commutative nor

associative.

Add, subtract, multiply, and divide real numbers expressed as fractions or decimals, placing

special emphasis on working with negative numbers.

Simplify algebraic expressions involving like terms.

Simplify and evaluate expressions involving sums, differences, products, quotients, and

exponents.

Apply the rules of powers to simplify numeric and algebraic expressions.

Find the solution set of a linear equation in one variable.

Solve linear inequalities by adding, subtracting, multiplying, or dividing.

Write algebraic expressions involving one or more operations or word phrases.

Write algebraic expressions for word phrases with two related variables involving concepts

such as area, perimeter, averages, quotients, products, differences, and sums.

Translate a word sentence into an algebraic sentence. Solve for the unknown.

Solve word problems on topics such as age, money, speed, and perimeter by translating the

words to math equations or inequalities and solving them.

Express the ratio of a and b as a fraction and as a decimal.

Express a ratio in its simplest form.

Find the unit ratio equivalent to a given ratio.

Find quantities given their ratios.

Use the cross-multiplication property to solve for an unknown in a proportion.

Solve word problems involving proportions.

Convert between percents, ratios, fractions, and decimals.

Given a% of b is c, solve for an unknown.


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Solve word problems on profit, loss, discount, taxes, percent change, percent error, and

simple interest.

Recognize a direct variation/proportionality. Given one instance, find another.

Graph direct variations.

Solve word problems on rate and speed.

Calculate rates of change.

Solve problems involving direct proportionality.

Estimate actual distances by reading a map.

Identify the x-intercept, y-intercept, and slope of a line of a linear relation.

Analyze graphs of linear relations.

Calculate and use the measures of spread of a data set.

Interpret the data displayed in different types of graphs.

Use the visual properties of box-and-whisker plots to analyze sets of spread data.

Group and organize continuous data in a frequency table and draw a histogram.

Given a survey, identify the population and the size of a sample.

Identify a random sample and ways of sampling to ensure randomness. Understand the

benefit of sampling and collecting data properly.

Identify random and fair samples. Recognize that data represented in the absolute form, as

opposed to relative, might be misleading.

Use organized lists, tables, and tree diagrams to list the different possible outcomes in a

given context.

Use the fundamental principle of counting to find the total number of outcomes in a given

context.

Use adequate counting techniques to find the probability of an event.

Analyze and solve word problems involving probability and counting.

Determine probabilities based on previous experience.

Discuss the consistency and reasonableness of experimental outcomes and predictions.

Judge the fairness of a game.

Interpret the result of a simulation.


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Vocabulary:

Natural numbers, Whole numbers, Divisibility, Exponent, Base, Factor, Prime number,

Composite number, Relatively prime, Prime factorization, GCF, LCM, Multiple

Fractions, Equivalent fractions, Comparing fractions, Improper fractions, Mixed numbers,

Reciprocal, Number line

Decimal fractions, Tenths, Hundredths, Thousandths, Place value, Value

Algebraic expression, Numeric expression, Variables, Substitution principle, Domain of a

variable, Formulas, Evaluate, Negative numbers, Integers, Real numbers, Rational numbers,

Order

Axioms, Theorems, Axioms of equality, Reflexive axiom, Symmetric axiom, Transitive

axiom, Closure axioms of addition and multiplication, Commutative axioms of addition and

multiplication, Associative axioms of addition and multiplication, Identity axiom of

addition, Axiom of additive inverses, Identity axiom of multiplication, Axiom of

multiplicative inverses, Distributive axiom

Numerical coefficient, Like/similar terms, Simplify, Property of the opposite of a sum,

Property of opposites in products, Product property of quotients

Power, Absolute value, Order of operations

Equation, Solution set, Solve, Inverse operations, Addition property of equality,

Multiplication property of equality, Inequality

Word phrases, Plus, Added to, Incremented, Sum, Total, More than, Increased by, Minus,

Subtracted from, Less than, Decreased by, Reduced by, Diminished by, Difference, Times,

Multiplied by, Product, Double of, Twice, Divided by, Quotient, Unknown

Ratio, Equivalent ratios, Unit ratios, Proportion, Cross-multiplication property

Percentage, Profit, Loss, Discount, Tax, Percent Change, Errors in measurement, Simple

interest

Direct variation, Proportionality, Table, Vary, Coordinate plane, Graph

Rate, Unit pricing, Speed, Scale, Map

Linear relation, Slope, Sign of a slope, Intercept

Set of data, Mean, Mode, Median, Range, Line plot, Stem-and-leaf plot, Bar graph,

Box-and-whisker plot, Line graph, Circle graph, Histogram, Survey, Sampling, Bias

Tree diagrams, Fundamental principle of counting, Probability, Fair, Simulation


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Level I Revision Exercises:

Ch. 1 Essentials of Arithmetic Section 1 Natural Numbers

1. Which of the following numbers is divisible by 11?

a) 55,517 b) 194,370 c) 301,456

2. Test each of the following numbers for divisibility by 2, 3, 5, 9, and 11.

a) 13,310 b) 604,877 c) 2,277,000

3. Give the prime factorization of 75. What are the prime factors of 75?

4. Find the greatest common factor of each pair of numbers.

a) 16 and 32 b) 1 and 50 c) 48 and 80

5. Find the least common multiple of each pair of numbers.

a) 16 and 32 b) 1 and 50 c) 48 and 80

6. Two pieces of cloth measuring 45 cm and 60 cm are to be cut into the longest possible strips

of equal length. How long will the strips of cloth be?

7. a) Find the smallest number which when divided by either 11 or 13 leaves a remainder of 7.

b) Find the smallest number which when divided by 10, 14, and 20 leaves a remainder of 8 in

each case.

Section 2 Fractions

1. Fill in the missing number to make the fractions equivalent.

a)

14 ?

18 72

b)

48 24

216 ?

c)

72 ?

84 7

2. Order the fractions from least to greatest.

8

12

7

8

5

6

1

4

2

3

3. Add. Express your answer in simplest form, or as a mixed number if necessary.

a)

3 2

8 5

b)

5 3

6 10

c)

1 1

6 3

4. Subtract. Express your answer in simplest form.

a)

6 3

7 5

b)

9 7

15 25

c)

7 5

8 12


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5. Add. Express your answer as a mixed number in simplest form.

a)

1 34 1

7 5

b)

2 72 3

25 15

c)

1 5 31 2 4

8 12 20

6. Subtract. Express your answer in simplest form.

a)

6 35 2

7 7

b)

1 57 2

12 12

c)

13 177 2

20 20

7. Multiply. Express your answer in simplest form, or as a mixed number if necessary.

a)

4 7

5 5

b)

3 5

8 7

c)

176

36

d)

85

15

e)

3 5

50 2

f)

72 32

96 48

8. Divide. Express your answer in simplest form, or as a mixed number if necessary.

a)

1 11 2

2 3

b)

4 33 5

7 7

c)

3 15 1

4 2

d)

38 2

4

e)

36 1

5

f)

32 22

4

9. An object whose mass is 1 kilogram weighs about

12

5 pounds. Find the approximate weight,

in pounds, of a television set whose mass is

57

8 kilograms.

10. Mona mixed

11

4 liters of orange juice with

5

8 liter of peach juice and

11

2 liters of carrot

juice. She plans to serve the mix in glasses of

1

4 liter. How many such glasses can she serve?


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Section 3 Representation of Decimals

1. Round to the nearest whole number.

a) 23.91 b) 23.42 c) 23.5

2. a) What digit is in the thousandths place of

521

1 000, ? Write the fraction in decimal form.

b) What digit is in the thousandths place of

2

1 000, ? Write the fraction in decimal form.

c) What digit is in the ten-thousandths place of

136

1 000, ? Write the fraction in decimal form up

to 4 decimal places.

3. What number is 2 hundredths more than 547.307?

Section 4 Operations With Decimals

1. Compute.

a) 1.3 + 5.5 b) 0.9 + 0.5 c) 41.4 + 23.99

d) 8 + 12.7 + 144.329 e) 65.82 + 7.981 f) 61 + 54.3 + 7.91

g) 0.75 0.34 h) 1.2 0.08 i) 0.3 0.02

j) 45.921 8.92 k) 54.27 7.05 l) 5.00 2.34

m) 4.2 4 n) 23.3 25 o) 8.4 17

p) 53.063 5 q) 15.025 29 r) 81.25 18

s) 70.89 3 t) 6.28 4 u) 0.904 8

v) 17.5 0.7 w) 6 0.12 x) 0.169 1.3

2. Find the price of 1.83 pounds of flour costing $0.85 per pound. Round your answer to the

nearest cent.

3. Divide. If the division does not terminate or repeat after three decimal places, stop and give

the answer rounded to two decimal places.

a) 30.3 9 b) 42 18 c) 56.6 ÷ 14


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Section 5 Simplifying Numerical Expressions

1. Simplify.

a) 30 ÷ 5 + 1 + 2 × 5 – 3 × 2 b) 30 ÷ 5 + [(1 + 2) × 5 – 3] × 2

c) 100 – [15 + 3 × (28 – 8)] d) 100 – 15 + 3 × (28 – 8)

e) 20.5 – [20 – 5 × (10 ÷ 4)] f) (25.5 – 20 – 5) × (10 ÷ 4)

g) 50 – 42 × 1.5 h) 33 × 22 – 54 ÷ 5

i) 92 – (102 – 4 × 7) j) 34 + 24 × 5

k) 70 + 82 ÷ 23 l) 53 – 72 ÷ 2

m)

11 1 2

12 4 3

n)

11 1 2

12 4 3

o)

11 1 2

12 4 3

p)

1 1 1 1 1

3 3 3 9 9

q)

4 1 13

5 2 2

r)

9 12 10

4 8

Section 6 Algebraic and Numerical Expressions

1. Evaluate each expression for x = 2 and y = 5.

a) x + 2y b) y + 2x c) xy + 7

d) 4y + (2x + 6)2 e) 2y (4x + 2) f) xy + 25

x

y

2. Let the domain of w be {3, 8, 12, 14, 17}.

What are the possible values of each of the following expressions?

a) w + 4 b) 3w c) 2w – 2

Chapter Summary

TB read pages 52-55 Chapter Test TB pages 56-58


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Ch. 2 The Set of Real Numbers Section 1 Negative Numbers

1. Write the numbers in order from least to greatest.

a) 0, +1, 2, 1, +2

b) 14, +31, 41, 13, +34, 43

c) +0.75, 1.25, +1.25, 1.75, +2.25

d) 0.05, +0.5, 0.8, 0.75, +0.95, +0.55

e)

1 1 1 1 1 1 1, , 3 , 5 , 3 , , 1

2 2 2 2 2 2 2

2. Simplify.

a) – (+5.3) b) – (–15) c)

19

2

d) – [– (–10)]

Section 2 Rational Numbers

1. Verify whether each of the following is a decimal fraction by writing an equivalent fraction

whose denominator is a power of 10.

a)

2

7 b)

4

125 c)

9

30 d)

1

64

Section 4 Axioms of Real Numbers

1. Simplify.

a) 2b[4(b + 3) + 5(4 + 3b) + 6b] + 4[5b + 3(2b + 7)]

b) 7[3x2 + (x2 + x + 5)] + 2[2(x2 + x + 7) + 2x]

c)

2 3

7 4 2

x x x

d)

3 16 4 2 8

2 2x x

Chapter Summary

TB read pages 86-88 Chapter Test TB pages 89, 90


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Ch. 3 Operations on Real Numbers Section 1 Addition of Real Numbers

1. Add.

a) 15 + (20) b) 8 + (8) c) 24 + (24) d) 18 + 11

e) 7 + 7 f) –10 + 3 g) 10 + –3 h) –10 + –3

i) 3 + (–5.18) j) –2 + (–8.1) k) –7 + 3.18

l)

3 1

2 2

m)

40

2

n)

4 4

5 5

2. Mercury is liquid at room temperature. It melts at about –39C. If the temperature of a mass of

mercury starts at –55C and increases by 23C, does this mass of mercury melt?

Section 2 Subtraction of Real Numbers

1. Simplify.

a) 12 – (5) b) 10 – (10) c) 7 – (7) d) 12 – 14

e) 8 – 8 f) –10 – 4 g) 10 – –4 h) –10 – –4

i) 13 – 6 j) 13 – (–6) k) –13 – (–6) l) –15 – (–8)

m) 0.8 – 2.6 n) 1.2 – 8 o) –1.9 – (–0.2) p) 6 – 7.5

q) 1.5 – 13 r) 0.9 – 2 s) –7.5 – 2.5 t) –6.87 – (–1.1)

2. The price of a share of a certain stock is $18 on Friday. By Monday, it shows a change of —5.

Use a number line to find the new price of this share. Did the price of the share increase or

decrease?


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Section 3 Multiplication of Real Numbers

1. Simplify.

a) 4(8) b) 6(12) c) 3(11) d) 5(28)

e) 6(2)(5) f) 5(9)(4) g) 3(3)(14) h) 17(3)(1)

i) (7)(5) j) 8(5)(5) k) 10(0) l) (1)(2)

m) (–11)(0.8) n) 2.5 × 4 o) (2)(1.5) p) (–0.25) 14

q) (6)(4.5) r) 1.5(1.5) s) 3(0.4) t) 7(0.7)

2. An amusement park bought a Ferris Wheel for $93,000. 45,213 people paid $2 each to ride the

wheel in its first year of operation. Ignoring the cost of operation, did the park recover the cost

of the wheel? If so, how much excess money did the park make?

Section 4 Division of Real Numbers

1. Simplify.

a) 51 (–17) b) (–48) 6 c) 121 (11)

d) (–335) (5) e) 20 (10 8) f) 26 (13)

g)

5 7

8 8

h)

5 11 3

9 9

i)

3

4

4

3

2. What is the average of six negative integers and their opposites? Explain how you got your

answer.


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Section 5 Simplifying Numerical Expressions

1. Simplify.

a) (8 + 15) + 5 b) (7 + 3) 4 c) (12 + 6) 2

d) 9 + [14 + (12)] e) 21 + [81 + (31)] f) 30 + [14 + 16]

g) (8 + 15) + 5 h) (7 + 3) 4 i) (12 + 6) 2

j) (7 – 23) × 5 + 9 k) 4 (–3 × 5)2 – 103

l) 62 ÷ (10 – 8)2 + 3 ×(–8) m) 45 (72 2 – 28 ÷ 4)

n) (45 – 23 5)3 ÷ 4 o) 10 – (35 – 52) + (120 ÷ 22)3

p)

10 1 14 15

21 3 25 2

q)

7 1 1 1

10 3 5 2

r)

4 1 3 10 91

7 2 4 21 15

s)

1 1 1 11

3 2 5 10

Section 6 Simplifying Algebraic Expressions

1. Simplify.

a) (2.25x + 7.25) + (1.25x + 0.25) b) [2.2 + (3.8m)] + (8.8 + 4.2m)

c) [9.6y + (3.3)] + [2.9 + (12.5y)] d) [3w (92.7)] + (92.7 3w)

e) (10a 3) 14a f) 7 (7b 14)

g) (12x + 4) (4x + 2) h) (6y 10) (9y 15)

2. Evaluate p q r

for p = –4.5, q = –8, and r = –3.

3. Write each expression as a product of two factors, one of which is −5.

a) 50x – 15y b) –30x – 95


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Section 7 Powers

1. Simplify.

a) 6 52 + 64 42 15(90)

b) 7 24 23 4 + 7(60)

c) 2 42 3 5 2

d)

03 2 35 5 4 4 12 10

e) 64 24 33 10

2. Simplify, assuming that x, y, m, and z are non-zero real numbers.

a)

22 2x x

b) 4 35 2y y c)

2

3 2z z

Chapter Summary

TB read pages 145, 146 Chapter Test TB pages 147-149

Ch. 4 Linear Equations and Inequalities in One Variable Section 1 Equations

1. Carlos scored 7 points higher on a test than Peter. If Peter’s score is represented by a and

Carlos’ score is represented by b, write an equation that relates the scores Carlos and Peter

achieved.

2. Find the solution set of the equation over the domain D.

If the equation has no solution, indicate so.

a) 3a = 81, D = {3, 4} b) 3a = 81, D ={3, 4}

Section 2 Solving Equations of the Form x + a = b

1. Solve and check your answer.

a) x + 2.3 = 4 b) x + 1.5 = 10 c) 25 = x 125

d) 17 = n 127 e) 12.8 = r + 12.3 f) 1.35 = s + 5.65

g) 0.36 = x 0.47 h) 16 = c + 9 i) 32 = d + 23

j)

2 2

5 3x

k)

3 7

8 12y

l)

7 9

15 10x


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Section 3 Solving Equations of the Form ax = b

1. Solve and check your answer.

a) 16x = 100 b) 10x = 72 c) 4x = 3

d) 1.2x = 6 e) 3x = 5 f) 5x = 14

g)

12

2x

h)

11 15

2r

i)

1 51

3 6x

2. Karen bought 7 identical books for her classmates. She paid $42.35 for all the books. Write an

equation and solve it to find the price of one book. Check your answer.

Section 4 Solving Equations of the form n(ax + b) = c

1. Solve the equation. Check your answer.

a) 2y + 3 = 17 b) 15m 12 = 48 c) 3x + 9 = 6

d) 1.2x 6 = 12 e) 3x 1.4 = 1 f) 2y + 5 = 8.6

g) 0.4x 0.6 = 2 h) 1.25x 0.5 = 2 i) 2.35y + 1.3 = 6

j)

15 6

3x

k)

2 5 3

5 6 4n

l)

13 0

2x

m)

1 22

3 5x

2. Solve and explain. Check your answer.

a) 2(x + 3) = 7 b) 7(x 4) = 27 c) 12(3 5x) = 5

d) 42 = 9(2x 7) e) 23 = 3(x + 7) f) 5(1 2x) = 6

g) 2 + 5(1 3x) = 8 h) 9(x 4) = 27 i)

47 2 12

7c


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Section 5 Solving Linear Equations in One Variable

1. Solve and check.

a) 3a (6 a) = 36 b) 6b + (8 3b) = 35

c) 24 = 6c + 2c 8 d) 4[2z 3(6 4z)] 12(z 1) = 4

e) 3d + 7 = 7d + 3 f) 2s 6 = 9s + 15

g) 8n 15 = n 43 h)

4 19

5 5z z

i)

2 21

3 3w

j)

1 8 2 1

2 3 3 4x x

k)

23 1 2 2

3c c

l)

1 1 3 7 16 5

4 2 2 5 2d d d

m)

5 3 6 1

2 3

x x

n)

2 1 3 1

4 5

x x

Section 7 Solving Linear Inequalities in One Variable

1. Solve and graph the solution set of each of the following inequalities.

a) x + 4 > 10 b) x + 2 5 c) x – 5 < 9 d) 6 x + 1

e) 3n < 15 f) 6n > 12 g) 3 < 6n h)

1

4 2

n

i)

3 3 7

4 5 10

x

j) 4 3

7

x

k)

2 1

3 3 2

x

l)

1 1

6 3 2

x

2. a) In 2 years, Nick’s age will be more than 14. Let x denote Nick’s age now. Write an

inequality based on the given information.

b) In 3 years, Julia will be younger than 12 years old. Let x represent Julia’s age. Write an

inequality based on the given information.

Chapter Summary

TB read pages 177, 178 Chapter Test TB pages 179, 180


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Ch. 5 Problem Solving Section 1 Writing Algebraic Expressions for Word Phrases

1. Write an algebraic expression for each phrase.

a) n is an even integer, give the next even integer.

b) n is an even integer, give the first odd integer after n.

c) h is an odd integer, give the next odd integer.

d) h is an odd integer, give the first even integer after h.

e) y is subtracted from fourteen

f) Five less than x

g) y is diminished by two

h) x decreased by sixteen

i) A half of y

j) One nth of d

k) Four fifths of c

l) y enlarged by a factor of 7

m) Fifty-nine plus four ninths of m

n) The opposite of 3 plus x is divided by 9

o) The quotient of nine by a number is incremented by four

p) Nine is divided by the product of a number with two

q) The perimeter of a rectangle of length 7 and width w

2. The sum of two numbers is 10. If x represents one number, write an expression in terms of x

for the other number increased by 12.

3. The difference of two numbers is 20. If x is the larger number, write an expression in terms of

x for 2 times the difference between the smaller number and 10.

4. The area of a rectangle is y square units. If the width is 12 units, write an expression in terms

of y for the length of the rectangle.


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Section 2 Word Problems

1. Write an algebraic sentence for each word sentence.

a) Six increased by three sevenths of a number is 8.

b) If 15 is subtracted from two thirds Mark’s weight, the result is 30.

c) The average of 13 and a number is less than twice the number.

d) The number of hours h increased by 13 equals 56.

2. Write an algebraic sentence and solve. Check your answer.

a) When 13.6 is added to three times a number, the result is 73.9. Find the number.

b) A number decreased by 16 equals 105. Find the number.

c) Five times a whole number is more than 92. Find the possible values of this number.

3. Linda scored 72 on her first algebra test. What must she score on the second test if her average

score on both tests is to be 81?

4. A movie theater has a certain number of rows of seats.

a) Let n represent the number of rows.

b) If each row has 25 seats, write an expression that represents the total number of seats in

the theater.

c) If exactly two of the rows have 4 seats fewer than the others, write an expression that

represents the total number of seats in the theater.

d) If it is known that the total number of seats in the theater as described in part c) is 517,

then how many rows of seats does the theater have?

5. The width of a rectangle is 3 cm less than its length. If the perimeter of the rectangle is 30 cm,

find the dimensions of the rectangle.

6. A number of passengers were on a bus. At the first stop, 6 more passengers got on the bus, and

no one got off. At the second station, as many passengers got on the bus as there were on it.

No one got off. At the last stop, 24 passengers got out of the bus and there were no passengers

left. How many passengers were on the bus before the first stop?

Chapter Summary

TB read page 200 Chapter Test TB pages 201-204


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Ch. 6 Variations Section 1 Ratios

1. A school has 735 students and 30 teachers. What is the student-teacher ratio? Express your

answer as a unit ratio. In your own words, what does this unit ratio represent?

2. A grocer sells 5 pounds of apples for $4.00. What is the ratio of dollars to pounds? Express

your answer as a unit ratio. In your own words, what does this unit ratio represent?

3. Two out of every five students in a certain school wear glasses. How many students in this

school wear glasses if the total number of students is 1,650?

4. The lengths of the sides of a triangle are in the ratio 2:4:5. The perimeter of the triangle is

44 cm. Find the length of each side.

5. A recipe calls for

5

9 cup of orange juice and

7

12 cup of pineapple juice. What is the ratio of

orange juice to pineapple juice in this recipe? Express your answer in the form a:b where a

and b are whole numbers with no common factors.

Section 2 Direct Variation/Proportionality

In 1 – 8, solve for x.

1. 3 21

1 x

2.

364

5

x 3.

x

7

19

14

4.

11

12 24

x

5.

3 2

4 8

x

6.

2 6

9 18x

7.

3

4

1

5

x 8.

12 1

13 2x

9. The ratio of boys to girls in Grade 8 is 5 to 3. How many girls are there in Grade 8 if there are

80 students in Grade 8?

10. Fill in the blank entries in each table, given the formula of the relation between the two

variables.

a) y = 12x

x –3 2 1 0 1 2 3

y

11. Assume y varies directly as x.

a) y = 27 when x = 3. Find y when x = 7.

b) y = 5.5 when x = 11. Find y when x = 94.


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12. Write an equation for the relation between x and y in each of the graphs below.

a) b) c)

x 0 1 2 3 4 5 6 7

y

3

2

1

4

5

6

7

x 0 1 2 3 4 5 6 7

y

3

2

1

4

5

6

7

x 0 1 2 3 4 5 6 7

y

3

2

1

4

5

6

7

Section 3 Applications

1. Amy has a choice between two sizes of bottled orange juice in a supermarket. One is 750 mL

and sells for $1.50 while the other is 1 L and sells for $2.00. Which is cheaper per mL, the

750 mL bottle or the 1 L bottle?

2. Flower shop A sells tulips at the rate of $5.40 per dozen.

Flower shop B sells tulips at the rate of $6.00 per dozen.

Tia went to the less expensive store and Mia went to other one. If each spent $9.00 buying

tulips, how many fewer tulips did Mia get than Tia?

3. Job A pays $950 for 180 hours of work. Job B pays $6.50 for each hour’s work. Which job

pays a higher salary? Explain.

4. Valeria can walk

1

2 a mile in

3

4 of an hour.

a) What is Valeria’s pace in miles per hour?

b) If Valeria can keep walking at the same pace, what distance can she walk in

12

2 hours?

5. Car A travels 50 miles on 2 gallons of fuel. Car B uses 3 gallons of fuel to travel 70 miles.

a) How many miles can car A travel per gallon of fuel? How many gallons of fuel does it

take car A to travel 1 mile?

b) How many gallons of fuel does it take car B to travel 1 mile? How many miles can car B

travel per gallon of fuel?

c) With regards to fuel consumption, which one of the two cars is more economical?

6. The scale on a map shows that 5 centimeters = 4 kilometers.

a) What number of centimeters on the map represents an actual distance of

5 kilometers?

b) What is the actual number of kilometers that is represented by 4 centimeters on the map?


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7. Jana measured the distance between two cities on a map and found it to be 6 inches. What was

the actual distance between the two cities if the scale on the map was 1

2 inch:8 miles?

Section 4 Percent

1. Write each percentage as a ratio.

a) 0.25% b) 35% c) 180%

2. Write each percentage as a decimal.

a) 65% b) 35% c) 0.75%

3. Write each percentage as a fraction.

a) 25% b) 0.5% c) 0.05%

4. Five out of 14 number 1 hits on the billboard charts this year were by female vocalists. What

percent of the number 1 hits were by female vocalists?

5. A professional basketball player missed 41 free throws out of 820. What percentage of the

shots did he miss?

6. A jeweler buys an adornment for $11,000. He sells it later for $10,900. What percent of the

initial investment is the loss?

7. What is the final price of an item on sale if the discount is 5% and the marked price is $120?

8. During a sale, the price of every item is reduced by 15%. An item is priced at $19.55 after the

reduction. What is its original price?

9. Fred bought a coat at a 40% discount. If he paid $140 for the coat, what was the original

price?

10. a) A store owner paid $40 for a jacket. She marked up the price of the jacket by 25% to

determine its selling price. What is the selling price of the jacket?

b) A customer buys a shirt that has an original selling price of $50. The shirt is discounted by

30%. The customer must pay a 5% sales tax on the discounted price of the shirt. What is

the total amount the customer pays for the discounted shirt?


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11. Nancy got a 15% pay raise this year. If her new salary is $4,200 a month, what was her

monthly salary before the raise?

12. Michelle deposited $3,000 in bank A at an annual interest rate of 4% and $2,400 in bank B at

an annual interest rate of 3.5%. How much did Michelle earn in interest in 1 year?

13. If $5,000 is invested for 3 years at an annual simple interest rate of 4%, what is the interest

earned during the 3-year period?

14. A department store places an item at 50% off. A week later, the item remains unsold, so the

store manager decides to take an additional 40% of the sale price. What percent of the

original price is the final price after both discounts are applied?

15. Items at a clothing store are on sale for 60% of the original price. Simona gets an additional

15% discount on the sale price for being part of the staff. If the orginal price of a jacket is

$200 and no sales tax applies, how much will Simona pay for the jacket?

16. To convert from kilograms to pounds, Emilia doubles the mass and adds 20% of the

Section 5 Patterns and Rules

1. Consider the sequence: 1, 3, 6, 10, 15, 21, …

a) What is the rule for generating this sequence?

b) What are the next three terms of this sequence?

Section 6 Linear Relations

1. In each of the following, given the slope and y-intercept of a line, write its equation in the

form y = mx + b.

a) Slope =

1

2 and y-intercept = –5 b) Slope = 3 and y-intercept = –5

c) Slope = 0 and y-intercept = –11 d) Slope = 3 and y-intercept = 0

Chapter Summary

TB read pages 47–49 Chapter Test TB pages 50–53


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Ch. 9 Statistics Section 1 Measures of Center and Variation

1. Miguel scored 78, 92, and 88 on three math exams. What must Miguel’s average on the next

two exams be so that his overall average on all five exams is 80?

2. Find the mode for each set of data.

a) {12, 12, 12, 15, 15, 15, 15, 20}

b) {10, 10, 10, 10, 10}

3. Find the median for each set of data.

a) {3, 6, 8, 10, 21} b) {6, 8, 12, 16, 21, 32}

4. Find the mean absolute deviation for each set of data.

a) {3, 6, 8, 10, 21} b) {6, 8, 12, 16, 21, 32}

5. A company tested 10 light bulbs from each of two brands for durability. The results are listed

in the table below.

Life Expectancy of a Light Bulb (in hours)

Brand A 890, 880, 800, 950, 20, 900, 880, 860, 830, 850

Brand B 840, 820, 880, 860, 790, 750, 780, 780, 750, 710

a) What is the mean life expectancy for the 10 light bulbs tested from each brand? Show your

work.

b) Based on the 10 bulbs tested, what is the median life for each of the brands?

c) Based on your answers in a) and b), which brand do you think is better? Give reasons for

your choice.

6. Ten college graduates received the following salaries, in thousands of U.S. dollars:

29, 34, 35, 36, 37, 38, 40, 41, 225, 300. Name the outliers in the set of data and describe their

effects on the mean and on the median.


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Section 2 Graphical Representation of Data

1. The line plot shows the scores Tamika received on her math exams.

15 16 17 18 19

a) What is the range of Tamika’s scores on the five exams?

b) What is the mode of Tamika’s scores on the five exams?

c) What is the median of Tamika’s scores on the five exams?

d) What is the average of Tamika’s scores on the five exams?

e) Tamika will take one more math exam. Is it possible for Tamika to end up with an average

of 18?

2. The stem-and-leaf plot shows the number of students who attended the school play in

14 performances.

Stem Leaf

6 4 4 7 9 Key

7 | 2 represents 72 7 0 2 5 8 8 8

8 4 6 7 7

a) What is the range of the number of students who attended the 14 performances?

b) What is the mode of the number of students who attended the 14 performances?

c) What is the median number of students who attended the 14 performances?

d) After the last two performances, the median of the number of students that attended all 16

performances was the same as that of the first 14. What must be true about the number of

students that attended the last two performances?


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3. Consider the following survey of 20 students from the U.S. and 20 students from Canada

about their favorite fruit.

Favorite Fruit

Number of Students

Fruit U.S. Canada

Apple 8 6

Peach 2 4

Orange 6 5

Banana 4 5

Plot the data using a bar graph. Label your graph appropriately.

4. Refer to the box-and-whisker plot shown below to answer the questions.

Grade Distribution for 100 Girls and 100 Boys

Boys

Girls

0 10 20 30 40 50 60 70 80 90 100

a) How many boys scored between 30 and 65?

b) How many girls scored between 40 and 90?

c) Below what value did 75% of all girls score?


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5. The chart below shows the salary distribution of 200 randomly picked female employees and

200 randomly picked male employees. The notation [a, b) stands for all numbers between a

and b, including a and excluding b.

0

10%

20%

30%

40%

< 20 [20 – 30) [30 – 40) [40 – 50) > 50

Salary in $1,000

Salary Distribution

Per

cen

tag

e o

f em

plo

yee

s

Male employees

Female employees

a) How many female employees have a salary less than $40,000?

b) How many male employees have a salary greater than $40,000?

c) How many more female employees than male employees are in the $20,000 to $30,000

range?

6. A group of 20 students were asked to choose their favorite food from the following list:

hamburger, tacos, and pizza.

The results are shown in the table below.

Favorite Food

Food Number of Votes

Hamburger 10

Tacos 4

Pizza 6

Draw a circle graph displaying the data. Give the measure of the angle formed in each of the

sectors. Show your work.


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Section 3 Histograms

1. A survey concerning the duration of telephone calls was conducted. Fifty calls were chosen at

random. The table below lists the duration of each of the calls in minutes.

2 7 15 33 3 2 1 23 11 28

20 1 12 8 4 24 31 1 45 2

14 25 3 22 17 4 25 2 27 18

33 14 37 7 42 18 36 9 31 8

48 4 32 14 38 32 16 38 26 30

a) Tally the durations of the calls using intervals of 10 minutes each. Start from 0.

b) Draw a histogram.

2. Denzel tossed four coins 200 times and noted the number of heads appearing each time he

tossed the coins. He summarized his findings in the table below.

Outcomes of Tossing Four Coins

Number of

heads Frequency

Cumulative

Frequency

0 10 10

1 52 62

2 84

3 42

4 12

a) Find the missing entries in the table under the “Cumulative Frequency” heading.

b) In your own words, what does it mean to have a cumulative frequency of 62 corresponding

to 1 heads?

c) For what percentage of the 200 times did the outcome of tossing the four coins show 2

heads?


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Section 4 Sampling and Sample Proportions

1. The sample size plays a key factor in designing a successful survey.

For populations in the millions, 1% 2% of the population is a good sample size.

For populations in the hundreds, 10% 15% of the population is a good sample size.

What is a good sample size to use if you want to survey the students in your school about their

favorite hobby? Describe a way of choosing the participants for the survey.

2. Give the sample size and classify the data collected in each of the following cases as a random

sample or not. Give reason(s) for your answers. Describe a way of randomly choosing the

participants for each of the surveys where you think the sample is not random.

a) Twenty names were randomly chosen from the California telephone book. The chosen

numbers were called and the respondents were asked whether or not they support enforcing

the seatbelt law. Of the 20 attempted calls, 18 responded.

b) The first 200 students to arrive at school were asked if they prefer that the school day

begins at 8:00 A.M. or at 8:30 A.M. The student body of the school has 1,008 students.

c) Every fifth person who enters a mall was asked about his/her favorite store at the mall. At

the mall entrance, 980 people were surveyed.

Section 5 Bias and Misleading Data

1. The adjacent graph gives the

impression that the circulation of the

State News magazine doubled from

2008 to 2009. Explain why this graph

is misleading.

50

52

54

56

2008 2009 Year

State News Circulation

Nu

mb

ers,

in

tho

usa

nd

s

2. A random sample of 50 men and 50 women were picked from a population consisting of 200

men and 800 women. They were asked if they support more spending for a new daycare

center. Is there any source of bias in the study? If so, what is it?

Chapter Summary

TB read pages 170, 171 Chapter Test TB pages 172–176


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Ch. 10 Counting and Predicting Chances Section 1 Methods of Listing and Counting

1. A person has 6 shirts, 5 pairs of pants, and 4 pairs of shoes. An outfit is made up of any one of

the shirts, any one of the pairs of pants, and any one of the pairs of shoes. How many different

outfits are there?

2. Books in a library are labeled by two letters followed by a nonzero digit. How many different

labels can be formed?

3. Products are assigned codes that consist of two letters followed by two different digits. How

many different codes can be formed?

Section 2 Probability

1. The cards shown below are placed on a table top facing down in random order and a card is

picked.

a) How many different possible outcomes are there?

b) Are the different outcomes equally likely to occur?

c) What is the probability the letter “C” is picked?

2. A pair of dice are rolled and the sum of the numbers rolled is observed.

The possible outcomes are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.

a) What is the probability of rolling a sum of 2 or 3?

b) What is the probability of rolling a sum greater than 3?

3. One marble is randomly picked from a bag containing four red marbles and four green

marbles. The color of the marble is recorded and the marble is placed back in the bag. What

is the probability of getting two marbles of the same color?

4. A wheel is divided into 36 sectors. 20 of the sectors are marked with the number 5. If the

wheel is spun, what is the probability it will stop at a sector marked by the number 5, given

that it is equally likely to stop at any of the 36 sectors?


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5. Refer to the diagram below to answer the question.

20 m

20 m

60 m

Seeds are spread out evenly in the rectangular lot. What is the probability the first bud will

blossom in the triangular region?

Section 3 Experimental Probability

1. A spinner awarded prizes 20 times out of the 50 times it was spun. What is the experimental

probability the spinner will award a prize the next time it is spun?

2. One hundred light bulbs were tested and 6 were found to be defective. What is the probability

a light bulb purchased from the same manufacturer is not defective?

3. A bag contains a collection of marbles. Each time a marble is taken out, its color is recorded

and then placed back in the bag before the next marble is taken out. This experiment is

repeated 100 times and the outcomes are summarized in the table below.

Red Green White Blue

10 7 8 75

There are 50 red marbles in the bag.

a) What is the estimated number of blue marbles in the bag?

b) What is the estimated total number of marbles in the bag?

4. One hundred bags of sugar labeled 5 kg were weighed and the findings were recorded.

Measured weight Number of bags

[4.90 – 4.95) 12

[4.95 – 5.00) 48

[5.00 – 5.05) 33

[5.05 – 5.10) 7

If a similar bag is weighed, what is the probability that its weight is less than 5 kg?


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Section 4 Probability Models

1. Anna wants to estimate the number of people at a mall that will use the ATM machine. Based

on past data, the probability that a person who is selected at random in the mall uses the ATM

machine is 0.4. Anna designs a simulation to estimate the probability that exactly two of five

people selected at a mall will use the ATM machine. For the simulation, Anna uses a number

generator that generates random numbers.

Any number from 0 through 3 represents a person who uses the ATM machine.

Any number from 4 through 9 represents a person who does not use the ATM machine.

For each trial, Anna generates 5 numbers. Anna ran 20 trials of the simulation and recorded

the results in the following table:

45193 51236 43590 66125 83709

13742 74908 25104 31254 36789

19203 25786 80967 81825 94087

71876 42865 14023 80659 06374

a) In the simulation, one result was “80967.” What does this result simulate?

b) Use the results of the simulation to estimate the probability that 2 of 5 people selected at a

mall will use the ATM machine.

c) Make a table of all the possible outcomes of the experiment and use it to find the theoretical

probability that 2 of 5 people selected at a mall will use the ATM machine. Compare it with

the result you obtained in part b).


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2. The table below contains 200 random digits from 0 to 9. 2 3 1 2 6 0 8 6 4 3 8 4 2 1 8 3 5 7 2 4

3 6 6 9 6 2 9 0 2 0 0 1 2 4 8 9 4 6 6 6

6 6 3 9 6 8 5 2 9 3 7 7 7 0 2 6 5 2 4 4

0 6 4 3 9 8 7 1 6 0 0 6 6 3 4 3 5 8 9 5

2 9 5 6 1 5 6 3 2 7 0 9 3 0 8 8 6 6 4 5

8 4 5 1 7 3 9 3 0 0 8 7 4 4 3 2 6 3 5 9

1 6 5 1 7 5 9 5 0 7 8 2 5 8 4 4 4 3 4 2

0 5 8 9 1 9 7 0 1 7 7 0 6 1 8 0 3 2 2 6

1 5 1 4 1 9 7 9 6 5 0 3 0 7 9 2 1 5 8 7

9 8 7 9 5 7 8 0 2 2 8 8 1 9 7 0 4 8 3 0

a) Explain how you can use the table to simulate an experiment with two outcomes, success

and failure with the probability of success 0.65. Use the table to simulate the experiment 50

times.

b) Is the experimental probability close to the theoretical probability?

Chapter Summary

TB read page 200 Chapter Test TB pages 201–203

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