assessON Maths Quest 8 provides one-to-one correspondence to the text with all questions automatically marked, providing students with instant feedback. Introduction. Maths Quest 8 for Victoria Third edition is specifically designed for VELS Mathematics and based on the award-winning Maths Quest series. Maths quest erothbridunin.tk - Ebook download as PDF File .pdf), Text File .txt) or read book online.
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Maths. Quest. 8. S Purkayastha. (An imprint of New Saraswati House (India) Pvt. The Math Quest Teacher's Resource Pack is based on guidelines and aids to. exciting Maths Quest resources specifically designed for the Queensland 8 Maths Quest Maths B Year 11 for Queensland. Rearrangement and substitution. Maths Quest 8 for the Australian Curriculum. NUMBER AND ALGEBRA • NUMBER AND PLACE VALUE. Are you ready? Try the questions below. If you have.
Converting fractions to 6 Alison sold the greatest number of chocolates in her Scout troop. Write this 7 fraction as a decimal. When changing a mixed number to a decimal.
Addition and subtraction of 1F decimals 1. Adding Example and 22 a 8. Add in the required zeros Chapter 1 Number skills 25 Addition and subtraction of decimals Adding and subtracting decimals is a very useful skill. When adding and subtracting decimals.
Then add as for 2 1 0. Ignore the decimal point when multiplying. After a week of intensive training she had reduced her time to Salmah spent the following amounts: By how much had she cut her time? On Monday she ran 1.
Jacaranda Maths Quest 8 Australian Curriculum 3e learnON & print
How much did he spend altogether? The first time she ran the m it took her It is often a good idea to use your estimating skills with decimal multiplication to check that the answer makes sense. DIY A How many kilometres has she run for the week? Multiplication and division of decimals Multiplication The method for multiplying decimals is almost the same as for multiplying whole numbers. L Sp he Example a 4. If the divisor is not a whole number. Write the decimal point in the answer directly above the decimal point in the question and divide as for short division.
Continued over page. Then set out the question as for division of whole numbers and divide as for whole numbers. There are 3 decimal places in Give answers correct to 2 decimal places. Division When dividing decimals. When dividing decimals by a whole number. When the divisor is a decimal. When multiplying decimals. Example 25a a When dividing. We will now consider the process involving whole numbers. These estimates generally involve rounding the digits to a particular place value before conducting the estimate.
Obtain an estimate for the calculation and determine who is correct. Clustering around a common value Worked example 26 illustrates an estimation technique that can be employed when a basic calculation involving similar values is required.
Dividing 2 decimals A Marilyn says the answer is Marilyn is correct because the approximate value is very close to When rounding lower place position. The digit position and the digit in the next 1 lies in the units position. Rounding to the nearest hundred would give the number 25 5 in the tens position is in the category 5 or greater. Zeros are added to the lower place positions to retain the place value.
When rounding to a given place value. Rounding was discussed in Year 7. This means that if you are rounding 25 to the nearest thousand. When next lower place position. When we round down to a given place value. The place position and the digit in the digit 6 lies in the tens position. When we round up to a given place value. Let us illustrate this with a simple example. Check your estimate with a calculator. Comment Using a calculator.
Chapter 1 Number skills 31 Rounding to the first digit In estimating answers to calculations. Rounding the dividend to a multiple of the divisor When performing division.
This is a sound estimate for the calculated answer of to the nearest whole number. Each of the estimation techniques may provide a slightly different answer to calcu- lations. The estimate with actual answer. Comment on the accuracy of your estimate.
The on how the rounded result compares estimate compares well to the actual with the actual answer. Write the Care must be taken to ensure that the calculated estimate has the correct place value.
Use any estimation technique to locate 55 the position of the decimal point. This indicates that the decimal point correct answer. The correct answer is When rounding up. Making the dividend a multiple of the divisor is another useful technique for estimating an answer involving division.
If the following digit is less than 5. A different estimated value may have been obtained. Clustering around a common value can be employed when a basic calculation involving similar values is required. Estimation is a method of checking the reasonableness of an answer or a calculator computation.
Chapter 1 Number skills 33 It should be noted that any of the rounding techniques could have been used in worked example Zeros are added to maintain the place value of the number. When rounding to the first digit. Rounding involves increasing the value of the desired digit if the following digit is 5 or greater.
If rounding down. When estimating. The correct digits for each one are shown in brackets. The first one has been worked. The binary number system is based on counting in lots of 2s.
Under this system we can have only two digits: Approximately how many millilitres of water would be lost if the tap was allowed to leak for 78 hours? About how much money would they take in sales? Chapter 1 Number skills 35 11 Find an approximate answer to each of the worded problems below. It uses the digits 0. If they each picked up pieces of rubbish. How much money did they make? Remember to write your answer in a sentence. How much money was paid altogether?
Computers operate using a binary system. This is a two-state system that can be simulated in many ways — a light can be switched on or off. How much money was taken at the door? If he swam non-stop.
Write each remainder obtained even if the remainder is 0. The decimal number 23 is written as and read as 23 to base 10 and Converting from the binary system to the decimal system Recall from Year 7 that numbers can be written in expanded notation by breaking them up into their place values.
Write the remainder obtained 2 3 Remainder 0 even if the remainder is 0. Note that we are counting in lots of 2 here instead of lots of Repeat the process outlined in step 2 2 1 Remainder 0 3 until the quotient is 0. We use this method to convert from binary form to decimal form.
Computers are able to cope with calculations in base 2 with speed and accuracy. To convert a decimal number to its binary equivalent. Using the binary system for everyday calculations would be very cumbersome and probably lead to frequent errors.
The binary system uses 2 as its base and uses only the digits 0 and 1. The decimal system uses 10 as its base and uses the digits 0. To convert a binary number to its decimal equivalent. Copy and complete each of them by filling in the blank spaces.
Convert your answer back to binary form to confirm your conversion. Example 32 a b c d e f 7 Convert the binary number 1 to its equivalent decimal form.
Example 31 a b c d e f 4 Copy and complete the expansions of the following binary numbers. What do you notice? Decimal number 1 2 3 4 5 6 7 8 9 10 Binary number 1 10 11 Binary addition Using the same techniques that we use on decimals. The only difference is that we must remember to group the numbers in lots of 2 rather than in lots of Chapter 1 Number skills 39 Operations on binary numbers Binary counting From the previous exercise.
The first five binary numbers below were obtained using this process. Using binary notation. The total is 1. To clearly see the counting pattern. Applying this principle to binary arithmetic. Once the numeral 9 is reached in the decimal system. This column adds to 2. This column adds to 1.
The total is 2. Multiply the digits as usual.
Maths Quest 8 for Victoria Australian Curriculum Edition & LearnON
As we are multiplying only 1s and 0s. Add the resulting rows. Binary operations are based on the same techniques as decimal operations.
In part a of worked example When adding binary numbers. Carefully enter the third row values in the correct place positions. The product of these two decimal numbers is The product of these two decimals is Counting in binary involves moving to the next highest place value if the place value in question is occupied by a 1.
When multiplying binary numbers. Bit Avenue is a cul-de-sac with ten houses on either side of the street. How can you tell without working out the decimal equivalent of his house number? Chapter 1 Number skills 43 Operations on binary 1J numbers 1 Referring to the table on page The numbering starts from the corner with even numbers on one side and odd numbers on the other.
Chapter 1 Number skills 45 summary Copy and complete the sentences below using words from the word list that follows. These are addition. The binary system uses different digits. WORD LIST multiple factor decimal points denominator greater multiplication prime brackets addition composite estimation equivalent mixed number of numerator division squaring subtraction square root proper up two ten down binary one lots decimal. If they had 12 whole cakes to start with.
How many 1A desks are required to be set up for the end-of-year exams? The gymnasium will have 18 rows of desks with 8 desks in each row. If they plan to give to the victims of Hurricane Katrina 3 1D 1 and How many kilometres has he run for the week?
On Monday he ran 4. One climber started to suffer altitude sickness and was escorted down by another climber to a point How far apart were the two groups? This chapter deals with directed numbers. From their base camp.
If you have difficulty with any of them. Mark the following numbers on the number line with a dot. Which two numbers are: Chapter 2 Positive and negative numbers 51 Integers on the number line Using positive and negative numbers in our daily lives Most people understand the concept of negative numbers as soon as they are able to use money.
Does the following example sound familiar? The phone rings and Deb is arranging to go to the city with her friends. Positive whole numbers. Other ways that negative numbers can be used are: Integers can be represented as: Once she has spent the money.
The concept of owing money can be expressed as a number less than zero or a negative number. Having spent all her money on Christmas presents. Positive numbers and negative numbers have both size and direction.
Positive or negative direction symbols are placed to the left of the first digit of the number and are not spaced. It is the basic reference value on the number line. Zero is neither positive nor negative. The further a number is to the left on a number line. The number line The number line can be used when comparing integers and when adding and sub- tracting integers.
Integers can be represented on a number line. The further a number is to the right on a number line. On a number line. Integers including zero are called directed numbers because they have both size and direction. Integers are positive whole numbers.
Symbols and their meanings: Example 1 a The minimum temperature in Moscow on 1 January was 15 degrees below zero.
L Spre A 0. Mark the 2. Example 3 a 0. Chapter 2 Positive and negative numbers 55 2 Which of the following are integers? So the point marked A has coordinates 2 2. The average temperature in Antarctica is greater than the freezing point of coolant in a car radiator with antifreeze added. A pair of A 5 coordinates or an ordered pair x. Positive integers and zero on the number plane The number plane or Cartesian plane has 2 axes.
Point A is 1 unit to the right of zero along the x-axis and 4 units up the y-axis from zero. The x-coordinate indicates the number of units from zero the point is along the x-axis and the y-coordinate indicates the number of units up the y-axis from zero.
The point with coordinates 1. The x-axis is the horizontal axis and the y-axis is the vertical axis. Point B is on the y-axis and so is 0 units to the right of zero along the x-axis and is 2 units up the y-axis from zero. The point with coordinates 3. An ordered pair x. Are there any strategies you can use to help you win the game?
The second player also chooses a number E CH LL from this list and adds it to the first number chosen. Plot the points 9 8 listed and join them with straight lines in the order given.
The first person chooses a number NG from the list 1. The first player A chooses again any number from the list can be used even if it has been used before and adds this to the total.
The player who chose the last number to make it 51 is the winner. Players take turns selecting a number and adding it to the total until a total of 51 is reached.
Play this game a number of times. The horizontal number line is the x-axis. The origin is the point 0. Each quarter is called a quadrant and is numbered from one to four in an anti- clockwise direction beginning with the top right-hand quadrant. Chapter 2 Positive and negative numbers 59 Integers on the number plane The axes on the number plane can be extended to include Second y First negative integers as shown. A is in the fourth quadrant. Points are represented by ordered pairs of integers x.
B is 1 unit to the left of the origin along the x-axis and is 0 units from the origin along the y-axis. B is on the x-axis.
C —2 —3. A is 2 units to the right of the origin along the x-axis and is 3 units down from the origin along the y-axis. The quadrants —3. A in the first quadrant B in the second quadrant C in the third quadrant D in the fourth quadrant E on the x-axis b The point at 0. A in the first quadrant B on the y-axis C in the third quadrant D in the fourth quadrant E on the x-axis.
Work —4 e Give the coordinates of a point. Name the shape you —2 C —3 have constructed. Name the completed shape. Plot the points listed and join them with straight lines in the order given. E c Show that the point 4. Point D is in the second quadrant.
Use the following number plane diagram for questions 7. A B 4 b Find the coordinates of a point. What is shisk-kabob? So let us add integers involving temperatures. Adding opposites always results in zero. For same signs. For different signs. The rules for addition of integers are: Chapter 2 Positive and negative numbers 65 remember 1. Draw a number line if you wish. Assume that the number is positive if there is no sign. To add integers.
See cases 1 to 4 on page 63 at the beginning of cad this section. It then fell 6 degrees by The number sentence that describes this situation is: The spider then travels a further 9 cm down. Subtraction of integers Consider the pattern: Chapter 2 Positive and negative numbers 67 11 Describe a situation to fit each of the number sentences below.
He watches the spider move about 12 cm up the wall then 5 cm down.
What was the temperature at 4 am? On a TI Graphics Calculator tip! Entering a negative number To enter a negative number into a graphics calculator. Write the number sentence. The keys to be entered for a negative worked example 9 are: Chapter 2 Positive and negative numbers 69 remember 1. To subtract an integer. Only the number after the subtraction symbol changes to its opposite. Order of operations: What was the temperature in the front of the freezer when his mother found the ice-cream in the morning?
How far above her starting point is she when she reaches the resting place? Multiplication of integers Consider the patterns in the following multiplication tables. Just before he went to bed. Dennis had a Example spoonful of ice-cream and left the freezer door ajar all night. When she is 6 m above her starting point. When multiplying two integers with different signs. The number must be negative for the cube of it to be negative.
When multiplying two integers with the same sign. Chapter 2 Positive and negative numbers 71 c 1 Write the question. HEET 2. How much did she have if she swam too? The film can be run either forwards positive or backwards negative. What about the signs of the numbers in the x3 and x5 columns? Your calculator will only give you the positive answer.
What happens when you try to evaluate — on the calculator? What is the sign of all the numbers? When a negative number is raised to an odd power. Calculate 3 — Write a statement showing the square root of When a negative number is raised to an even power. Integer x x2 x3 x4 x5 2 —2 3 —3 4 —4 2 Look at your results in the x2 column. This only applies to even roots. It follows that. When a positive number is raised to any power. You are reminded that the same conclusions apply to numbers whose powers or roots are not integers.
When dividing zero by any number other than itself. There- fore. When dividing two integers that have the same sign. Division of integers The division operation is the inverse of multiplication. Rules of division 1. Fill in the blocks that have not been shaded.
When dividing two integers that have different signs. Chapter 2 Positive and negative numbers 75 10 Copy and complete the following table. Consider each answer carefully. Division with negative numbers You can check your answers with a graphics calculator.. When dividing with two integers that have different signs.
When dividing with two integers that have the same sign. Chapter 2 Positive and negative numbers 77 remember Rules of division 1. E represents exponents. It stops every 5 steps to pounce on a ball of wool. This does not show when to evaluate the exponent. Order of operations Working from left to right. If there are 26 steps above ground and 14 below.
Combined operations When simplifying expressions containing mixed operations. DM represents division and multiplication. If exponents and of are both included. B still represents brackets. On a TI calculator. When simplifying expressions containing mixed operations. Chapter 2 Positive and negative numbers 79 O Graphics Calculator tip! The screen opposite shows the calculation for worked example Notice that you need to enter brackets so that the correct order of operations is applied. SHEE T 2.
They pass each other on Backpedal Bridge at 12 noon. What is its final position? Auckland is 11 hours ahead of Berlin Germany time. What average mass reduction is needed per month? She immediately starts to lower the drawbridge. What is the time difference between: E ti me i Melbourne and Berlin? Work iii How far apart were they at 10 am?
Marion looks out of the window of her castle and spies Robin at m down the road. Give reasons. Use an open —3 1 —2 —1 0 x 2 —2 —2 or unshaded circle to indicate that the number itself is not included.
Chapter 2 Positive and negative numbers 81 2 1 Describe the integers graphed on the number line to the right. W —2 —1 0 x 5 Arrange these numbers in descending order: Use the number plane at right for questions 3 and 4. Graphical representation of directed numbers Directed numbers on the number line Positive and negative numbers have both size and direction. They include zero. Directed numbers are all values on the number line. Symbols for directed numbers on a number line: Use a closed or shaded circle to show that the number itself is included.
The fourth quadrant contains positive x-values and negative y-values. Use an open dot to show that —2 1—3 3. Directed numbers on the number plane The four quadrants of the number plane divided by y the horizontal x axis and the vertical y axis can 2 1 display points with ordered pairs made up of any 4 A directed numbers.
B 2 1—2. The second quadrant contains negative x-values and positive y-values. The third quadrant contains both negative x. A closed or shaded circle indicates that the number is included. When graphing number lines.. Use estimation to locate the boundary points. Show all points fitting the 4 description. The first quadrant contains both positive x. Chapter 2 Positive and negative numbers 83 Graphical representation of 2I directed numbers 1 True or false? Math cad y Directed 1 numbers 0.
The point halfway between two points is —2 D called the midpoint. Multiplying or dividing different signs gives a negative result: Rules for integers Addition The rules for addition of integers are as follows. Multiplication and division The rules for the multiplication and division of integers are as follows. Directed number operations — fractions The rules for addition. When adding same signs.
When adding different signs. When adding opposites. Multiplying or dividing same signs gives a positive result: Subtraction The rules for subtraction of integers are add the opposite: C E e Give the coordinates of F. They are different signs. They are the same sign. Chapter 2 Positive and negative numbers 85 Rules for fractions Addition and subtraction Write all fractions with the same denominator.
You will need to convert an improper fraction answer to a mixed number yourself. The screen above right shows the calculation for worked example Remember that to obtain a fraction answer press MATH. Directed It is a good idea to place brackets around this addition.
Directed number operations with fractions Mixed numbers are entered into a graphics calculator by O CASI separately adding the whole number and fraction parts.
Chapter 2 Positive and negative numbers 87 remember Addition Write all fractions with the same denominator. Subtraction Write all fractions with the same denominator. If the signs are different.
If the sign is different. Multiplication Cancel common factors in numerators and denominators. Opposites add to zero. If mixed numbers are involved in multiplication and division of fractions. If the signs are the same. If the sign is the same. Multiplication 6. Include the zeros. Positive decimals 5 Addition 3.
The signs are different. Example 23 a 0. Directed number operations 2K — decimals 2. What is the greatest number of questions you can answer incorrectly and still get a positive score? Explain your reasoning. Assume they are climbing at a constant rate. If no numbers fit the description. Values increase as we move to the of the number line. Four A quarters or make up the grid. They have both size and. Fill in the gaps by choosing the correct word or expression from the word list that follows.
Each B 2 3. The point 0. Name the shape that has been drawn. It climbs 3 cm and slips back 2 cm. Plot the following points in the order given. Write a number sentence to help you find how far the snail is from the bottom of the bucket. C 2I a At what level was he then? A scuba diver at 52 metres below sea level made his ascent in 3 stages of 15 metres each. B F —2 25 Calculate. D and E. Questions 21 to 24 relate to the figure below right. Each student is required to download a uniform for each activity they participate in.
Margaret has misplaced the individual order forms but knows that 36 students are in the concert band. In this chapter you will learn how to sort through information and present it in a variety of formats. Nine students are involved in music and debating. This year.
Jacaranda Maths Quest 8 Victorian Curriculum 1st Revised Edition learnON & Print
From this information. B and C have in common. Group A: Group C: The questions below refer to the following groups of numbers.
Group B: A set is a collection of things or numbers that belong to a well-defined category. Today he is regarded as the originator of set theory. The members are called elements of the set. A unit set contains only one element. Tuesday is a member of the set of days of the week. The following conventions are associated with set notation. This set is referred to as a described set. His passion was mathematics. Chapter 3 Set notation and theory 97 Introducing sets Georg Cantor — was born in Russia but lived and worked most of his life in Germany.
Commas separate each element. The following provides some examples of how sets are written and spoken. The braces. There may be more than one possible answer.
This is a listed set. Another way to represent a set is to use a set builder method. The elements in the set represent each of the Australian capital cities.
This is a described set. If a generalisation of a set is given. If a pronumeral represents any particular member.
Chapter 3 Set notation and theory 99 remember 1. The elements of the set are only listed once and can appear in any order. A set can be defined as a listed set. If the members of a set are individu- ally stated. A null or empty set contains no elements and is denoted by a pair of empty braces. The set is enclosed in braces. Sets can be represented by a capital letter. Are there any unit or null sets among your answers? Chapter 3 Set notation and theory 8 State whether each of the following is true or false.
From this set. The number of elements in a set is known as the cardinal number of the set and is given the symbol n. If a set contains an unlimited number of elements. These contain respectively 0 and 1 elements. Finite and infinite sets A set that contains a definite or countable number of elements is said to be a finite set. Set A is finite because it contains exactly 3 elements.
In some cases there may be more than one correct answer. The universal set The universal set.
Remember that 1 is not a prime number. Using set notation. The set of alphabet letters or the set consisting of the first two counting numbers could be universal sets. There are many different universal sets and the set itself can be quite small. We then regard the set P as a superset of T.
Set D is a finite set because it contains a Note: Sets that have a definite number of definite number of elements. A and B are disjoint sets. G is a superset of determine which sets are supersets and J. J is a superset of K. Disjoint sets have no elements in common. G is a superset of K. Since K is contained in G. Disjoint and overlapping sets Disjoint sets are sets that have no elements in common with each other.
If the sets do have some elements in common. Since K is contained in J. Overlapping sets have elements in therefore examples of overlapping sets. Complementary sets contain elements that are not in set P. Equivalent sets are those that have the same number of elements but not necessarily the same kind of elements they can be paired in one-to-one correspondence. Complement sets The complement set of A contains all the elements of the universal set in question that are not in set A itself.
So sets B and C may be defined as overlapping sets since they have an element in common. Each subset of the power set is con- sidered to be an element of the power set. Remember to include the empty set and the given set. Power set The power set is a set that contains all possible subsets of a particular finite set. This includes both the empty set and the given set. Equal sets have exactly the same elements.
The power set is denoted by the symbol P. The number of elements in a set is known as the cardinal number of the set. Overlapping sets have some elements in common. For example: Equal sets have the same elements. The power set is a set that contains all possible subsets of a particular finite set.
From worked example 10 we can see that a relationship exists between the number of elements in a set and the number of elements in its power set. Example 4 ii State the cardinal number of each of the sets.
Disjoint sets are sets that have no elements in common. A null set contains 0 elements and a unit set contains 1 element. The universal set. If set X is a subset of set Y. Finite sets contain a definite countable number of elements and infinite sets contain an infinite number of elements. A subset is a set that forms part of another set. Example 5 From this set. From this set list the elements of each of the following sets. Disjoint and b Name any overlapping sets. Chapter 3 Set notation and theory What is the official name of the United Kingdom?
Use the universal set to find the sets as defined below. The corresponding letter and the number of elements in each set. Gymnastics Swimming that is. Archery Diving are elements of the universal set Water polo that are not elements of A. High jump m Sets A and B are overlapping sets m hurdles Shot-put m hurdles because they have common m Long jump Discus m Javelin Pole vault elements.
All other sets that are subsets of the uni- versal set are represented as circles inside the rectangle. Show the position of all the elements in the Venn diagram. Sets A and C. These diagrams came to be called Venn diagrams. Aquatic events Elements that rest inside the C rectangle but outside the circles. This contains the elements 1. The English mathemat- ician John Venn — further developed this concept and included rectangles in these diagrams. The circles may overlap overlapping sets or may not overlap disjoint sets.
There is no limit to the number of these circles or the size of the region enclosed by the circle. The intersection set is the shaded area. Intersection of sets. In worked example A Note: Circles A and B will overlap as they have common elements. This circle contains the elements 2.
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Maximum Price.Integer x x2 x3 x4 x5 2 —2 3 —3 4 —4 2 Look at your results in the x2 column. The results were displayed on the tree diagram below. We use numbers in all sorts of ways — counting, shopping, telephone numbers, measuring, for references, in day-to-day conversation and for basic calculations.
The union of two sets is represented by the symbol. These books are on the booklist aswell. Let us look at a variety of logic statements with valid and invalid conclusions.
Special groups of numbers Sometimes in mathematics there are terms or words that need to be learned so that mathematicians all around the world can communicate and be sure of understanding exactly what they all mean.