Adrian - Maths Pathwaytests.mathspathway.com/tests/c9e1014f-886e-4fd6-bcda-78a... · 2016-08-22 · 26×347=9022 Using this fact, solve: 0.0026×34.7 You must show full working out

Question 1

A rectangle is translated 5 units to the left and 2 units upfrom its starting position. Draw the final position of therectangle.

Question 2

Using words, describe how the hexagon has beentranslated.

MathsPathway Assessment

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You completed 8 activities for this test

You have 11 online questions

You have 10 printed questions

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Question 3

Fill this in.The first one has been done for you.

Question 4

Write these numbers with words.

4,120

7,066

1,111


Question 5

If I rotate a spinner from the bottom right segment to thebottom left segment, is it the same angle as if I do it theother way around? Explain why or why not.

Question 6

Angela was asked to draw a 14 turn, and drew the picture

below.Explain her mistake.

Question 7

Complete the net below for a cube by adding 3 morefaces.

Question 8

Draw a net for a cylinder.

Question 9

Redraw the rectangle after it has been reflected aboutthe line.

Question 10

Redraw the hexagon after it has been reflected about theline.


Remember to also complete your online test (log in at https://7f-epping.mpclass.com)


Question 1

Use a protractor to measure the angle below.

Question 2

Construct a 235 ° angle.

Question 3

Convert the multiplication below into an indexexpression.8 × 3 × 3 × 8 × 3 × 8 × 8

Question 4

Here is a fact:

26 × 347 = 9022

Using this fact, solve:

0.0026 × 34.7

You must show full working out.


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Question 5

For the following situation, define a single variable.Hence re-write the information in the language ofalgebra.

James spends his money during the week.On Tuesday, James has $80.On Wednesday, James has $50.On Thursday, James has $10.


Ali KHASRI MathsPathway Assessment | Page 2 of 2

Question 1

Below are partial images required to prove that co-interior angles add to 180° when two parallel lines are crossed byanother line. Complete the images and fill in the blanks to explain the required logic for each step of the proof.

We want to show that ____________.

Alternate angles are _______.Therefore, ____.

Straight angles are ______.Therefore, _____________, and the proof iscomplete.

Question 2

Your friend Joseph has answered a question given by yourteacher and asks you to see if he is correct or not. It turnsout he is incorrect. Explain why.


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Question 3

Below are partial images required to prove that the interior angle sum of a triangle is 180°. Complete the diagrams andfill in the blanks to explain the required logic for each step of the proof.

We want to prove that______________.

Alternate angles are ________.Thus, _____.


Straight angles are _____.Thus _____________, and the proof iscomplete.

Question 4

Simplify the fraction 3012 , showing full working out line-by-

line.


Question 5

Yvonne is having a glass of apple juice with breakfast.The glass weighs 150 g and holds 150 mL, so she says thather drink weighs 300g.Explain why Yvonne is mistaken.

Question 6

Re-write one of these fractions so that theirdenominators match.

Hence, rewrite the original number sentence,placing a < , > or = symbol instead of the box.

96

?3324

Question 7

Given the areas of the triangle and square below,determine the area of the star.Include units.

Question 8

Re-write this list of numbers in ascending order:0.9, 0.59, 0.49, 0.99, 0.19




Question 1

By drawing a collection of triangles and squares and circling groups, show that 34 and 6

8 are equivalent fractions.

Question 2

By first drawing hats on some of these men, and by

circling groups, show that 23 and 6

9 are equivalent

fractions.

Question 3

Given that congruent triangles can be formed by drawinga line through a parallelogram, prove that opposite sidesof a parallelogram have equal length:

Question 4

On this fraction wall, only some bricks have been labelled.Label all the rest of the bricks.


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Question 5



Question 6

Use the data in the table to complete the columns forGST for the four countries shown. Remember to include akey for GST.Insert GST rates to the right of the Personal Tax ratecolumns.

CountriesPersonal Tax

rateGST

Australia 30 10

Canada 15 5

France 33 20

United Kingdom 21 20


Question 7

Draw the triangle after it has been rotated 90°anticlockwise about the point shown and then reflectedabout the line.



Question 1


Question 2


Question 3






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Question 4

Show working line by line to give a simpler way to do theworking for the following number sentence.3 × (30 + 5)

Question 5

Show that 4 × (3 + 2) = (4 × 3) + (4 × 2). You must use adrawing in your explanation.


Question 6







Question 7

Evaluate the following, showing full working out line-by-line:

□ + 1315 = 943 + 1308

Question 8

Alex has attempted to prove that corresponding anglesmatch when two parallel lines are crossed by anotherline.He has only gotten as far as the diagram below.

By first placing labels on this diagram, write a numbersentence using algebra that explains what we are tryingto prove.

Question 9

The following picture shows two parallel lines crossed byanother line.One of the intersection points has been surrounded by adotted box.By writing a sentence to explain your logic, determine themissing angle in the solid box. Draw another dotted boxin the appropriate position to support your logic.

Question 10

By breaking this pentagon up into triangles and/orquadrilaterals, determine the sum of the interior anglesof the pentagon.Use this information to evaluate the missing angle.


Question 11

Write a number sentence to express the total angles inthe picture below, and solve it to find the value of themissing angle.

Question 12

Write 14% as a simplified fraction.You must show full working out.

Question 13

Write 45 as a percentage.



Question 14

Below are partial images required to prove that the interior angles of a quadrilateral add to 360°. Complete the imagesand fill in the blanks to explain the required logic for each step of the proof.

We want to prove that___________________________.

First we split the quadrilateral into _______________.__ is split into __ and __.__ is split into __ and __.

Now proving that ________________ = 360 ° isequivalent to proving(____________) + (____________) = 360 ° .

Because we know that triangles have 180 ° , we cansay:_____________ = 180 ° , and_____________ = 180 ° .

Therefore, (____________) + (____________)= 180 ° + 180 ° = 360 ° .

Thus _________________ = 360 ° , and the proof iscomplete.



Question 1



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Question 2

Answer this question by first writing a matching numbersentence, and then a simpler version of that numbersentence. You must show full working out.

When a number is subtracted from 12, the answer is thesame as 3 plus 5. What is the number?

Question 3

This picture shows a group of adults. Draw beards on 45 of

the people.

Question 4

This picture shows a group of children and adults.What fraction of the group are children?You must write your answer both in words and usingnumerals.

Question 5

Solve:

1637 − 214



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Question 1

Show that 2 ÷ 10 000 = 0.0002 by dividing 2 by 10 severaltimes.

Question 2

For combinations of multiplication and subtraction, the order of operations does matter.Show that this is true in an example. Use a starting number of 5, and the operations × 4 and −3.You must use expressions with brackets in your working out.

Question 3

For combinations of addition and subtraction, the order of operations doesn’t matter.Show that this is true in an example. Use a starting number of 5, and the operations +4 and −3.You must use expressions with brackets in your working out.


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Question 4

Here is a fact:

26 × 347 = 9022


0.0026 × 34.7


Question 5

Redraw this picture with extra positives to make 0.

Question 6

Write 114 × 33 in expanded form.


Question 7

Write 3 × 3 × 3 × 4 × 4 in index form.




Question 1


Question 2


Question 3


Question 4


Question 5

Given the following equations, explain the rules relatingto odd and even answers when dividing.

42 ÷ 7 = 636 ÷ 6 = 635 ÷ 7 = 549 ÷ 7 = 756 ÷ 8 = 7

22 ÷ 2 = 11


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Question 6

Evaluate the following, showing full working out line-by-line:

□ + 1315 = 943 + 1308

Question 7

Five friends won a competition in class. Their prize was apacket of 48 chocolates. If they divide the chocolatesfairly between themselves, how many does each personget and how many will be left over?

Question 8

Sharon has just moved house, and has 43 shirts that needto be packed away into 5 empty drawers. She wants todivide them evenly between the drawers, but realisesthat 43 ÷ 5 = 8 remainder 3. Describe what Sharon mightdo with the remainder.

Question 9

What decimal is this equal to?

300 + 3 +3

10Write your answer in both numeral form and word form.

Question 10



Question 11



Question 12

A sports club has a working bee to arrange. The followingjobs need doing and each requires a certain time if doneby one person.

Garden clean-up: 2 hours.Window cleaning: 1 hour.Wall repair: 1 hour.Painting the club room: 4 hours.

Only 4 people turn up. The organiser plans the worktimetable. The total hours required for the work is 8hours, but with 4 people to do the work, it will take 4hours to finish because the painting job takes one person4 hours, but the others can happen at the same time. Heputs person 1 and 2 to work on painting. Person 3 and 4are given the job of garden clean-up for the first 2 hoursand then they have to choose either window cleaning orwall repair.

In the scenario, a number of strategies and/or operationshave been used. However, the organiser made somemistakes in his thinking. Identify his mistakes and what heshould have done.


Question 13

Brian is training for a long distance run. He trains 2 timesa week and runs 15 laps of the 500 metre running track.He trains for 10 weeks before the competition. Before hestarted training, it was taking him 80 minutes to run the15 laps. Each week his time improves, knocking 2 minutesoff the running time.

(a) How many laps will he have run in that time?

(b) How many metres will he have run?

(c) What will his likely running time be at the end of histraining?

Question 14

Explain why this picture is impossible.


Question 15

Given the areas of the triangle and square below,determine the area of the star.Include units.

Question 16

Manny’s mum is organising a party for him. She gets himto write a list of people he wants to invite and work outhow many more chairs they will need to borrow.

Manny has 18 people in his football team, 11 in hisbasketball team and 7 in his debating team – he is invitingthem all. In the basketball team, 3 of the players are alsoin the football team and 2 of the players are alsodebaters.

Manny counts the chairs at home and finds 6 kitchenchairs, 4 outdoor chairs, a bench that seats two peopleand 2 folding chairs that can be used. Manny’s parentswon’t need chairs at the party but he and his brother will.

Show your working out for this problem. Use equations tohelp show your answer.

(a) How many young people will be at the party?

(b) How many chairs will they need to borrow?




Question 1

By drawing jumps on this number line, show that 43 + 2

3 = 63 .

Question 2


Question 3


Question 4


Question 5



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Question 6

Using these two circles, show that 34 and 6

8 are equivalent

fractions.

Question 7

Using these two rectangles, show that 12 and 3

6 are

equivalent fractions.

Question 8

On this fraction wall, only some bricks have been labelled.Label all the rest of the bricks.


Question 9


Question 10

By drawing shaded rectangles in a number sentence, evaluate 54 + 1

4 .

Question 11

By drawing shaded rectangles in a number sentence, evaluate 65 − 2

5 .




Question 1

Label the diagram below so that it has one pair of parallellines, and one pair of equal angles.

Question 2

Write a number sentence expressing the value of a in thediagram below.

Question 3

Write a number sentence expressing the value of themissing angle in the diagram below.

Question 4

Translate the following information into the language ofalgebra. You answer should include an algebraicexpression, and clear definitions of any variables.

Justin is making a large pot of tea for several people, andwants to know how many grams of loose leaf tea to putinto the pot.His grandmother told him that you should put in 3 gramsfor each person who is having tea, plus an extra 3 grams“for the pot”.


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Question 5

Draw all the lines about which the trapezium issymmetrical.

Question 6

The pentagon is said to be symmetrical about the line.Explain why.

Question 7

Plot the linear relationship y = x − 4


Question 8

Manny’s mum is organising a party for him. She gets himto write a list of people he wants to invite and work outhow many more chairs they will need to borrow.

Manny has 18 people in his football team, 11 in hisbasketball team and 7 in his debating team – he is invitingthem all. In the basketball team, 3 of the players are alsoin the football team and 2 of the players are alsodebaters.

Manny counts the chairs at home and finds 6 kitchenchairs, 4 outdoor chairs, a bench that seats two peopleand 2 folding chairs that can be used. Manny’s parentswon’t need chairs at the party but he and his brother will.


(a) How many young people will be at the party?

(b) How many chairs will they need to borrow?

Question 9

Is the following statement true or false?“An obtuse triangle cannot also be isosceles.”If true, explain why.If false, give a counter-example.




Question 1

Write down the prime factorisation of 92, and show yourworking in a factor tree.

Question 2

Show that 2 ÷ 1 000 000 = 0.000002 by dividing 2 by 10several times.

Question 3

Draw the final position of the rectangle after it has beenrotated about the point 90° anticlockwise.

Question 4

Describe why 29 is a prime number.


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Question 5 Question 6

John is finding the factors of a large number. Using acalculator, he has just worked out that 20 is a factor ofthis number.

Suddenly, he realises that 4 must be a factor of the largenumber as well. Explain why John is correct.

Question 7

Consider the number 864.

(a) Can it be divided evenly by 2? Explain how you know.

(b) Can it be divided evenly by 5? Explain how you know.

(c) Can it be divided evenly by 10? Explain how you know.


Question 8







Question 9

Isaac has attempted to answer a question where he hadto label all the angles in a diagram.

Without doing any measuring or calculating, the teacherwas able to tell immediately that Isaac was wrong.Explain how this is possible.

Question 10

Anh does not know that opposite angles are equal, butshe could still work out the missing angle below.By writing a sentence, explain how she could work it out.

Question 11

List all 7 factors of 64

Question 12

Use an example where the small number is 3 and thebigger number is 18 to help answer the question. Howcan you prove that a small number is a factor of a biggernumber?

Question 13

Which of the following numbers are factors of 72? Circlethese.

8930364


Question 14

Alex has attempted to prove that corresponding anglesmatch when two parallel lines are crossed by anotherline.He has only gotten as far as the diagram below.

By first placing labels on this diagram, write a numbersentence using algebra that explains what we are tryingto prove.

Question 15

The following picture shows two parallel lines crossed byanother line.One of the intersection points has been surrounded by adotted box.By writing a sentence to explain your logic, determine themissing angle in the solid box. Draw another dotted boxin the appropriate position to support your logic.

Question 16

By breaking this pentagon up into triangles and/orquadrilaterals, determine the sum of the interior anglesof the pentagon.Use this information to evaluate the missing angle.


Question 17

Write a number sentence to express the total angles inthe picture below, and solve it to find the value of themissing angle.

Question 18

Below are partial images required to prove that the interior angles of a quadrilateral add to 360°. Complete the imagesand fill in the blanks to explain the required logic for each step of the proof.

We want to prove that___________________________.

First we split the quadrilateral into _______________.__ is split into __ and __.__ is split into __ and __.Now proving that ________________ = 360 ° isequivalent to proving(____________) + (____________) = 360 ° .

Because we know that triangles have 180 ° , we cansay:_____________ = 180 ° , and_____________ = 180 ° .Therefore, (____________) + (____________)= 180 ° + 180 ° = 360 ° .

Thus _________________ = 360 ° , and the proof iscomplete.

Question 19

Consider the operations +3 and −6. By using 7 as your starting number, show that the order of operations doesn’t matterhere.


Question 20

Consider the operations ÷ 3 and +6. By using 12 as your starting number, show that the order of operations does matterhere.

Question 21

Using both words and numbers, write down theoperations in the following expression:

12 ÷ 4 × 6

Question 22

Shari’s mum is organising a dinner. She needs to write alist of people to invite and work out how many platesthey will need to borrow.

Shari has 6 friends in her netball team, 12 in herswimming squad, 4 from her band and one friend fromschool – all will be invited. 4 of the swimmers are alsonetballers and one member of the band is in the netballteam. Shari and her mum will be at the dinner as well.

Shari counts up the plates. One set has 4, another set has6 and another set has 8.


(a) How many people will be at the dinner?

(b) How many plates will they need to borrow?


Question 23

Draw the cirlce after it has been reflected about the lineand then translated 3 units down.

Question 24

Use charges to draw the integer 3.Include 2 negative charges in your drawing.



Question 1

The image below contains a picture before and after arotation transformation.Using a symmetry argument, explain why the missingangle must be 40 ° .

Question 2

List all 7 factors of 64

Question 3

How can you prove that a small number is a factor of abigger number? Use an example where the small numberis 4 and the bigger number is 40 to help answer thequestion.

Question 4

Which of the following numbers are factors of 72? Circlethese.

8930364

Question 5

Create a stem and leaf plot from the following data.Remember to include a key.88 92 95 89 96 87 86


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Question 6

Draw the triangle after it has been rotated 90°anticlockwise about the point shown and then reflectedabout the line.

Question 7

Draw this 3D shape from above.

Question 8

Draw this 3D shape from the right.


Jake MILAN MathsPathway Assessment | Page 2 of 2

Question 1

Show that 2 ÷ 1 000 000 = 0.000002 by dividing 2 by 10several times.

Question 2

Samira has attempted to answer a question where shehad to label all the angles in a diagram.

Without doing any measuring or calculating, the teacherwas able to tell immediately that Samira was wrong.Explain how this is possible.

Question 3

Anh does not know that opposite angles are equal, butshe could still work out the missing angle below.By writing a sentence, explain how she could work it out.

Question 4

Substitute h = 3 and T = 100 into the expression hT(h − 2)and evaluate.You must show full working out line-by-line.


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Question 5

Find the lowest common denominator of 56 and 3

4 . Hence

re-write the below number sentence using < , = or > in

place of the □. You must show full working out.

− 56□ − 3

4

Question 6

By drawing a flowchart or otherwise, write an expressionthat shows all of these operations in one go:

Start with xSubtract 1Multiply by xMultiply by 5

Question 7

By drawing a flowchart or otherwise, write an expressionthat shows all of these operations in one go:

Start with zMultiply by 10Add yDivide by 7

Question 8

In a certain school of 60 students, the students have only two options if they wish to play sport; basketball and netball.

There are 20 students who play basketball, and 45 who play netball. Of these, 15 play both basketball and netball.

Display all of this information in a Venn diagram, and determine the probability that a student chosen from the school atrandom plays only netball.


Question 9

Re-write one of the fractions so that the denominatorsmatch.Hence rewrite the number sentence with a < , > or =in place of the ?.

−149

? −53

Question 10

Write an expression for 15 divided by g.Hence evaluate that expression for g = 5.You must show full algebraic working.

Question 11

Below is an incomplete two-way table which includesinformation on a business’ transportation and sleeppreferences.

Bike Car Total

Before midnight 70

After midnight

Total 100

Use the following information to complete this two waytable.1. Half the people in the survey ride their bike to work2. 20% of the people who drive their car prefer to go tobed after midnight

What percentage of employees who ride their bike towork also prefer to stay up past midnight?




Question 1

Label the diagram below so that it has two pairs of linesof equal length, and one pair of equal angles.

Question 2

Write a number sentence expressing the value of a in thediagram below.

Question 3

Write a number sentence expressing the value of themissing angle in the diagram below.

Question 4

A farmer has 51 eggs to sell at market. He can only sellthem in packets of 6. How many packets can he make,and how many eggs will be left over?

Question 5

Sharon has just moved house, and has 43 shirts that needto be packed away into 5 empty drawers. She wants todivide them evenly between the drawers, but realisesthat 43 ÷ 5 = 8 remainder 3. Describe what Sharon mightdo with the remainder.

Question 6



96

?3324


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Question 7

Write these numbers with words.

4,120

7,066

1,111


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Question 1

Given the following equations, explain the rules relatingto odd and even answers when dividing.

42 ÷ 7 = 636 ÷ 6 = 635 ÷ 7 = 549 ÷ 7 = 756 ÷ 8 = 7

22 ÷ 2 = 11

Question 2


Question 3

Fifteen gold bars were stolen from a bank by fourrobbers. When the robbers arrived back to their hideout,they attempted to divide the loot. However, one of themrealised that 15 ÷ 4 = 3 remainder 3. Describe what youthink will happen to the remainder.

Question 4


Question 5




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Question 6

Shade in 53 of a rectangle.

Question 7

Shade in 1 14 of a rectangle.


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Question 1

For the following situation, define a new variable for eachpiece of information.Hence re-write the information in the language ofalgebra.

Andrew has 10 dollars. Ben has 15 dollars. Chris has 9dollars.

Question 2

Substitute x = 4, y = 9 and z = 1 into the expression

4xz( zy3 − 1) and evaluate.

You must show full working out line-by-line.

Question 3

Create a stem and leaf plot from the following data.Remember to include a key.75 67 72 68 64 68 74

Question 4

Re-write this list of numbers in descending order:0.15, 0.11, 0.31, 0.38, 0.19

Question 5

Write an expression for 15 divided by g.Hence evaluate that expression for g = 5.You must show full algebraic working.


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Question 1

Solve:

1.2 + 287.98


Question 2

Here is a fact:

26 × 347 = 9022


0.0026 × 34.7



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Question 3

Solve:

1265 × 48


Question 4

Evaluate 7 × 7843.

You must show working line by line.

Question 5

Solve:

4000 × 335



Matthew CLEAVER-MUHVIC MathsPathway Assessment | Page 2 of 2

Question 1

Here is a fact:

26 × 347 = 9022


0.0026 × 34.7


Question 2

Describe why 23 is a prime number.

Question 3 Question 4

Kate is finding the factors of a large number. Using acalculator, she has just worked out that 55 is a factor ofthis number.

Suddenly, she realises that 11 must be a factor of thelarge number as well. Explain why Kate is correct.


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Question 5

Consider the number 864.

(a) Can it be divided evenly by 2? Explain how you know.

(b) Can it be divided evenly by 5? Explain how you know.

(c) Can it be divided evenly by 10? Explain how you know.

Question 6

By first finding the lowest common denominator, evaluatethe following. You must simplify your result if possible,and show full working out line-by-line.

104

+67

Question 7

By first finding the lowest common denominator, evaluatethe following. You must simplify your result if possible,and show full working out line-by-line.

34

−16

Question 8


Question 9

Fifteen gold bars were stolen from a bank by fourrobbers. When the robbers arrived back to their hideout,they attempted to divide the loot. However, one of themrealised that 15 ÷ 4 = 3 remainder 3. Describe what youthink will happen to the remainder.

Question 10



Question 11



Question 12

Mark and label the position of the fraction 34 on this number line.

Question 13



8927

?103

Question 14

Re-write this list of numbers in ascending order:0.9, 0.59, 0.49, 0.99, 0.19

Question 15

By shading in parts of the rectangles below, show that 1 23

is equivalent to 53 .


Question 16

By marking and labelling all quarters as both improper fractions and mixed numerals, show that 94 is equivalent to 2 1

4 .

Question 17

A barrel is falling down a waterfall, and is one quarter ofthe way down. Mark its position with a dot.



Question 1

Draw an example of a right angle, as well as an anglewhich is smaller than a right angle.

Question 2

Write a number sentence that matches the following.Hence find the mystery number.

24 divided by 2 is equal to a number divided by 4.

Question 3

Solve:

4000 × 335


Question 4

Solve

91842 ÷ 5

Your answer should be a whole number, with a remainderif needed.You must show full working out.


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Question 1





Question 2

Evaluate the following, showing working out, line by lineand writing your answer as a simplified improper fraction:

( ⁻ 1 × ( ⁻ 2 − ⁻ 1) ×12 ) ÷ ( ⁻ 1 × 0.2)


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Question 3

For the following situation, define a new variable for eachpiece of information.Hence re-write the information in the language ofalgebra.

Andrew has 10 dollars. Ben has 15 dollars. Chris has 9dollars.

Question 4

Write an expression for h multiplied by 9.Hence evaluate that expression for h = 3.You must show full algebraic working.


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Adrian - Maths Pathwaytests.mathspathway.com/tests/c9e1014f-886e-4fd6-bcda-78a... · 2016-08-22 · 26×347=9022 Using this fact, solve: 0.0026×34.7 You must show full working out