Year 8 Yearly 2014 Baulko

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YEARLY EXAMINATION

YEAR 8 2014

MATHEMATICSTime Allowed 85 minutes plus 5 minutes Reading time.

I NSTRUCTIONS:

Write your Name and Class at the top of the page

Writein Penand draw diagrams in Pencil

Department of Education approved calculators are permitted

The use of mathematical templates is permitted.

Show all necessary working

Marks may not be awarded for untidy or carelessly arranged work

No grid paper is to be used unless provided with the examination paper

Outcome A B C D Total

Number 1,4,9,10 /4 4,7 /4 1,4 /8 1 /3 /19

Measurement 2,13 /2 1,5,6 /8 3, 5 /7 /17

Algebra 3,5,6,15 /5 2 /2 3 /6 4 /3 /16

Geometry 7,12,14,16 /4 2 /4 2 /5 /13

Statistics 8,11, 17 /3 3 /4 /7

Total /18 /18 /18 /18 /72

Name:

Class:


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SECTION A (18 Marks) Marks

ANSWERS

1. What is the next number in the numberpattern?

1, 1, 2, 3, 5, 8, 13

1

2. In your words and without using formulas orpronumerals, explain Pythagoras Theorem. 1

3. Make the subject of:

1

4. A bag contains 3 yellow marbles, 4 greenmarbles and 5 blue marbles. If I draw amarble from the bag randomly, what is the

probability of the marble not being yellow?Simplify your answer.

1

5. Expand and simplify:

1

6. Complete the table of values for the followingequation:

X -1 0 1

Y

1

7. ABCD is a rhombus.

Find the value ofx(No reasoning needed) 1

8. Describe the difference between a census anda sample. 1


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ANSWERS9.

Divide $424 in the ratio of 3 : 5 1

10.If ,

100

PRTI find the value ofR when

I= 36,P = 400, T= 2.

1

11. Find the mean of the following set ofnumbers:

-2, -4, 0, -3, -2, 3, and 41

12. Find the value ofxgiving reasons.

1

13. A rhombus has an area of and one ofits diagonals is 24cm. Find the length of itsother diagonal

1

14. Give one additional property that will make akite a rhombus. 1

15. Solve for

2

16. In your words, clearly define what a circle is.(Do not use formulas or equations). 1

17. A class has received the following marks for atest out of 10:

4, 10, 8, 2, 5, 5, 9, 9

Jason did the test after everyone else, if hismark is the new median. What are the

possibilities of Jasons score?

1


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SECTION B (18 Marks) Marks

ANSWERS

1. A pencil case in the form of a rectangularprism has length, width and height equal to20cm, 13cm, and 5cm respectively. What isthe exact length of the longest pencil that canfit into the pencil case?

3

2.Given the formula: a=

z

yx 22

and y > 0.

Find the exact value ofyif:

a = 17, x= 6, z= 5

2

3. The table below is a stem-leaf plot for theresults of a class test with a maximum markof 45.

Stem leaf

1 3 8 8

2 1 2 2 4 4 6 7 9

3 2 3 4 5 5 6 7 8 8

4 0 1 3 5 5

(i) Find the median mark.

(ii) Find the lower and upper quartiles.

(iii) Display the results using a box andwhisker plot.

1

2

1


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ANSWERS4. What is the sum of the 5t , 6t and 7t prime

numbers? 2

5. Find the perimeter of the following shape.Provide all necessary reasoning.

3

6. You are given that DF = EG = 3cm,

CH = 5cm, and FG = 4cm. DF, CH and EGare all perpendicular toFG. Find anapproximation for the area of shape belowusing Simpsons Rule.

2

7. Assuming that both brands sell the same typeand quality of items. Which item has bettervalue? You must justify your answer withcalculations.

Item A: 500g for $4.50

Item B: 300 grams for $2.75

2

= =Diagram not

to scale

D C

BA 6 m

5 m3 m


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SECTION C (18 Marks) Marks

ANSWERS

1. Let represent the Triangular number.

i)

Draw a diagram to show that 15 is atriangular number.

ii)

By writing the general form of andin terms of n, prove algebraicallythat all square numbers are the sum oftwo consecutive triangular numbers.

1

3

2. Given that ABCD is a parallelogram. (Youmay assume the property that opposite sidesof a parallelogram are equal)

Prove the property that diagonals bisecteach other in a parallelogram.

4


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ANSWERS3. A parabola is given by the equation:

.

i)Find the coordinates of the x and yintercepts of the parabola.

ii)What are the coordinates of the lowestpoint of the parabola?

iii)Neatly draw the parabola labelling allimportant features.

2

2

2


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ANSWERS

4. In a group of 140 tourists it was found that 88had visited Britain, 90 had visited Australia,76 had visited New Zealand, 48 had visited

both Britain and Australia, 43 had visited bothBritain and New Zealand, 50 had visited both

New Zealand and Australia, while 19 hadvisited all three countries.

i)Draw a Venn diagram to illustrate theinformation above.

ii)

A tourist is chosen at random from thisgroup, find the probability that thechosen tourist visited Australia and

exactly one other country.

2

2


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SECTION D (18 Marks) Marks

Answers

1. While taking a 4 week holiday, Sarahreceived a payment of $2444 whichrepresented her holiday loading (17.5%) plusher usual pay over the 4 weeks. Calculate heryearly salary (excluding the 17.5% holidayloading).

3

2. For the following diagram. CDE is a rightangled triangle, and CAD is a straight line.

a) Find the size of ACE (giving fullreasoning for each step).

b) Hence or otherwise, find the size of

CDE (giving full reasons).

c) Hence or otherwise, find the value ofx. (giving full reasons)

2

1

2


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ANSWERS3. A perfect cylindrical chicko roll is to be

delivered in a minimum sized box in theshape of a square prism, as shown in thediagram below.

What is the remaining capacity of the boxafter the chicko roll is put in? Give youranswer correct to 1 decimal place.

3

4. Jason has the following arrangement witheach of three shop owners. The owner giveshim the same amount of money Jason has inhis wallet, and then Jason will spend $10 inthe shop.

i)Let be the amount of money Jasonhas initially and be the amount ofmoney he walks out of the first shop

with. Express in terms of .

ii)If Jason has no money left after hecomes out of the third shop. How muchmoney did Jason start off with? Showall necessary working.

1

2


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ANSWERS5. A container in the shape of a right cone is

placed such that the apex is at the bottom asshown in the diagram. The radius of the baseof the cone is 15cm and its slant height is

26cm. BCDE, BC AB and DE AB

If the container is filled to a depth of 8cm.What is the area of the circular surface of thewater at that instant?

4

End of Paper

Year 8 Yearly 2014 Baulko

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