2012 Year8 Yearly

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S Y D N E Y B O Y S H I G H S C H O O LM O O R E P A R K , S U R R Y H I L L S

Year 8Yearly Examination 2012

Mathematics

General Instructions Examiner:A Ward Working time 90 minutes

Write using black or blue pen, pencil maybe used for diagrams

All necessary working MUST be shown inevery question if full marks are to beawarded.

Marks may not be awarded for untidy orbadly arranged work.

If more space is required, clearly write thenumber of the QUESTION on one of the

back pages and answer it there. Indicatethat you have done so.

All answers must be given in simplestexact form unless stated otherwise.

Clearly indicate your class by placing anX, next to your class.

NAME:Class Teacher Section Mark

8MaA Ms Nesbitt A /18

8MaB Ms Kilmore/Mr Boros B /18

8MaC Mr Elliott C /18

8Ma1 Ms Evans/Ms Chen D /18

8Ma2 Mr Hespe/Mr Elliott E /18

8Ma3 Mr Boros F /18

Total / 108

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SBHS 2012 Year 8 Yearly

Page 1 of 12

Section A (17 Marks)Question Answer Marks

1)Evaluate:

586 3.278

284.3

to 3 decimal

places.

1

2) Rewrite 78

with a denominator of 24. 1

3) Solve: 3 9 6x 14) Divide 40 in the ratio 3:5. 15) The diagonals of a rhombus are 46cm and

25cm, Find its area.

1

6) Increase $4.60 by 15%. 17) Find the mean of the following set of

scores: 7,6,8,12,9

1

8) If {0,1,2,3,4,5}E and {0,2,4}A write down the complement set A .

1

9) Express a speed of 80 km/has a speed inmetres per second.

1

10) Write down the perimeter of the following shape in terms of aand b. 1

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Page 2 of 12

11) Construct a line parallel to AB passing through C using compasses and a straight edgeonly.

3

12) Find the value of BAC giving reasons for your answer. 2

13) What is meant by the term 'sample space'? 1

14)If

1 9 1 16 17, , , and

3 7 5 11 10P Q R S T then the largest and smallest fractions are:

(A) SandR (B) Sand P (C) Tand S (D) Tand P (E) TandR

Circle correct answer.

2

End of Section A.

.C

A

B

A

B D

C

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Page 3 of 12

Section B (18 Marks)

Question Answer Marks

1) Simplify: 62

10

4

x

x

1

2) A student surveys his class to ask how many members are in each family The results were:6,3,3,2,4,5,4,5,8,5,4,8,6,7,6,5,8,4,7,6.

a) Construct a frequency table to show the results.

b) What is the range?

c) What is the mode?

d) Calculate the mean.

5

3) Find the area of the following: 1

4) If 2.5x , evaluate 25 2x x x 1

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Page 4 of 12

5) Factorise fully: 2 2x y xy 1

6)

James adds up 4 consecutive oddintegers, if the smallest one is 2m-1, then

what is the sum?

2

7) Solve: 2 5 9 3x x

2

8) A pattern is made from matches as shown below. If there are 87 matches, how manytriangles have been formed.

3

9) If the edge of a square is increased by 50% the percentage increase in area is:(A) 100 (B) 150 (C) 225 (D)125 (E) None


2

End of Section B.

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Page 5 of 12

Section C (18 Marks)

Question Marks

1) A hardware store has a closing down sale. They advertise a ladder at $256, while its costprice is $274. Express the profit/loss as a percentage of cost price.

1

2) The angles of a triangle are in the ratio 2:3:4. Find the size of the largest angle in degrees. 2

3)If

1 5 2

2 5x

then what is the value ofx?2

4) In this Venn diagram: w, x, y andzare all unknown positive integers.

a)

Write an algebraic expression for P A B

using any of the variables w, x, y and z.

b) Write an algebraic expression for P(A) using any of the variables w, x, y andz.

2

x w z

y

A B

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Page 6 of 12

5) Convert 350mm2to cm2. 1

6) If y% of an amount is $8, how much is the full amount? 2

7) Solve | 3 | 7x 2

8) Plot the graph of 2 3y x , by first completing a relevant table of values and thenchoosing a scale for your graph. Show the values where the graph crosses the xandyaxes.

4

9) Danny starts at year 1994 and counts downward 7 at a time, giving the sequence of years1994, 1987, 1980... A year which he will count is:

(A) 1788 (B) 1789 (C) 1790 (D) 1791 (E) 1792


2

End of Section C.

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Page 7 of 12

Section D (18 Marks)


1) a) Complete a multiplication table modulo 7.

b)

Solve: 3 4 1x (mod 7)

c) Find the square root(s) of 2 modulo 7.

2

3

2

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Page 8 of 12

2) Expand and simplify:a) 2 (3 4 ) 8 6 5 (2 4)x y z y x z z x y

b) x 4 x 7

c) 2

2 1x

1

2

2

3) Showing all reasoning, prove that segment 2AC AB . 4

4) If y is positive and if x y , then which of the following statements is false?(A)

2 0x y (B) 0x y (C) 0xy (D)1 1

0x y

(E) 1 0x

y


2

End of Section D.

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Page 9 of 12

Section E (18 Marks)


1) Graph the solution set of the following inequality on a real number line:4 3

82

x

3

2) Simplify 2 147m

m

2

3) An equilateral triangle has lengths 2x-3,x+6 and 5y. Find the value ofy. 2

4) A bag contains 2 red, 7 blue and 6 greenmarbles. One ball is drawn at random

and replaced afterwards.

a) What is the probability of

choosing a green marble?

b) What is the probability of

choosing a marble which is not

blue?

c) Three marbles are now removed

and the probability of a red is now

zero and the probability of a blue

is now 0.5. Which marbles were

removed?

4

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Page 10 of 12

5) Two rally cars were involved in a handicap time trial. The distance time graph indicateshow far each has travelled.

Use the graph to determine:

a) the handicap advantage given to car Y

b) the distance travelled by each car.

c)

how far had each car travelled when car X caught car Y

d) how long it took each car to travel 300km.

e) the average speed of each car.

5

6) Students in a Maths test can score 0, 1, 2 or 3 marks in each of six questions. There is oneway of scoring 18 and six ways of scoring 17, The number of ways of scoring 16 is:

(A) 6 (B) 12 (C) 15 (D) 21 (E) 42


2

End of Section E.

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Page 11 of 12

Section F (16 Marks)


1) A right angled triangle has hypotenuselengthpcm and one other side of length

q cm. Ifpand qdiffer by 1, then find the

length of the remaining side in terms of q

in centimetres.

3

2) A hollow cube with side length 2cm hasone of its corners cut off leaving a

triangular hole, which is equilateral of

side 1cm. Find the surface area of the

remainder of the outside of the cube.

3

3) Write in descending order:360 300 180 120 602 ,3 ,5 ,7 ,8

2

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Page 12 of 12

4) Calculate the exact values ofxandy. 4

5) Sarah, Ben and Louise each bought a birthday present for their mother. They decided tocombine the three purchase prices and each pay an equal amount. If each had paid the

purchase price of their own present, Sarah would have paid $1 more, Ben $3 less andLouise would have paid $20.What was the total cost of the three presents?

4

6) A 5 litre container full of orange juice has 2 litres of juice removed, it is then 'topped up'with 2 litres of water and mixed. It then has 2 litres of the mixture removed and is againfilled with water. What percentage of the final mixture is orange juice?(A)27 (B) 25 (C) 30 (D) 36 (E) 24


2

End of Section F.

End of Examination,

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Revision 2

Extra Working Space

Question Number Answer Marks

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Revision 2

Extra Working Space

Question Number Answer Marks

2012 Year8 Yearly

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