Gozo College Boys’ Secondary School Victoria - …gc.victoriaboys.skola.edu.mt/hypapers/Maths Scheme A...Form 3-Mathematics-Scheme A-Half Yearly-Non-Calculator Paper 2012-2013 Page

Form 3-Mathematics-Scheme A-Half Yearly-Non-Calculator Paper 2012-2013 Page 1 of 5

Gozo College Boys’ Secondary School Victoria - Gozo, Malta

‘Ninu Cremona’

Half Yearly Examination 2012 – 2013

Form 3 Time: 30 min

Name: _______________________ Class:_________

• Answer all questions. • This paper carries 25 marks. • Calculators, protractors and other mathematical instruments, except rulers are not

allowed. • You are not required to show your working. However, space for working is

provided if you need it.

1. Simplify the following:

a) 3u – (– 2u) b) ab + 2ba

( 1, 1 marks)

2. Solve the following:

a)

b) 4w = w – (w – 8)

y = _______ w = _______

Question 1 2 3 4 5 6 7 8 9 10 Total

Mark

C

Mathematics – Scheme A

Non – Calculator paper


(2, 2 marks)


3. Look at these two sequences below.

Sequence A: 4, 2, 1, ½, ¼. Sequence B: ˗6, ˗2, 2, 6, 10.

Which of the above sequences is linear? Explain.

_______________________________________________________________

_______________________________________________________________

(2 marks)

4. Simplify: a) a8 × a4 ÷ a5 b) (2b3)2

(1, 1 marks)

5. Adam, a store keeper buys a piano for €2,000. He makes a profit of

50%, calculate the selling price.

Selling price = €__________

(2 mark)

6. Work out:

a)

b)

(1, 2 marks)


7. In a triangle ABC, B = 90o, AB = 6 cm and BC = 8 cm. Find AC.

AC = ______cm

(1 mark)

8. Calculate the size of:

a) one exterior angle of a regular decagon (10 sides).

Ans: ______o b) one interior angle of a regular decagon.

Ans: ______o

Simon wishes to draw a regular decagon using LOGO. The perimeter of the decagon is 200 turtle steps.

Fill in the missing commands.

Repeat ____ [ FD _____ RT _____ ]

(1, 1, 2 marks)

^

A B

C

c)


9. In a block of flats, 24 flats have two bedrooms and 32 flats have one bedroom. Give the ratio of the number of two-bedroomed flats to the number of one

bedroomed flats.

Two-bedroomed flats : One-bedroomed flats

_______ : _______

b) Share €49 amongst two people John and Kate so that their shares are in the

ratio of 3 : 4 respectively.

John = € ________

Kate = €________

(1, 2 marks)

10. These co-ordinates form a straight line.

a) Fill in the missing co-ordinate.

b) Circle the correct equation of this line:

y = 5 – x OR y = x – 5

(1, 1 marks)

END OF PAPER

(4, 1)

(3, 2)

(2, 3)

(A, 0) A = _____

a)

Form 3-Mathematics-Scheme A-Half Yearly-Main Paper 2012-2013 Page 1 of 9

Gozo College Boys’ Secondary School Victoria - Gozo, Malta

‘Ninu Cremona’

Half Yearly Examination 2012 – 2013

Form 3 Time: 1.5 hours

Name: _______________________ Class:_________

• Answer all questions. • This paper carries 75 marks. • Calculators, protractors and other mathematical instruments are allowed.

• All necessary working must be shown.

1. Find the missing number:

(2 marks)

2. Expand and simplify:

a) (z + 3)(z – 3) b) (c + 2)(c + 5) + 2c(c + 7)

(2, 3 marks)

Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Total

main

Non-

Cal.

Global

mark

Mark

C

Mathematics – Scheme A

Main paper


3. Factorise fully:

a) 12ac – 8bd b) ½ mv2 – ½ mu2

(1, 2 marks)

4. The purchase price of a watch is €70.80. If this price includes

VAT at 18%, find the price before VAT was added.

Ans: €________

Tony is given €500 for his birthday. He puts the money in a savings account

with an interest rate of 5% p.a. How much interest does he earn after two

years?

Interest: €_______

What annual rate of interest is necessary to give an interest of €238 after

one year on an investment of €2800?

Rate: ______%

(2, 2, 2 marks)

a)

b)

c)


NAME OF STUDENT: _________________________________ CLASS: _____________

5. In a school, 33 classrooms are required if each class has 32 students. How

many classrooms would be required if the class size was reduced to 22?

Ans: _____ classes

The ratio of two sums of money is 4 : 5. The first sum is €6. What is the total

sum of money?

Total sum = €________

(2, 2 marks)

6. Use trial and improvement to solve the equation x3 + x = 335. Give the answer

correct to 1 decimal place.

x x3 x

3 + x Large or Small

Ans: x = ________

(4 marks)

a)

b)


7. In the figure, AB = 11.7 cm, AD = 9.9 cm and BC = 7.3 cm.

a) Find side BD, giving your answer to 1 decimal place.

BD = ________ cm

b) Find side DC and hence find side AC.

DC = ________cm

AC = ________cm

(2, 2, 1 marks)

8. Simplify these algebraic fractions as much as possible:

a)

b)

(1, 2 marks)

A

B

C

11.7 cm 7.3 cm

D 9.9 cm


NAME OF STUDENT: __________________________________ CLASS: ____________

9. a) Write down the next two terms of the following sequences.

i) 27, 21, 15, 9, ____, _____.

ii) 2, 6, 12, 20, ____, _____.

b) This is a pattern made up of rectangles.

i) Draw the next pattern in the space provided below.

ii) Complete this table

iii) Write down the nth term.

iv) How many rectangles are there in the 50th pattern?

v) Which pattern will have 292 rectangles?

(2, 1, 2, 2, 1, 2 marks)

Pattern number 1 2 3 4 5 6

Number of rectangles

Pattern 1 Pattern 2 Pattern 3 Pattern 4


10. ABCDE is a pentagon. ABF and DCF are straight lines such that 4x + y = 180o

a) Calculate the sum of interior angles of a pentagon. ___________o

b) Find the value of x. ___________o

c) What is the value of angle ABC? ___________o

d) Calculate the value of y. ___________o

(2, 2, 1, 1 marks)

A B

C

F

D

E

3x

4x

3x 4x

4x

y

y


11. OAB is a sector of a circle of radius 4.5cm.

a) Calculate the length of the arc AB giving your answer correct to 1 d.p.

Length of arc = ______cm

b) Calculate the area of sector OAB giving your answer correct to 2 d.p.

Area of sector = ________cm2

(3, 3 marks)

12. Daniel, a form 3 student was asked how many hours he spends on the following

activities on Saturdays. Fill in the table and draw a pie chart to represent this information.

(2, 3 marks)

Activity Time in

hours Angle

Sleeping 10 150o

Watching TV 1 15o

Playing video games

3

Chatting on the computer

2

Homework 3

Eating 1 15o

Go out with

friends 4

Total 24 360o

120o

4.5cm


13. A plane leaves airport A and flies a distance of 62 km to airport B on a bearing of 060°. It

then changes direction and flies a distance of 55 km to another airport C on a bearing of

110° from B.

a) Draw and label a scale diagram to show the plane’s journey.

Use a scale of 1 cm to represent 10 km.

b) Measure the length of AC. _______cm

c) What is the true distance between airports A and C? _______km

d) Measure the bearing of airport C from airport A. ________o

(4, 1, 1, 1 marks)

A

B

C

55 km

62 km

N

A


14. a) Complete the table for y = 2x + 3.

b) Draw and label the graph of y = 2x + 3 on the grid below.

Use 1cm to represent 1 unit on the y-axis and 2cm to represent 1 unit on the x-axis.

c) From the graph, find the gradient for the line y = 2x + 3.

(Working must be shown.)

d) Write down the co-ordinates of the y-intercept of this line. Co-ordinates of y-intercept = ( , )

(2, 4, 2, 1 marks)

END OF PAPER

x ˗2 ˗1 0 1 2 3

2x ˗4 ˗2 2 4 6

+3 +3 +3 +3 +3 +3

y ˗1 1 3 5 9

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Gozo College Boys’ Secondary School Victoria - …gc.victoriaboys.skola.edu.mt/hypapers/Maths Scheme A...Form 3-Mathematics-Scheme A-Half Yearly-Non-Calculator Paper 2012-2013 Page