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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
Form 3-Mathematics-Scheme A-Half Yearly-Non-Calculator Paper 2012-2013 Page 2 of 5
(2, 2 marks)
Form 3-Mathematics-Scheme A-Half Yearly-Non-Calculator Paper 2012-2013 Page 3 of 5
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)
Form 3-Mathematics-Scheme A-Half Yearly-Non-Calculator Paper 2012-2013 Page 4 of 5
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)
Form 3-Mathematics-Scheme A-Half Yearly-Non-Calculator Paper 2012-2013 Page 5 of 5
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
Form 3-Mathematics-Scheme A-Half Yearly-Main Paper 2012-2013 Page 2 of 9
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)
Form 3-Mathematics-Scheme A-Half Yearly-Main Paper 2012-2013 Page 3 of 9
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)
Form 3-Mathematics-Scheme A-Half Yearly-Main Paper 2012-2013 Page 4 of 9
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
Form 3-Mathematics-Scheme A-Half Yearly-Main Paper 2012-2013 Page 5 of 9
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
Form 3-Mathematics-Scheme A-Half Yearly-Main Paper 2012-2013 Page 6 of 9
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
Form 3-Mathematics-Scheme A-Half Yearly-Main Paper 2012-2013 Page 7 of 9
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
Form 3-Mathematics-Scheme A-Half Yearly-Main Paper 2012-2013 Page 8 of 9
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
Form 3-Mathematics-Scheme A-Half Yearly-Main Paper 2012-2013 Page 9 of 9
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