Embed Size (px)
Citation preview
71
Centre Number
Candidate Number
General Certificate of Secondary Education
January 2009
Mathematics
Module N3 Paper 1
(Non-calculator)Higher Tier
[GMN31]
FRIDAY 9 JANUARY
9.15 am – 10.15 am
4242
TIME
1 hour.
INSTRUCTIONS TO CANDIDATES
Write your Centre Number and Candidate Number in the spaces
provided at the top of this page.
Write your answers in the spaces provided in this question paper.
Answer all eleven questions.
Any working should be clearly shown in the spaces provided since
marks may be awarded for partially correct solutions.
You must not use a calculator for this paper.
INFORMATION FOR CANDIDATES
The total mark for this paper is 44.
Figures in brackets printed down the right-hand side of pages indicate
the marks awarded to each question or part question.
You should have a ruler, compasses, set-square and protractor.
The Formula Sheet is on page 2.
For Examiner’s use only
Question Marks Number
1
2
3
4
5
6
7
8
9
10
11
TotalMarks
GMN31
Formula Sheet
Area of trapezium = 1–2 (a + b)h
Volume of prism = area of cross section × length
In any triangle ABC
Area of triangle = 1–2 ab sin C
Cosine rule: a2= b2
+ c2– 2bc cos A
Volume of sphere = 4–3πr3
Surface area of sphere = 4πr2
Volume of cone = 1–3πr2h
Curved surface area of cone = πrl
Quadratic equation:
The solutions of ax2+ bx + c = 0, where a ≠ 0, are given by
a
h
b
Crosssection
length
B
c
A
b
Ca
r
h
r
l
Sine rule : sin sin sin
aA
bB
cC
= =
x b b aca
=±– –
24
2
4242 2 [Turn over
Examiner Only
Marks Remark
1 (a)
Diagram not
drawn accurately
Calculate the area of the triangle.
Answer ________ cm2 [2]
(b) Convert 8.4 m2 to cm2
Answer ________ cm2 [2]
4242 3 [Turn over
7 cm
4.8 cm
10 cm
Examiner Only
Marks Remark
2 Joe uses 3–4 of a tin of paint to paint a garden shed.
What is the least number of tins he requires to paint 10 similar sheds?
Answer ____________ [3]
4242 4 [Turn over
Examiner Only
Marks Remark
3 A survey was carried out in Belfast City centre to find out the opinions of
people on the subject of ‘healthy living’.
A sample of 100 people was questioned.
(a) (i) Explain why these 100 people might not represent the opinions of
the Belfast public on ‘healthy living’.
______________________________________________________
___________________________________________________ [1]
(ii) One of the questions used in the survey was “Do you not think
that thin people are healthier than fat people?”
Give a reason why this question may not have been a suitable
question for the survey.
Reason _______________________________________________
____________________________________________ [1]
(b) The same survey was carried out inside a leisure centre in Lisburn.
Give two reasons why the survey should not have been carried out in
this location.
Reason __________________________________________________
________________________________________________ [1]
Reason __________________________________________________
________________________________________________ [1]
4242 5 [Turn over
Examiner Only
Marks Remark
4 The heights, in cm, of 11 children in a nursery class were:
81 86 90 97 88 79 83 91 93 85 88
Illustrate this using a stem and leaf diagram. [3]
5 (a) Factorise
(i) 28 – 7y
Answer ____________ [1]
(ii) p – pt
Answer ____________ [1]
(b) (i) Expand 5(3 – y)
Answer ____________ [1]
(ii) Expand and simplify (x – 3) (x + 1)
Answer ____________ [2]
(c) Write down an expression for the nth term of the sequence
2, 7, 12, 17, ...
Answer ____________ [2]
4242 6 [Turn over
6 The PSNI recorded the speeds of a number of vehicles passing under a
bridge on the M2 motorway during a 2 minute period one morning.
The speeds recorded are in miles per hour (mph).
Speed x (mph) Frequency f
44 � x < 50 3
50 � x < 56 7
56 � x < 62 8
62 � x < 68 6
68 � x < 74 5
74 � x < 80 1
(a) Which of the class intervals contains the median speed?
Answer ________________ [1]
(b) On the graph paper draw a frequency polygon for the data. [2]
8
Fre
quen
cy
6
4
2
1
7
5
3
0
44 50
Speed (mph)
56 62 68 74 80
Examiner Only
Marks Remark
4242 7 [Turn over
Examiner Only
Marks Remark
7 Two identical regular polygons join with a square to form a tiling pattern.
Explain why these polygons must be regular octagons.
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
__________________________________________________________ [3]
8 Write 120 as a product of prime factors and express your answer in index
notation.
Answer ________________ [3]
4242 8 [Turn over
BLANK PAGE
(Questions continue overleaf)
4242 9 [Turn over
Examiner Only
Marks Remark
9 Eileen constructed a cumulative frequency table from her mobile phone bill
to display her call times over the previous month. The results are shown in
the table below.
Time in minutes Cumulative frequency
<5 29
<10 62
<15 114
<20 153
<25 179
<30 195
(a) Draw a cumulative frequency graph, on the opposite page, to display
the data. [3]
(b) From your graph, estimate the interquartile range.
Answer __________ minutes [2]
(c) Eileen’s pricing plan with the phone company allows her free calls
provided that they last no more than 12 minutes.
From your graph, estimate the number of calls which will be charged
to Eileen’s account by the phone company.
Answer __________ calls [2]
4242 10 [Turn over
100
120
140
160
180
200
80
Cum
ula
tive
freq
uen
cy
60
40
20
0
0 5
Time in minutes (�)
10 15 20 25 30
4242 11 [Turn over
10 Calculate ×
Give your answer as a mixed number.
Answer ____________ [3]
11 Solve the equation
Show your working. A solution by trial and improvement will not be accepted.
Answer x = ____________ [4]
4242 12 [Turn over
Examiner Only
Marks Remark
41
42
2
3
x x+ =22
2 13
2– –
4242 13 [Turn over
THIS IS THE END OF THE QUESTION PAPER
935-047-1
General Certificate of Secondary Education
January 2009
Mathematics
Module N3 Paper 2
(With calculator)Higher Tier
[GMN32]
FRIDAY 9 JANUARY
10.30 am – 11.30 am
4243
TIME
1 hour.
INSTRUCTIONS TO CANDIDATES
Write your Centre Number and Candidate Number in the spaces
provided at the top of this page.
Write your answers in the spaces provided in this question paper.
Answer all thirteen questions.
Any working should be clearly shown in the spaces provided since
marks may be awarded for partially correct solutions.
INFORMATION FOR CANDIDATES
The total mark for this paper is 44.
Figures in brackets printed down the right-hand side of pages indicate
the marks awarded to each question or part question.
You should have a calculator, ruler, compasses, set-square and
protractor.
The Formula Sheet is on page 2.
GMN32
TotalMarks
71
Centre Number
Candidate Number
For Examiner’s use only
Question Marks
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
Formula Sheet
Area of trapezium = 1–2 (a + b)h
Volume of prism = area of cross section × length
In any triangle ABC
Area of triangle = 1–2 ab sin C
Cosine rule: a2= b2
+ c2– 2bc cos A
Volume of sphere = 4–3πr3
Surface area of sphere = 4πr2
Volume of cone = 1–3πr2h
Curved surface area of cone = πrl
Quadratic equation:
The solutions of ax2+ bx + c = 0, where a ≠ 0, are given by
a
h
b
Crosssection
length
B
c
A
b
Ca
r
h
r
l
Sine rule : sin sin sin
aA
bB
cC
= =
x b b aca
=±– –
24
2
4243 2 [Turn over
Examiner Only
Marks Remark
1 Calculate the area of a circle of radius 2.5 cm.
Answer ____________ [3]
2 A new table is priced at £140
In a sale it is reduced by 35%
Calculate the sale price.
Answer £ __________ [3]
4243 3 [Turn over
Examiner Only
Marks Remark
3 The table shows the engine capacity in litres and the fuel consumption
(number of miles per gallon (mpg)) for a selection of new cars.
Car Engine capacity (litres) Fuel consumption (mpg)
Aster 1.3 45
Viva 2.0 37
Megro 2.5 32
Lazio 1.6 42
Torino 1.8 39
Serene 1.0 50
(a) Draw a scatter graph on the grid opposite to show the data in the table.
[2]
(b) Draw a line of best fit for the data. [1]
(c) Using your line of best fit, what fuel consumption in mpg would you
expect from a car with an engine capacity of 2.2 litres?
Answer ________ mpg [1]
4243 4 [Turn over
4243 5 [Turn over
50
40
30
20
10
0
0 1.0 2.0 3.0
Engine capacity (litres)
Fuel
consu
mpti
on (
mpg)
Examiner Only
Marks Remark
4 (a)
Calculate
(i) angle p Answer ____________° [1]
(ii) angle q Answer ____________° [1]
4243 6 [Turn over
65°115°
108°p
q
Diagram not
drawn accurately
Examiner Only
Marks Remark
(b) Measure the bearing of L from M.
Answer _____________° [1]
4243 7 [Turn over
L
M
N
Examiner Only
Marks Remark
5 In a game of Foozball a player scores 2 ‘Goals’ worth x points each, 3
‘Overs’ worth y points each and 1 ‘Nearly’ worth z points.
(a) Write down an expression in terms of x, y and z for the total number of
points scored by this player.
Answer __________________ [2]
(b) If the total points scored by this player were 19, how many points could
each of the 3 scores have been worth?
Give one possible solution.
Points
1 Goal = __________
1 Over = __________
1 Nearly = __________ [2]
6 Ciara is using Trial and Improvement to find a value of x to satisfy the
equation
x + 1_x = 6
The table shows her first trial.
Value of x x + 1_x Comment
2 2.5 Too Low
Complete the table to help her find the correct value of x to 1 decimal place.
Answer x = __________ [4]
4243 8 [Turn over
Examiner Only
Marks Remark
4243 9 [Turn over
7 Carol leaves £1200 in the bank for three years.
It earns compound interest of 6% each year.
Calculate the total amount Carol has in the bank at the end of the three
years.
Answer £ ____________ [3]
8 The PSNI recorded the speeds of a number of vehicles passing under a
bridge on the M2 motorway during a 2 minute period one morning.
The speeds recorded are in miles per hour (mph).
Speed s (mph) Frequency
44 � s < 50 3
50 � s < 56 7
56 � s < 62 8
62 � s < 68 6
68 � s < 74 5
74 � s < 80 1
Calculate an estimate for the mean speed.
Answer ________ mph [4]
Examiner Only
Marks Remark
9
A straw of length 15 cm just fits inside a cylindrical container of length
12 cm as shown. Calculate the diameter of the cylinder.
Answer ________ cm [3]
15 cm
12 cm
4243 10 [Turn over
10
(a) (i) Find the gradient of the line l Answer ____________ [1]
(ii) Hence write down the equation of this line in the form y = mx + c.
Answer ____________________ [2]
(b) Here are the equations of another 4 lines
Line 1: y = 2x Line 2: y = –2 Line 3: y = x – 3 Line 4: y = 2x – 2
Which one of these lines is parallel to the line with equation y = x – 2?
Answer _____________ [1]
4243 11 [Turn over
Examiner Only
Marks Remark
–5–6 –4 –3 –2 –1 1 2 3 4 5x
y
–1
–2
–3
0
1
2
3
4
5
6
6
–4
–5
–6
l
Examiner Only
Marks Remark
11 A coat has a sale price of £54.40 which is a saving of 15% on the original
price.
What was the original price of the coat?
Answer £ __________ [3]
4243 12 [Turn over
Examiner Only
Marks Remark
12 The diagram shows a trapezium.
AB is parallel to DC. AB = 13 cm, AD = 6 cm and CD = 8 cm.
Calculate the size of angle B.
Answer __________° [3]
D
6 cm
8 cm
13 cm
C
BA
Diagram not
drawn accurately
4243 13 [Turn over
13
O is the centre of the circle.
(a) Explain why angle PQR = 90°
_______________________________________________________[1]
(b) Calculate
(i) angle PRQ, Answer __________° [1]
(ii) angle POQ. Answer __________° [1]
52°S
RQ
O
P
Diagram not
drawn accurately
4243 14 [Turn over
Examiner Only
Marks Remark
THIS IS THE END OF THE QUESTION PAPER
935-051-1 [Turn over
