General Past Paper
By topic
By year
General Past Paper Contents By Year
2001 P1 Q2
2003 P2 Q13
2004 P2 Q3
2005 P2 Q112005 P2 Q12
2003 P2 Q3
2003 P2 Q2
2005 P2 Q42006 P2 Q7 2004 P1 Q7
2004 P2 Q5
2003 P1 Q10
2005 P1 Q3
2002 P2 Q4
2003 P2 Q12
2002 P2 Q6
2004 P2 Q8
2004 P2 Q12
2004 P2 Q6
General Past Paper Contents By Topic
Percentage
Pythagoras & Area
Volume
Perimeter(Circumference)
Trigonometry 1
Mean from a Frequency Table
Wages
Pythagoras
Distance, Speed & Time
Angles in a Kite
Pythagoras & Circle
Angles in a circle
Pattern & Formula 1Pattern & Formula 2
Trigonometry 2
Trigonometry 3 Area – composite
Formula – using
Trigonometry 4
2005 P2 Q12
The diagram below shows the fan belt from a machine.
The fan belt passes around 2 wheels whose centres are 30 centimetres apart.
Each wheel is 8 centimetres in diameter.
Calculate the total length of the fan belt. (RE 4)
30 cm 8 cmFan belt
8 cm
C = d30 cm
30 cmTotal = 25.12 + 30 + 30 1 mark
Total = 85.12 cm 1 mark
2005 General Paper 2 Question 12
C = 3.14 x 8 1 markC = 25.12cm 1 mark
2003 P2 Q13
20m
26m
A large advertising banner is hanging from a building.
The banner is an isosceles triangle.
The top edge of the banner is 20 m long and each of the other two sides is 26m long.
Find the area of the banner.
A = ½ x b x h
b = 20 m
h = ?26m
10m
h
h² = 26² - 10²h² = 676 - 100
h² = 576 h = 576
h = 24
A = ½ x b x hA = ½ x 20 x 24
A = 240 cm²
2003 General Paper 2 Question 13
2005 General Paper 2 Question 11
2005 P2 Q11
BYe Olde Shoppe
35cm
90cm
A
C
A rectangular shop sign is supported by a metal bar AB.
The length of the shop sign is 90 cm and the bar AB is attached to the wall 35 cm above the sign.
Calculate the size of the shaded angle ABC. (RE 3)
Do not use a scale drawing.
Trigonometry
SOH CAH TOA
35
90
x
HYP
ADJ
OPP
Tan (angle) = OPP/ADJ
Tan x = 35/90 1 mark
x = tan-1(35÷90) 1 mark
x = 21.250…. = 21.3° 1 mark
2004 General Paper 2 Question 3
2004 P2 Q3
The sketch shows the net of a three-dimensional shape. The net consists of a rectangle and two equal circles of radius 3 centimetres.
Find the VOLUME of the three-dimensional shape formed by this net. (RE 3)
25 cm
3 cm
FORMULAE sheet(Circumference circle) C = D (Area circle) A = r²(CSA of cylinder) A = 2rh(Volume cylinder) V = r²h(Volume prism) V = Ah
V = r²hV = 3.14x 3²x 25V = 706.5 cm³
2001 General Paper 1 Question 2
A student pays a train fare of £24.
If this represents 60% of the full adult fare, what is the full adult fare?
(RE 3)
60 % = £24 1 mark
Adult fare = 100%Student fare = 60% of the adult fare
1 % = £24 ÷ 60 = £0.40 1 mark100 % = £0.40 x 100 = £40 1 mark
2001 P1 Q2
2003 General Paper 2 Question 3
2003 P2 Q3
The number of letters in each of the first one hundred words of a news story were counted. The results are shown in the table below.
Number of letters Frequency Number of letters x frequency
12345678
5121826181173
Total = Total =
Find the mean number of letters per word, to 1 decimal place. (KU 4)
1 x 5 =
5 2 x 12 =
24 3 x 18 =
54 4 x 26 = 104 5 x 18 = 906 x 11 = 667 x 7 = 498 x 3 = 24
100 416
Mean =
416 100 = 4.16 = 4.2
2003 General Paper 2 Question 2
2003 P2 Q2
Alice Anderson has a part-time job in a call centre.
Her basic rate of pay is £6.50 per hour.
At weekends she gets paid overtime at time and a half.
Last week she was paid £136.50, which included 4 hours overtime.
How many hours did she work at the basic rate? (RE 4)
Overtime: 6.50 x 1.5 = £9.75 per hour 1 mark
4 x £9.75 = £39 1 mark
£136.50 - £39
= £97.50 1 mark
£97.50 ÷ 6.50
= 15 hours 1 mark
2005 General Paper 2 Question 4
2005 P2 Q4
The diagram below shows the shape of Sangita’s garden.Sangita plants a hedge along side AB.
13 m
8 m
7 m
B
A
Calculate the length of the hedge. (RE 4)
7m
13m – 8m
5m
Pythagoras
x
xx² = 7² + 5²
x² = 49 + 25
x² = 74x = 74x = 8.6 m (to 1d.p.)
2006 General Paper 2 Question 7
2006 P2 Q7
Amy and Brian travel from Dundee to Stonehaven.
The distance between Dundee and Stonehaven
is 80 kilometres.
Amy takes 1 hour 30 minutes to travel by car.
Brian takes the train which averages
a speed of 60 kilometres per hour.
What is the difference between their journey times? (RE 4)Brian: T = D ÷ S
T = 80 ÷ 60T = 1.3333…. hrs
T = 0.3333….hrs x 60 = 20 minT = 1.3333….hrs = 1 hr 20 min
Difference = 1 hr 30 – 1 hr 20
Difference = 10 minutes
2004 General Paper 1 Question 7
2004 P1 Q7
DEFG is a kite.
Angle GDF = 69°
Angle EFD = 33°
Calculate the size of angle DGF.
(RE 3)
D
G E
69°
33°
69°
180 – (90+69) = 11°
21°
F
33°
33°
180 – (90+33) = 57°
57°
Angle DGF = 21 + 57
= 78°
2004 General Paper 2 Question 5
2004 P2 Q5
QO
R
P
PQ is a diameter of the circle with centre O.
R is a point on the circumference of the circle.
PR is 12 cm, RQ is 5.5 cm.
Calculate the length of the radius of the circle. (RE 4)
Q
R
P
12 cm5.5 cm
PythagorasPQ² = 12² + 5.5² 1 markPQ² = 144 + 30.25PQ² = 174.25PQ = 174.25 = 13.2 1 markAsked for Radius, so 13.2 ÷ 2 = 6.6 cm 1
mark
1 mark
2003 General Paper 1 Question 10
2003 P1 Q10
A70°
B C
O
E
D
The diagram isa circle, centre O,a tangent AC to the circle at Ban angle DBA, which is 70°.
Calculate the size of shaded angle BOE. (3 RE)
DBO = 20º 1 mark
As OBA is right-angled (radius meets a tangent)
BDO = 20º
Triangle BDO is isosceles
DOB = 140º 1 mark
(180 –20-20)
EOB = 40º 1 mark
(180 –140)
20º
20º 140º
2005 General Paper 1 Question 3
2005 P1 Q3
Sandra is working on the design for a bracelet. She is using matches to make each shape.
Shape 1 Shape 2 Shape 3 Shape 4
(a) Draw shape 4. (1 RE)
(b) Complete the table. (2 RE)
(c) Find a formula for calculating the number of matches, (m), when you know the number of shapes, (s).
(2 RE)
(d) Which shape number uses 61 matches? (2 RE)
Shape number (s)1 2 3 4 5 6
13
Number of matches (m)
5 9 2113 17 25
m =
4 4 4
4s + 1
53
s = 15
m = 4 x 13 + 1m = 52 + 1m = 53
4 x 1 = 4, so need +1 = 5
4 x 2 = 8, so need +1 = 9etc.
m = 4s + 161 = 4s + 14s = 61 – 14s = 60 s = 60 ÷ 4 s = 15
2002 General Paper 2 Question 4
A fence for a garden is made by joining iron bars as shown below.
1 section 2 sections 3 sections
(a) Copy and complete this table.
Number of sections (s) 1 2 3 4 12
Number of iron bars (b) 8 22
(b) Find a formula connecting the number of iron bars (b) with the number of sections (s)
(c) A fence has been made by joining 176 iron bars. How many sections will this make?
15 29
b =
+ 7
+ 7
+ 7
7s (7x1=7 =8)
+ 1
7x12 + 1
85
176 = 7s + 1175 = 7s s = 25
+1
2002 P2 Q4
2003 General Paper 2 Question 12
5 km
7°Airport
An aircraft is approaching Glasgow Airport.
The angle of elevation of the aircraft from the airport is 7°.
The aircraft is a distance of 5 km from the airport.
Find the height of the aircraft to the nearest metre. (KU 4)
Do not use a scale drawing.
7°
5x
Trigonometry
SOH CAH TOA
OPPHYP
ADJ
2003 P2 Q12
opp
sin (angle)hyp
sin 75
o x
sin 7 5ox
0.6093..km 609mx
2002 General Paper 2 Question 6PQRS is a rhombus.
Its diagonals PR and SQ are 20 cm and 12 cm long respectively.
P
Q
R
S
12 cm
Calculate the size of the shaded angle PQR.
Do not use a scale drawing. (RE 4)
10 cm
6 cmx
Trigonometry
SOH CAH TOA
ADJ
OPP
HYP
2002 P2 Q6
opp
tan (angle)adj
10
tan6
ox 1tan (10 6)x
o59x
20 cm
o oPQR 59 2 118
2004 General Paper 2 Question 8The floor of a conservatory consists of a rectangle and a semi-circle.
The floor has the shape shown below. Measurements are in metres.
1.5 m
2.2 m
Find the total area of the floor. (4 KU)
Area1 (Rectangle) = lbA = 2.2 x 1.5
A = 3.3 m²
Area2 (semi-circle) = ½ r²A = ½ x 3.14 x 1.1²
D = 2.2m, so r = 1.1m
A = 1.8997 m²
Total Area = 3.3 + 1.8997
= 5.1997 = 5.2 m²
2004 P2 Q8
2004 General Paper 2 Question 12The current, C amps, of an electrical appliance is calculated using the formula
•A hairdryer has a power rating of 850 watts.
•The fuse used should be the one just bigger than the calculated current.
•The choice of fuses is 3 amp, 5 amp and 13 amp.
Which fuse should he use. (RE 3)
,where watts is the power rating.240P
C P
850240
C = 3.541666…….
You would choose the 5 amp fuse. The 3 amp is too small and 13 amp is too big. 2004 P2
Q12
2004 General Paper 2 Question 6
2004 P2 Q6
P Q
RS
7 cm
10 cm
4 cm
PQRS is a trapezium.•PQ = 7 centimetres
•QR = 4 centimetres
•SR = 10 centimetres
•Angles PQR and QRS are both right angles.
Calculate the size of angle PSR.Do not use a scale drawing.
4 cm
10 - 73 cmx
ADJ
OPPHYP
opp
tan (angle)adj
4
tan3
ox 1tan (4 3)x o55.1x
oPSR 55.1
Trigonometry
SOH CAH TOA
200 General Paper Question
200 P Q
200 General Paper Question
200 P Q