general past paper by topic by year. general past paper contents by year 2001 p1 q2 2003 p2 q13 2004...

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



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 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


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 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 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 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 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 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 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 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 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


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


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 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

general past paper by topic by year. general past paper contents by year 2001 p1 q2 2003 p2 q13 2004...

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