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##### General Past Paper

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**General Past Paper**By topic By year**General Past Paper Contents By Year**2003 P1 Q10 2001 P1 Q2 2002 P2 Q4 2003 P2 Q2 2002 P2 Q6 2003 P2 Q3 2003 P2 Q12 2003 P2 Q13 2005 P1 Q3 2004 P1 Q7 2006 P2 Q7 2004 P2 Q3 2005 P2 Q4 2004 P2 Q5 2005 P2 Q11 2005 P2 Q12 2004 P2 Q6 2004 P2 Q8 2004 P2 Q12**General Past Paper Contents By Topic**Angles in a Kite Trigonometry 1 Angles in a circle Trigonometry 2 Area – composite Trigonometry 3 Distance, Speed & Time Trigonometry 4 Mean from a Frequency Table Volume Formula – using Wages Pattern & Formula 1 Pattern & Formula 2 Percentage Perimeter(Circumference) Pythagoras Pythagoras & Area Pythagoras & Circle**2005 General Paper 2 Question 12**8 cm 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) Fan belt 8 cm 30 cm C = pd 30 cm C = 3.14 x 8 1 mark C = 25.12cm 1 mark 30 cm Total = 25.12 + 30 + 30 1 mark Total = 85.12 cm 1 mark 2005 P2 Q12**2003 General Paper 2 Question 13**20m 26m 10m h 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 h² = 26² - 10² A = ½ x 20 x 24 h² = 676 - 100 A = ½ x b x h h² = 576 A = 240 cm² b = 20 m h = Ö576 h = ? h = 24 2003 P2 Q13**2005 General Paper 2 Question 11**HYP OPP 35 x 90 ADJ A 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. 35cm B C Ye Olde Shoppe 90cm Tan (angle) = OPP/ADJ Tan x = 35/90 1 mark x = tan-1(35÷90) 1 mark Trigonometry SOH CAH TOA x = 21.250…. = 21.3° 1 mark 2005 P2 Q11**2004 General Paper 2 Question 3**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) FORMULAE sheet (Circumference circle) C = pD (Area circle) A = pr² (CSA of cylinder) A = 2prh (Volume cylinder) V = pr²h (Volume prism) V = Ah 3 cm 25 cm V = pr²h V = 3.14x 3²x 25 V = 706.5 cm³ 2004 P2 Q3**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) Adult fare = 100% Student fare = 60% of the adult fare 60 % = £24 1 mark 1 % = £24 ÷ 60 = £0.40 1 mark 100 % = £0.40 x 100 = £40 1 mark 2001 P1 Q2**2003 General Paper 2 Question 3**104 90 5 x 18 = 66 6 x 11 = 49 7 x 7 = 24 8 x 3 = 416 100 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. 5 1 x 5 = 24 2 x 12 = 54 3 x 18 = 4 x 26 = 416 100 Find the mean number of letters per word, to 1 decimal place. (KU 4) Mean = = 4.2 = 4.16 2003 P2 Q3**2003 General Paper 2 Question 2**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 2003 P2 Q2**2005 General Paper 2 Question 4**13 m B 7 m A 8 m 13m – 8m 5m The diagram below shows the shape of Sangita’s garden. 7m Sangita plants a hedge along side AB. x Pythagoras x x² = 7² + 5² x² = 49 + 25 x² = 74 Calculate the length of the hedge. (RE 4) x = 74 x = 8.6 m (to 1d.p.) 2005 P2 Q4**2006 General Paper 2 Question 7**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 Difference =1 hr 30– 1 hr 20 T = 80 ÷ 60 Difference =10 minutes T = 1.3333…. hrs T = 0.3333….hrs x 60 = 20 min T = 1.3333….hrs = 1 hr 20 min 2006 P2 Q7**2004 General Paper 1 Question 7**69° 180 – (90+33) = 57° 180 – (90+69) = 11° 33° D DEFG is a kite. Angle GDF = 69° Angle EFD = 33° Calculate the size of angle DGF. (RE 3) 69° 21° G E 57° Angle DGF = 21 + 57 = 78° 33° 33° F 2004 P1 Q7**2004 General Paper 2 Question 5** 1 mark R Q 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) R Q P O Pythagoras 12 cm 5.5 cm PQ² = 12² + 5.5² 1 mark PQ² = 144 + 30.25 PQ² = 174.25 PQ = 174.25 = 13.2 1 mark Asked for Radius, so 13.2 ÷ 2 = 6.6 cm 1 mark 2004 P2 Q5**2003 General Paper 1 Question 10**140º D O E 70° C A B DBO = 20º 1 mark As OBA is right-angled (radius meets a tangent) 20º 20º BDO = 20º Triangle BDO is isosceles DOB = 140º 1 mark (180 –20-20) • The diagram is • a circle, centre O, • a tangent AC to the circle at B • an angle DBA, which is 70°. • Calculate the size of shaded angle BOE. (3 RE) EOB = 40º 1 mark (180 –140) 2003 P1 Q10**2005 General Paper 1 Question 3**4 x 1 = 4, so need +1 = 5 4 x 2 = 8, so need +1 = 9 etc. m = 4 x 13 + 1 m = 52 + 1 m = 53 m = 4s + 1 61 = 4s + 1 4s = 61 – 1 4s = 60 s = 60 ÷ 4 s = 15 4 4 4 Sandra is working on the design for a bracelet. She is using matches to make each shape. Shape 1 Shape 3 Shape 4 Shape 2 • Draw shape 4. (1 RE) • Complete the table. (2 RE) • 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) 13 17 25 53 m = 4s + 1 s = 15 2005 P1 Q3**2002 General Paper 2 Question 4**7x12 + 1 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. 15 85 29 + 7 + 7 + 7 • Find a formula connecting the number of iron bars (b) with the number of sections (s) b = 7s + 1 (7x1=7=8) +1 (c) A fence has been made by joining 176 iron bars. How many sections will this make? 176 = 7s + 1 175 = 7s s = 25 2002 P2 Q4**2003 General Paper 2 Question 12**5 km HYP 7° Airport 5 OPP x 7° ADJ 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. Trigonometry SOH CAH TOA 2003 P2 Q12**2002 General Paper 2 Question 6**HYP OPP ADJ PQRS is a rhombus. Its diagonals PR and SQ are 20 cm and 12 cm long respectively. Calculate the size of the shaded angle PQR. Do not use a scale drawing. (RE 4) P Trigonometry SOH CAH TOA 20 cm Q S 10 cm x 6 cm R 12 cm 2002 P2 Q6**2004 General Paper 2 Question 8**2.2 m 1.5 m The floor of a conservatory consists of a rectangle and a semi-circle. The floor has the shape shown below. Measurements are in metres. Area1 (Rectangle) = lb A = 2.2 x 1.5 A = 3.3 m² Area2 (semi-circle) = ½ pr² 1 A = ½ x 3.14 x 1.1² A = 1.8997 m² 2 D = 2.2m, so r = 1.1m Total Area = 3.3 + 1.8997 = 5.1997 = 5.2 m² Find the total area of the floor. (4 KU) 2004 P2 Q8**2004 General Paper 2 Question 12**The 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) = 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**7 cm P Q OPP HYP 4 cm S R 10 cm ADJ 4 cm x 3 cm 10 - 7 Trigonometry SOH CAH TOA 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. 2004 P2 Q6**200 General Paper Question**200 P Q**200 General Paper Question**200 P Q