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General Past Paper By topic By year General Past Paper Contents By Year 2001 P1 Q2 2002 P2 Q4 2002 P2 Q6 2003 P1 Q10 2003 P2 Q2 2003 P2 Q3 2003 P2 Q12 2003 P2 Q13 2004 P1 Q7 2004 P2 Q3 2004 P2 Q5 2004 P2 Q6 2004 P2 Q8 2004 P2 Q12 2005 P1 Q3 2005 P2 Q4 2005 P2 Q11 2005 P2 Q12 2006 P2 Q7 General Past Paper Contents By Topic Angles in a Kite Angles in a circle Area – composite Distance, Speed & Time Mean from a Frequency Table Formula – using Pattern & Formula 1 Pattern & Formula 2 Percentage Perimeter(Circumference) Pythagoras Pythagoras & Area Pythagoras & Circle Trigonometry 1 Trigonometry 2 Trigonometry 3 Trigonometry 4 Volume Wages 2005 General Paper 2 Question 12 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. Fan belt 30 cm 8 cm Calculate the total length of the fan belt. C = pd 30 cm 8 cm C = 3.14 x 8 1 mark C = 25.12cm 1 mark 30 cm Total = 25.12 + 30 + 30 1 mark (RE 4) Total = 85.12 cm 1 mark 2005 P2 Q12 2003 General Paper 2 Question 13 20m A large advertising banner is hanging from a building. 26m 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. 10m A=½xbxh b = 20 m h=? h 26m h² = 26² - 10² h² = 676 - 100 h² = 576 h = 576 h = 24 A=½xbxh A = ½ x 20 x 24 A = 240 cm² 2003 P2 Q13 2005 General Paper 2 Question 11 35cm A C Ye Olde Shoppe 90cm OPP 35 HYP x 90 ADJ Trigonometry SOH CAH TOA B 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. Tan (angle) = OPP/ADJ Tan x = 35/ 90 1 mark x = tan-1(35÷90) 1 mark 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. FORMULAE sheet (Circumference circle) (Area circle) 3 cm (CSA of cylinder) (Volume cylinder) (Volume prism) C A A V V = = = = = pD pr² 2prh pr²h Ah 25 cm Find the VOLUME of the three-dimensional shape formed by this net. (RE 3) V = pr²h V = 3.14 x 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? Adult fare = 100% (RE 3) Student fare = 60% of the adult fare 60 % = £24 1 % = £24 ÷ 60 = £0.40 100 % = £0.40 x 100 = £40 1 mark 1 mark 1 mark 2001 P1 Q2 2003 General Paper 2 Question 3 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 1 2 3 4 5 6 7 8 5 12 18 26 18 11 7 3 Number of letters x frequency 1x5= 5 2 x 12 = 24 3 x 18 = 54 4 x 26 = 104 5 x 18 = 90 6 x 11 = 66 7 x 7 = 49 8 x 3 = 24 Total = 100 Total = 416 Find the mean number of letters per word, to 1 decimal place. (KU 4) Mean = 416 100 = 4.16 = 4.2 2003 P2 Q3 2003 General Paper 2 Question 2 Alice Anderson has a part-time Overtime: 6.50 x 1.5 job in a call centre. = £9.75 per hour 1 mark Her basic rate of pay is £6.50 4 x £9.75 = £39 1 mark 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. £136.50 - £39 = £97.50 1 mark £97.50 ÷ 6.50 How many hours did she work = 15 hours 1 mark at the basic rate? (RE 4) 2003 P2 Q2 2005 General Paper 2 Question 4 The diagram below shows the shape of Sangita’s garden. Sangita plants a hedge along side AB. 13 m B 7m x 8m A Calculate the length of the hedge. (RE 4) 13m5m – 8m 7m x Pythagoras x² = 7² + 5² x² = 49 + 25 x² = 74 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 T = 80 ÷ 60 T = 1.3333…. hrs Difference = 1 hr 30 – 1 hr 20 Difference = 10 minutes 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 D DEFG is a kite. Angle GDF = 69° 69° Angle EFD = 33° Calculate the size of angle DGF. (RE 3) G 21° E 57° 69° 180 – (90+33) = 57° Angle DGF = 21 + 57 180 – (90+69) = 11° = 78° 33° 33° 33° F 2004 P1 Q7 2004 General Paper 2 Question 5 PQ is a diameter of the circle with centre O. R P Q O 1 mark R is a point on the circumference of the circle. PR is 12 cm, RQ is 5.5 cm. R Calculate the length of the radius of the circle. (RE 4) Pythagoras 5.5 cm PQ² = 12² + 5.5² PQ² = 144 + 30.25 Q P PQ² = 174.25 PQ = 174.25 = 13.2 Asked for Radius, so 13.2 ÷ 2 = 6.6 cm 1 mark 12 cm 1 mark 1 mark 2004 P2 Q5 2003 General Paper 1 Question 10 DBO = 20º D 20º O 20º A 140º E 70° B The diagram is a circle, centre O, a tangent AC to the circle at B an angle DBA, which is 70°. 1 mark As OBA is right-angled (radius meets a tangent) BDO = 20º C Triangle BDO is isosceles DOB = 140º 1 mark (180 –20-20) EOB = 40º (180 –140) Calculate the size of shaded angle BOE. 1 mark (3 RE) 2003 P1 Q10 2005 General Paper 1 Question 3 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 m = 4 x 13 + 1 m = 52 + 1 m = 53 (1 RE) (a) Draw shape 4. (b) Complete the table. Shape number (s) (2 RE) 1 2 3 4 5 6 13 m = 4s ofneed matches (m) 5 4 9 4 13 4 17 21 + 125 53 4Number x 1 = 4, so +1 = 5 61 = 4s + 1 4 x 2 = 8, so need +1 = 9 (c) Find a formula for calculating the number of 4s matches, = 61 – 1(m), when you etc. m = 4s 4s= 60 +1 know the number of shapes, (s). (2 RE) (d) Which shape number uses 61 matches? s = 60 4 (2 RE) s =÷ 15 s = 15 2005 P1 Q3 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 7x12 + 1 (a) Copy and complete this table. Number of sections (s) 1 2 3 4 12 15 22 29 85 7 7 +bars + 7of+iron (b) Find a formula connecting the number (b) with the Number of iron bars (b) number of sections (s) 8 b = 7s + 1 (7x1=7 +1=8) (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 Airport 7° HYP 5 OPP 7° An aircraft is approaching Glasgow ADJ Airport. Trigonometry O O A The angle of elevation of the S HC HT A aircraft from the airport is 7°. opp The aircraft is a distance of 5 km sin (angle) hyp from the airport. x o sin 7 Find the height of the aircraft to 5 the nearest metre. (KU 4) x sin 7o 5 Do not use a scale drawing. x 0.6093..km 609m x 2003 P2 Q12 2002 General Paper 2 Question 6 PQRS is a rhombus. Its diagonals PR and SQ are 20 cm and 12 cm long respectively. Calculate the size of the shaded P angle PQR. Do not use a scale drawing. (RE 4) 20 cm Q 10 cm OPP S HYP x 6 cm ADJ R 12 cm Trigonometry O O A S HC HT A opp tan (angle) adj 10 o tan x 6 1 x tan (10 6) x 59o PQR 59o 2 118o 2002 P2 Q6 2004 General Paper 2 Question 8 The floor of a conservatory consists of a rectangle and a semi-circle. The floor has the shape shown below. Measurements are in metres. 2.2 m 1.5 m Area1 (Rectangle) = lb A = 2.2 x 1.5 A = 3.3 m² Area2 (semi-circle) = ½ pr² A = ½ x 3.14 x 1.1² A = 1.8997 m² D = 2.2m, so r = 1.1m Find the total area of the floor. (4 KU) Total Area = 3.3 + 1.8997 = 5.1997 = 5.2 m² 2004 P2 Q8 2004 General Paper 2 Question 12 The current, C amps, of an electrical appliance is calculated using the formula C P 240 , where P watts is the power rating. • 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. 850 C 240 (RE 3) = 3.541666……. You would choose the 5 amp fuse. The 3 amp is too small 2004 P2 Q12 and 13 amp is too big. 2004 General Paper 2 Question 6 P 7 cm Q HYP 4 cm S 10 cm R 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. OPP 4 cm x 3 cm 10 - 7 ADJ Trigonometry O O A S HC HT A opp tan (angle) adj 4 o tan x 3 1 x tan (4 3) x 55.1o PSR 55.1o 2004 P2 Q6 200 General Paper Question 200 P Q 200 General Paper Question 200 P Q