M thematics. National 5 Practice Paper B. Paper 1. Duration 1 hour. Total marks 40

Transcription

1 M thematics Natinal 5 Practice Paper B Paper 1 Duratin 1 hur Ttal marks 40 Yu may NOT use a calculatr Attempt all the questins. Use blue r black ink. Full credit will nly be given t slutins which cntain apprpriate wrking. State the units fr yur answer where apprpriate.

2 FORMULAE LIST The rts f are ax 2 + bx + c = 0 x = b ± b2 4ac 2a Sine rule: a sin A = b sin B = c sin C Csine rule: a 2 = b 2 + c 2 2bc cs A r cs A = b2 + c 2 a 2 2bc Area f a triangle: A = 1 ab sin C 2 Vlume f a Sphere: V = 4 3 πr3 Vlume f a cne: V = 1 3 πr2 h Vlume f a pyramid: V = 1 3 Ah Standard deviatin: x x 2 x s = = 2 x 2 /n, where is the sample size. n 1 n 1

3 1. Evaluate Evaluate Slve the inequality Given that = 2 +, evaluate Vectr 3 has cmpnents ( 2 ) and vectr 2 has cmpnents ( 4 ). 1 1 Calculate (a) Factrise p (b) Hence simplify 2 4q 2. 3p + 6q 2

4 7. Find the equatin f the straight line shwn in the diagram. Give yur answer in the frm = Part f the graph f = cs is shwn abve. If cs 60 = 0, state tw values fr fr which cs = Multiply ut the brackets and cllect like terms

5 10. A sample f students was asked hw many times each had visited the cinema in the last three mnths. The results are shwn belw (a) Frm the abve data, find the median, the lwer quartile and the upper quartile. 3 (b) Cnstruct a bxplt fr the data. 2 (c) The same sample f students was asked hw many times each had attended a ftball match in the same three mnths. The bxplt belw was drawn fr this data. Cmpare the tw bxplts and cmment Tw functins are given belw. = = + 3 Find the values f fr which = Express in its simplest frm y 8 y 3 2 2

6 13. y x The equatin f the parabla in the abve diagram is = (a) State the crdinates f the minimum turning pint f the parabla. 2 (b) State the equatin f the axis f symmetry f the parabla (a) Express 4 2 as a surd in its simplest frm. 2 (b) Express as a fractin in its simplest frm 1 x x x 0 2 [End f questin paper]

7 M thematics Natinal 5 Practice Paper B Paper 2 Duratin 1 hur and 30 minutes Ttal marks 50 Yu may use a calculatr Attempt all the questins. Use blue r black ink. Full credit will nly be given t slutins which cntain apprpriate wrking. State the units fr yur answer where apprpriate.

8 1. A spider weighs apprximately kilgrams. A humming bird is 18 times heavier. Calculate the weight f the humming bird. Give yur answer in scientific ntatin A micrwave ven is sld fr 150. This price includes VAT at 20%. Calculate the price f the micrwave ven withut VAT (a) The price, in pence, f a cartn f milk in six different supermarkets is shwn belw Use an apprpriate frmula t calculate the mean and standard deviatin f these prices. Shw clearly all yur wrking. 4 (b) In six lcal shps, the mean price f a cartn f milk is 73 pence with a standard deviatin f 17.7 pence. Cmpare the supermarket prices with thse f the lcal shps. 2

9 4. A pendulum travels alng an arc f a circle, centre C. The length f the pendulum is 20 centimetres. The pendulum swings frm A t B. The length f the arc AB is 28.6 centimetres. Find the angle thrugh which the pendulum swings frm A t B A cntainer t hld chclates is in the shape f part f a cne with dimensins as shwn belw. Calculate the vlume f the cntainer. Give yur answer crrect t ne significant figure. 5

10 6. Slve the equatin = 0 Give yur answers crrect t ne decimal place The diagram belw shws a circular crss-sectin f a cylindrical il tank. In the figure belw, O represents the centre f the circle. PQ represents the surface f the il in the tank. PQ is 3 metres. The radius OP is 2.5 metres. Find the depth, metres, f il in the tank. 4

11 8. The ppulatin f Newtwn is The ppulatin f Newtwn is increasing at a steady rate f 5% per annum. The ppulatin f Auldtwn is The ppulatin f Auldtwn is decreasing at a steady rate f 20% per annum. Hw many years will it take until the ppulatin f Newtwn is greater than the ppulatin f Auldtwn? 5 9. A TV signal is sent frm a transmitter (T) via a satellite (S) t a village (V), as shwn in the diagram. The village is 500 kilmetres frm the transmitter. The signal is sent ut at an angle f 3 angle f 40. and is received in the village at an Calculate the height f the satellite abve the grund Change the subject f the frmula t. = 3 2 2

12 11. Lk at the cubid shwn n the crdinate diagram. The crdinates f pint are 3 1 z D y E (a) State the crdinates f A O G C B F x (b) State the crdinates f (c) What is the shrtest distance between pints and? At the carnival, the height, metres, f a carriage n the big wheel abve the grund is given by the frmula = 10 + sin, secnds after starting t turn. (a) Find the height f the carriage abve the grund after 10 secnds. 2 (b) Find the tw times during the first turn f the wheel when the carriage is 12.5 metres abve the grund. 4 [End f questin paper]