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.
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
1. Evaluate 1 2 1 3. 2 2. Evaluate 1 1 3 4 2 3. Slve the inequality 2 + 1 3 4. Given that = 2 +, evaluate 3. 2 5. Vectr 3 has cmpnents ( 2 ) and vectr 2 has cmpnents ( 4 ). 1 1 Calculate 4 2. 2 6. (a) Factrise 2 4 2. 1 p (b) Hence simplify 2 4q 2. 3p + 6q 2
7. Find the equatin f the straight line shwn in the diagram. Give yur answer in the frm = +. 3 8. Part f the graph f = cs is shwn abve. If cs 60 = 0, state tw values fr fr which cs = 0 0 360. 2 9. Multiply ut the brackets and cllect like terms. 3 2 + 4 1 3
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. 4 5 4 1 4 3 2 2 4 6 2 3 4 4 1 3 1 2 3 1 1 (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. 1 11. Tw functins are given belw. = 2 + 2 1 = + 3 Find the values f fr which =. 3 12. Express in its simplest frm y 8 y 3 2 2
13. y x The equatin f the parabla in the abve diagram is = 1 2 16. (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. 1 14. (a) Express 4 2 as a surd in its simplest frm. 2 (b) Express as a fractin in its simplest frm 1 x 2 + 1 x x 0 2 [End f questin paper]
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.
1. A spider weighs apprximately 1 06 10 kilgrams. A humming bird is 18 times heavier. Calculate the weight f the humming bird. Give yur answer in scientific ntatin. 2 2. A micrwave ven is sld fr 150. This price includes VAT at 20%. Calculate the price f the micrwave ven withut VAT. 3 3. (a) The price, in pence, f a cartn f milk in six different supermarkets is shwn belw. 66 70 89 75 79 59 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
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. 4 5. 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
6. Slve the equatin 2 2 + 3 1 = 0 Give yur answers crrect t ne decimal place. 4 7. 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
8. The ppulatin f Newtwn is 50 000. The ppulatin f Newtwn is increasing at a steady rate f 5% per annum. The ppulatin f Auldtwn is 108 000. 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. 5 10. Change the subject f the frmula t. = 3 2 2
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? 4 12. 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]