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

Transcription

1 N5 M thematics Natinal 5 Practice Paper C 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: Csine rule: a sin A = b sin B = c sin C 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 x x 2 Standard deviatin: s = =, where is the sample size. n 1 x 2 n 1 x 2 /n

3 1. Evaluate Evaluate Simplify = 4 (a) Evaluate 2 1 (b) Given that =, find Slve, by factrising + 2 = 0. 3

4 6. A htel bks taxis frm a cmpany called Quick-Cars. The receptinist ntes the waiting time fr every taxi rdered ver a perid f tw weeks. These times, in minutes, are shwn belw (a) Fr the given data, calculate: (i) the median 1 (ii) the lwer quartile 1 (iii) the upper quartile 1 (b) Calculate the interquartile range. 1 In anther tw week perid, the htel bks taxis frm a cmpany called Fast-Cabs. The median waiting time fr Fast-Cabs is fund t be 27.5 minutes and the interquartile range fr Fast-Cabs is fund t be 5 minutes. (c) Use this infrmatin t cmpare the tw cmpanies Part f the graph f = sin + is shwn in the diagram. y O x State the values f and. 2

5 8. In the diagram belw, A is the pint 1 and B is the pint 4 3. (a) Find the gradient f the line AB. 1 (b) AB cuts the -axis at the pint 0. Write dwn the equatin f the line AB. 2 (c) The pint 3 lies n AB. Find the value f = 2 + (a) Write in the frm (b) State the crdinates f the turning pint f. 1

6 10. Andrew and Daisy each bk in at the Sleepwell Ldge. (a) (b) Andrew stays fr 3 nights and has breakfast n 2 mrnings. His bill is 145. Write dwn an algebraic equatin t illustrate this infrmatin. 1 Daisy stays fr 5 nights and has breakfast n 3 mrnings. Her bill is 240. Write dwn an algebraic equatin t illustrate this infrmatin. 1 (c) Find the cst f ne breakfast (a) Evaluate 2 24 (b) Simplify 2 2 2x + 2 (c) Simplify 2 x [End f questin paper]

7 N5 M thematics Natinal 5 Practice Paper C 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. Bacteria in a test-tube increase at the rate f 4.6% per hur. At 12 nn, there are bacteria. At 5 pm, hw many bacteria will be present? Give yur answer crrect t 3 significant figures The tangent, MN, tuches the circle, centre O, at L. Angle JLN = 47 Angle KPL = 31 Find the size f angle JLK Change the subject f the frmula = 3 + t. 3

9 4. A mug is in the shape f a cylinder with diameter 10 centimetres and height 14 centimetres. (a) Calculate the capacity f the mug. 2 (b) 600 millilitres f cffee are pured in. Calculate the depth f the cffee in the mug The diagram belw shws a big wheel at the fairgrund. The wheel has 16 chairs equally spaced n its circumference. The radius f the wheel is 9 metres. As the wheel rtates in an anticlckwise directin, find the distance a chair travels in mving frm psitin T t psitin P in the diagram. 4

10 6. Find the rts f the equatin = 0. Give yur answers crrect t ne decimal place Tw perfume bttles are mathematically similar in shape. The smaller ne is 6 centimetres high and hlds 30 millilitres f perfume. The larger ne is 9 centimetres high. What vlume f perfume will the larger ne hld? 3 8. Determine the nature f the rts f the equatin 2 2 = 0. 4

11 9. A pny shelter is part f a cylinder as shwn in figure 1. It is 6 metres wide and 2 metres high. The crss-sectin f the shelter is a segment f a circle with centre O, as shwn in figure 2. OB is the radius f the circle. Calculate the length f OB The diagram shws a parallelgram, PQRS. (a) Calculate the size f angle PQR. D nt use a scale drawing. 3 (b) Calculate the area f the parallelgram. 3

12 11. (a) Slve the equatin 2 n + = (b) Prve that sin 3 + sin cs 2 = sin (a) A driver travels frm A t B, a distance f miles, at a cnstant speed f 75 kilmetres per hur. Find the time taken fr this jurney in terms f 1 (b) The time taken fr the jurney frm B t A is hurs. Calculate the average speed fr the whle jurney. 4 [End f questin paper]