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

Transcription

1 N5 M thematics Natinal 5 Practice Paper E 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 f Multiply ut the brackets and cllect like terms In an experiment invlving tw variables, the fllwing values fr and were recrded The results were pltted and a straight line was drawn thrugh the pints. Find the gradient f the line and write dwn its equatin Slve the equatin 2 x + 9 = Given = 0 shw that x = 1 ± 3 2 4

4 6. The diagram belw shws part f the graph f = (a) State the crdinates f the maximum turning pint. 2 (b) State the equatin f the axis f symmetry. 1 The line = 20 is drawn. It cuts the graph f = at R and S as shwn belw. (c) S is the pint (6, 20). Find the crdinates f R. 2

5 7. A badge is made frm a circle f radius 5 centimetres. Segments are taken ff the tp and bttm f the circle as shwn. The straight edges are parallel. The badge measures 7 centimetres frm the tp t the bttm. The tp is 8 centimetres wide. Calculate the width f the base Sketch the graph f = sin = (a) Find the value f 2 as a surd in its simplest frm. 3 (b) Find the value f given that =

6 10. The height f a triangle is 2 centimetres and the base is 2 centimetres. The area f the triangle is 7 square centimetres. Calculate the value f 5 [End f questin paper]

7 N5 M thematics Natinal 5 Practice Paper E 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 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

9 1. = 2. Find the value f when = and = 3 10 Give yur answer in scientific ntatin Calculate the area f triangle PQR In the evening, the temperature in a greenhuse drps by 10.4% per hur. At 8 p.m. the temperature was 28 Celsius. Find the temperature at 11 p.m. 3

10 4. Relative t crdinate axes, the pint A has crdinates (2, 4, 6). (a) Find the crdinates f C and D. 2 (b) Write dwn the crdinates f B Shamp is available in travel size and saln size bttles. The bttles are mathematically similar. The travel size cntains 200 millilitres and is 12 centimetres in height. The saln size cntains 1600 millilitres. Calculate the height f the saln size bttle. 3

11 6. A jeweller uses tw different arrangements f bead and pearls. The first arrangement cnsists f 2 beads and 5 pearls and has an verall length f 5.2 centimetres. The secnd arrangement cnsists f 3 beads and 2 pearls and has an verall length f 5.6 centimetres. Find the length f ne bead and the length f ne pearl A pharmaceutical cmpany makes vitamin pills in the shape f spheres f radius 0.5 centimetres. (a) Calculate the vlume f ne pill. 3 Give yur answer t 3 significant figures. The cmpany decides t change the shape f each pill t a cylinder. The new pill has the same vlume as the riginal and its diameter is 1.4 centimetres. (b) Calculate the height f the new pill. 3

12 8. David walks n a bearing f 050 frm hstel A t viewpint V, 5 kilmetres away. Hstel B is due east f hstel A. Susie walks n a bearing f 294 frm hstel B t the same viewpint. N V 50 5 km A B Calculate the length f AB, the distance between the tw hstels The chain f a demlitin ball is 12.5 metres lng. When vertical, the end f the chain is 1.5 metres frm the grund. It swings t a maximum height f 2.5 metres abve the grund n bth sides. (a) At this maximum height, shw that the angle which the chain makes with the vertical, is apprximately (b) Calculate the maximum length f the arc thrugh which the end f the chain swings. Give yur answer t 3 significant figures. 4

13 10. Find the range f values f such that the equatin = 0 0 has real rts (a) Slve algebraically the equatin 3 sin 1 = (b) Simplify n cs 2 [End f questin paper]