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

Transcription

1 N5 M thematics Natinal 5 Practice Paper D 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. Find the gradient f the straight line jining pints A(3, -7) and B(-5, 3) Evaluate 3 5 f Find the equatin f the straight line AB. 3

4 4. The marks scred by a grup f students in their Octber test are listed belw (a) Calculate: (i) The median mark; (ii) The semi-interquartile range fr the data. 2 The teacher arranges extra revisin classes fr the students befre their next test in December. In this test the median mark is 67 and the semi-interquartile range is 7. (b) Make tw apprpriate cmments cmparing the marks in the Octber and December tests Marmalade is n special ffer. Each jar n special ffer cntains 12.5% mre than the standard jar. A jar n special ffer cntains 450 g f marmalade. Hw much des the standard jar cntain? 3

5 6. The diagram shws a square based pyramid. Express in terms f and William Watsn Fast Fds use a lg based n parts f three identical parablas. The lg is represented n the diagram belw. The first parabla has turning pint P and equatin = (a) State the crdinates f P. 2 (b) If R is the pint (2,0), find the crdinates f Q, the minimum turning pint f the secnd parabla. 1 (c) Find the equatin f the parabla with turning pint S. 2

6 3 8. Write as a single fractin in its simplest frm. 3 m + 4 m Part f the graph f = cs is shwn in the diagram. State the values f and Evaluate Express as a surd in its simplest frm. 3

7 12. A piece f gld wire 10 centimetres lng is made int a circle. The circumference f the circle is equal t the length f the wire. Shw that the area f the circle is exactly 2 square centimetres Tw variables and are cnnected by the relatinship = +. Sketch a pssible graph f against t illustrate this relatinship when and are bth less than zer. 3 [End f questin paper]

8 N5 M thematics Natinal 5 Practice Paper D 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.

9 Q1. The average Scttish huse price is The average price is expected t rise by 2.5% per mnth. What will the average Scttish huse price be in 3 mnths? Give yur answer crrect t three significant figures. 3 Q2. The heights, in millimetres, f six seedlings are given belw (a) Calculate: (i) the mean; 1 (ii) the standard deviatin; 3 f these heights. Shw clearly all yur wrking. (b) Later the same six seedlings are measured again. Each has grwn by 4 millimetres. State: (i) the mean; 1 (ii) the standard deviatin; 1 f these new heights. Q3. Slve algebraically the equatin 4 sin + 1 =

10 Q4. A sprts centre charges different entrance fees fr adults and children. (a) One evening 14 adults and 4 children visited the sprts centre. The ttal cllected in entrance fees was Let punds be the adult entrance fee and punds be the child s entrance fee. Write dwn an equatin in and t describe the abve infrmatin. 1 (b) The fllwing evening 13 adults and 6 children visited the sprts centre. The ttal cllected in entrance fees was Write dwn a secnd equatin in and. 1 (c) Calculate the entrance fee fr an adult and the entrance fee fr a child. 4 Q5. The diagram belw shws part f a parabla with equatin f the frm = (a) Write dwn the equatin f the axis f symmetry f the graph. 1 (b) Write dwn the equatin f the parabla. 2 (c) Find the crdinates f C. 2

11 Q6. A garden, in the shape f a quadrilateral, is represented in the diagram. Calculate: (a) (b) the length f the diagnal BD; D nt use a scale drawing. 3 the area f the garden. Q7. The curved part f a drway is an arc f a circle with radius 500 millimetres and centre C. The height f the drway t the tp f the arc is 2000 millimetres. The vertical edge f the drway is 1800 millimetres. Calculate the width f the drway. 5

12 Q8. Find the values f such that the equatin = 0 has equal rts. 4 Q9. A gift bx, 8 centimetres high, is prism shaped. The unifrm crss-sectin is a regular pentagn. Each vertex f the pentagn is 10 centimetres frm the centre O. Calculate the vlume f the bx. 5 Q10. Express 4 3, x 3, x 0, x 3 x as a fractin in its simplest frm. 3

13 Q11. A rectangular lawn has a path, 1 metre wide, n 3 sides as shwn. The breadth f the lawn is metres. The length f the lawn is three times its breadth. The area f the lawn equals the area f the path. (a) Shw that = 0. 3 (b) Hence find the length f the lawn. 4 [End f questin paper]