# National Quali cations SPECIMEN ONLY. Forename(s) Surname Number of seat. Date of birth Day Month Year Scottish candidate number

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1 N5 SQ9/N5/0 Date Not applicable Duration hour FOR OFFICIAL USE National Quali cations SPECIMEN ONLY Mark Mathematics Paper (Non-Calculator) *SQ9N50* Fill in these boxes and read what is printed below. Full name of centre Town Forename(s) Surname Number of seat Date of birth Day Month Year Scottish candidate number D D M M Y Y Total marks 40 You may NOT use a calculator. Attempt ALL questions. Use blue or black ink. Pencil may be used for graphs and diagrams only. Write your working and answers in the spaces provided. Additional space for answers is provided at the end of this booklet. If you use this space, write clearly the number of the question you are attempting. Square-ruled paper is provided at the back of this booklet. Full credit will be given only to solutions which contain appropriate working. State the units for your answer where appropriate. Before leaving the examination room you must give this booklet to the Invigilator. If you do not, you may lose all the marks for this paper. *SQ9N500*

2 FORMULAE LIST The roots of ax + bx + c = 0 are b± ( b 4ac) x = a Sine rule: a b c = = sina sin B sin C Cosine rule: a b c bc A A b c a + = + cos or cos = bc Area of a triangle: A= absin C Volume of a sphere: V = 4 πr Volume of a cone: V = πr h Volume of a pyramid: V = Ah Standard deviation: s = Σ( x x) Σx ( Σx) n =, n n where n isthe sample size. *SQ9N500* Page two

3 . Evaluate MARKS DO NOT WRITE IN THIS MARGIN. Multiply out the brackets and collect like terms ( x+ )( x 4x + ).. Two forces acting on a rocket are represented by vectors u and v. 7 u = and v = 5 4. Calculate u + v, the magnitude of the resultant force. Express your answer as a surd in its simplest form. *SQ9N500* Page three

4 4. Solve the equation x + 7x 5 = 0. MARKS DO NOT WRITE IN THIS MARGIN 5. Express 4 6 with a rational denominator in its simplest form. *SQ9N5004* Page four

5 6. Teams in a quiz answer questions on film and sport. This scattergraph shows the scores of some of the teams. MARKS DO NOT WRITE IN THIS MARGIN 5 y Sport Score 0 7 Film Score x A line of best fit is drawn as shown. (a) Find the equation of this straight line. (b) Use this equation to estimate the sports score for a team with a film score of 8. Total marks 4 *SQ9N5005* Page five

6 7. (a) Multiply out the brackets and simplify: x x + x. MARKS DO NOT WRITE IN THIS MARGIN (b) Find the exact value of this expression when x = 6. Total marks mv 8. Change the subject of the formula p = to v. *SQ9N5006* Page six

7 9. A parabola has equation y = x 8x + 9. (a) Write the equation in the form y = ( x p) + q. MARKS DO NOT WRITE IN THIS MARGIN (b) Sketch the graph of y = x 8x + 9, showing the coordinates of the turning point and the point of intersection with the y-axis. Total marks 5 *SQ9N5007* Page seven

8 MARKS 0. Brian and Bob visit a ski resort. Brian buys full passes and 4 restricted passes. The total cost of his passes is 85. DO NOT WRITE IN THIS MARGIN (a) Write down an equation to illustrate this information. (b) Bob buys full passes and restricted passes. The total cost of his passes is 0. Write down an equation to illustrate this information. (c) Find the cost of a restricted pass and the cost of a full pass. Total marks 5. Express 4 x x 4 x+,, x 4 as a single fraction in its simplest form. *SQ9N5008* Page eight

9 . A cylindrical pipe has water in it as shown. MARKS DO NOT WRITE IN THIS MARGIN x O A B 8 cm The depth of the water at the deepest point is 5 centimetres. The width of the water surface, AB, is 8 centimetres. The radius of the pipe is r centimetres. The distance from the centre, O, of the pipe to the water surface is x centimetres. (a) Write down an expression for x in terms of r. (b) Calculate r, the radius of the pipe. Total Marks 4 [END OF SPECIMEN QUESTION PAPER] *SQ9N5009* Page nine

12 *SQ9N50* Page twelve

13 N5 National Quali cations SPECIMEN ONLY SQ9/N5/0 Marking Instructions Mathematics Paper (Non-Calculator) These Marking Instructions have been provided to show how SQA would mark this Specimen Question Paper. The information in this publication may be reproduced to support SQA qualifications only on a non-commercial basis. If it is to be used for any other purpose, written permission must be obtained from SQA s Marketing team on marketing@sqa.org.uk. Where the publication includes materials from sources other than SQA (ie secondary copyright), this material should only be reproduced for the purposes of examination or assessment. If it needs to be reproduced for any other purpose it is the user s responsibility to obtain the necessary copyright clearance.

14 Part One: General Marking Principles for National 5 Mathematics This information is provided to help you understand the general principles you must apply when marking candidate responses to questions in this Paper. These principles must be read in conjunction with the specific Marking Instructions for each question. The marking schemes are written to assist in determining the minimal acceptable answer rather than listing every possible correct and incorrect answer. (a) (b) (c) (d) (e) (f) (g) (h) Marks for each candidate response must always be assigned in line with these general marking principles and the specific Marking Instructions for the relevant question. Marking should always be positive, ie marks should be awarded for what is correct and not deducted for errors or omissions. Credit must be assigned in accordance with the specific assessment guidelines. Candidates may use any mathematically correct method to answer questions except in cases where a particular method is specified or excluded. Working subsequent to an error must be followed through, with possible credit for the subsequent working, provided that the level of difficulty involved is approximately similar. Where, subsequent to an error, the working is easier, candidates lose the opportunity to gain credit. Where transcription errors occur, candidates would normally lose the opportunity to gain a processing mark. Scored out or erased working which has not been replaced should be marked where still legible. However, if the scored out or erased working has been replaced, only the work which has not been scored out should be judged. Unless specifically mentioned in the specific assessment guidelines, do not penalise: Working subsequent to a correct answer Correct working in the wrong part of a question Legitimate variations in solutions Bad form Repeated error within a question Page

15 Part Two: Specific Marking Instructions for each question Question Marking scheme Give one mark for each Ans: 7 5 Max Mark Illustrations of evidence for awarding a mark at each start simplification and know how to divide fractions consistent answer or 8 5 Ans: x 5 x 0 x + three terms correct eg x 8 x + x remaining terms correct collect like terms eg x x + x 5 x 0 x + Ans: 7 add vectors correctly 9 4 find magnitude express as surd in simplest form Ans: x = 5, x = 5 one correct factor correct factorisation solve equation x + 5 or x (x + 5)( x ) x = 5, x = 5 Page

16 5 Ans: 6 know how to rationalise denominator consistent answer 6 6 a Ans: y = x + find gradient substitute gradient and (,) or (7,5) into y b = m(x a) or y = mx + c m = eg y = (x ) or = + c state equation of line in simplest form y = x + or x y + = 0 or equivalent 6 b Ans: 8 + = 7 use equation to calculate sports score 8 + = 7 7 a Ans: x + x 0 or equivalent multiply x / x / correctly x multiply x / x / correctly x 0 or 7 b Ans: 6 find exact value of expression 6 or Ans: v = p m multiply by mv = p divide by m p v = m square root p v = m Page 4

17 9 a Ans: y = (x 4) + p correct q correct y = (x 4) y = (x 4) + 9 b Ans: insert correct diagram correct shape and position parabola with minimum turning point in first quadrant coordinates of y-intercept shown coordinates of turning point shown (0,9) (4,) 0 a Ans: f + 4 r = 85 construct equation f + 4 r = 85 0 b Ans: f + r = 0 construct equation f + r = 0 0 c Ans: restricted pass costs 0 full pass costs 5 evidence of scaling calculate r or f communicate answer 6 f + 8 r = 70 6 f + 9 r = 90 r = 0 or f = 5 restricted pass costs 0 full pass costs 5 Ans: x ( x+ )( x 4) correct common denominator ( x+ )( x 4 ) correct numerator 4( x 4) ( x+ ) simplify x ( x+ )( x 4) Page 5

18 a Ans: r 5 state expression r 5 b Ans: 0 6 cm correct use of Pythagoras theorem expand bracket solve equation r = (r 5) + 9 r = r 0 r r = 0 6 Total Marks for Paper 40 [END OF SPECIMEN MARKING INSTRUCTIONS] Page 6

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