FOR OFFICIAL USE

N5 National

MathematicsPaper 1

(Non-Calculator)

Fill in these boxes and read what is printed below.

Full name of centre Town

Forename(s) Surname Number of seat

Day Month Year Scottish candidate number

* X7 4 7 7 5 0 1 *

* X7 4 7 7 5 0 1 0 1 *

©

D D M M Y Y

MarkQuali  cations2014

Date of birth

TUESDAY, 06 MAY

9:00AM– 10:00 AM

Total marks— 40

Attempt ALL questions.

Write your answers clearly in the spaces provided in this booklet. Additional space for answersis provided at the end of this booklet. If you use this space you must clearly identify thequestion number you are attempting.

Use blue or black ink.

You may NOT use a calculator.

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 donot, you may lose all the marks for this paper.

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Page three

1. Evaluate 512

22×

9.

Give the answer in simplest form.

2. Multiply out the brackets and collect like terms:

(2 x -5) (3 x +1).

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PERFORMED WELL: Multiply a fraction by a mixed number. Most candidates multipliedcorrectly but some were unable to give the answer in its simplest form.

PERFORMED WELL Expand brackets.

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Page four

3. Express x 2 -14x + 44 in the form (x -a) 2 + b.

4. Find the resultant vector 2u -v when u =��

�

��

2�

�3��

5

and v = ��

�

��

0�

�4�.�

7

Express your answer in component form.

2

2

PERFORMED WELL Complete the square. Most candidates gave the correct value for a, butsome gave an incorrect value for b.

PERFORMED WELL: Using components to find the resultant of two three-dimensionalvectors.

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Page five

5. In triangle KLM

• KM = 18 centimetres

K

L

M

18 cm

• sin K = 0·4

• sin L = 0·9

Calculate the length of LM.

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DEMANDING: Sine Rule. A common error was to use sin0∙4 and sin0∙9 instead of 0∙4 and 0∙9.Many candidates were unable to work out

18´0 ×40 ×9

correctly.

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Page six

6. McGregor’s Burgers sells fast food.

The graph shows the relationship between the amount of fat, F grams, andthe number of calories, C, in some of their sandwiches.

Calories

0 Fat (grams) F

C

A

B

A line of best fit has been drawn.

Point A represents a sandwich which has 5 grams of fat and 200 calories.

Point B represents a sandwich which has 25 grams of fat and 500 calories.

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Page seven

6. (continued)

(a) Find the equation of the line of best fit in terms of F and C.

(b) A Super Deluxe sandwich contains 40 grams of fat.

Use your answer to part (a) to estimate the number of calories thissandwich contains.

Show your working.

Total marks

3

1

4

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DEMANDING(a): Equation of Straight Line. Most candidates found the correct gradient butsome did not know how to progress from there. Many did not gain the final mark becausethey did not give their final equation in terms of F and C and/or did not simplify it.

y=15x+125 was a common answer, which gained 2 of the 3 available marks.

DEMANDING(b): Calculate a value using the equation of straight line. A high number ofcandidates were unable to work out 15×40 correctly.

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THISMARGIN7. The diagram below shows part of the graph of y = ax2

y = ax2y

x0

(-3, 45)

Find the value of a. 2

Page eight

PERFORMED WELL: Find the value of a in the quadratic function y = ax2. Most candidatessubstituted correctly for x and y in the equation but some were unable to find the correct

value for a.

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THISMARGIN8. Express 40 + 4 10 + 90 as a surd in its simplest form.

9. 480 000 tickets were sold for a tennis tournament last year.

This represents 80% of all the available tickets.

Calculate the total number of tickets that were available for this tournament.

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PERFORMED WELL: Reverse use of percentage. Performance in this type of question isimproving. Most candidates scored full marks, but there were still a significant number

who simply worked out 80% of 480000 or 480000 plus 20% of 480000.

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THISMARGIN10. The graph of y = a sin (x + b)° , 0 < x < 360 , is shown below.

y

x

3

2

1

0

-1

-2

-3

20 40 60 80100

120140160180

200220

240

260280

300320340360

Write down the values of a and b. 2

Page ten

DEMANDING: Trigonometric graph. Some candidates gave the correct value for a, butvery few gave the correct value for b.

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THISMARGIN11. (a) A straight line has equation 4 x + 3 y = 12 .

Find the gradient of this line.

(b) Find the coordinates of the point where this line crosses the x-axis.

Total marks

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DEMANDING (a): Find the gradient of a straight line given its equation. Most candidatesstarted to rearrange the equation but didn’t divide by 3 correctly.

DEMANDING (b): Find the x-intercept of a straight line given its equation. A surprisingnumber of candidates did not know to substitute y=0 into the original equation. Manycandidates who did substitute y=0 were then either unable to solve the resulting equationcorrectly or left their answer as x=3 instead of giving the coordinates of the point where theline crossed the x-axis

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12. The diagram below shows a circle, centre C.

P

Q

A

C B

The radius of the circle is 15 centimetres.

A is the mid-point of chord PQ.

The length of AB is 27 centimetres.

Calculate the length of PQ. 4

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13. The diagram below shows the path of a small rocket which is fired into theair. The height, h metres, of the rocket after t seconds is given by

h(t) = 16t -t2

h

t0

(a) After how many seconds will the rocket first be at a height of 60 metres?

(b) Will the rocket reach a height of 70 metres?Justify your answer.

Total marks

[END OF QUESTION PAPER]

4

3

7

Page thirteen

DEMANDING: Quadratic Equation Problem. Most candidates scored few marks for thisquestion. Many candidates thought that h(t) meant 60t and started with 60t=16t-t2 leading to60=16-t leading to t=-44. Some candidates started with 60=16t-t2 but were unable to goany further. Few candidates gave a correct response. Successful responses tended to beusing trial and error methods as opposed to solving a quadratic equation.

DEMANDING: Quadratic Equation Problem. Few candidates used a suitable strategy orgave an appropriate justification for their answer. Very few realised the significance of theturning point. Some set up a quadratic equation but thought that because it wouldn'tfactorise it had no roots. Many candidates used a substitution method for both parts of thisquestion.

FOR OFFICIAL USE

N5 National

MathematicsPaper 2

Fill in these boxes and read what is printed below.

Full name of centre Town

Forename(s) Surname Number of seat

Day Month Year Scottish candidate number

* X7 4 7 7 5 0 2 *

* X7 4 7 7 5 0 2 0 1 *

©

D D M M Y Y

MarkQuali  cations2014

Date of birth

TUESDAY, 06 MAY

10:20AM–11:50 AM

Total marks— 50

Attempt ALL questions.

Write your answers clearly in the spaces provided in this booklet. Additional space for answersis provided at the end of this booklet. If you use this space you must clearly identify thequestion number you are attempting.

Use blue or black ink.

You may use a calculator.

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 donot, you may lose all the marks for this paper.

X747/75/02

PB

With

SQA

Cou

rse R

epor

t

Advi

ce

* X7 4 7 7 5 0 2 0 3 *

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Page three

1. There are 964 pupils on the roll of Aberleven High School.

It is forecast that the roll will decrease by 15% per year.

What will be the expected roll after 3 years?

Give your answer to the nearest ten.

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PERFORMED WELL Depreciation. Most candidates scored full marks but a significantnumber used an inefficient method.

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Page four

2. The diagram shows a cube placed on top of a cuboid, relative to thecoordinate axes.

Bz y

x0

C

A (8,4,6)

B

A is the point (8,4,6).

Write down the coordinates of B and C. 2

DEMANDING Three dimensional coordinates. This question proved to be challenging formany.

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Page five

3. Two groups of people go to a theatre.

Bill buys tickets for 5 adults and 3 children.

The total cost of his tickets is £158·25.

(a) Write down an equation to illustrate this information.

(b) Ben buys tickets for 3 adults and 2 children.

The total cost of his tickets is £98.

Write down an equation to illustrate this information.

(c) Calculate the cost of a ticket for an adult and the cost of a ticket for achild.

Total marks

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4

6

PERFORMED WELL: Construct and solve simultaneous equations. Most candidates scored fullmarks but some did not achieve the final mark in 3(c), which required them to correctlycommunicate the answer to the question. Some stopped when they got to a=22∙5 andc=15∙25, rather than continue to give an answer of eg an adult ticket cost £22∙50 and a childticket cost £15∙25.

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Page six

4. A runner has recorded her times, in seconds, for six different laps of a runningtrack.

53 57 58 60 55 56

(a) (i) Calculate the mean of these lap times.

Show clearly all your working.

(ii) Calculate the standard deviation of these lap times.

Show clearly all your working.

1

3

DEMANDING(b): Interpret Statistics. Although performance in this type of question isimproving, many candidates still do not understand that standard deviation is a measure ofconsistency.

PERFORMED WELL a): Calculate mean and standard deviation of a data set.

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Page seven

4. (continued)

(b) She changes her training routine hoping to improve her consistency.

After this change, she records her times for another six laps.

The mean is 55 seconds and the standard deviation 3·2 seconds.

Has the new training routine improved her consistency?

Give a reason for your answer.

Total marks

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Page eight

5. A supermarket sells cylindrical cookie jars which are mathematically similar.

COOKIES COOKIES15 cm

24 cm

The smaller jar has a height of 15 centimetres and a volume of 750 cubiccentimetres.

The larger jar has a height of 24 centimetres.

Calculate the volume of the larger jar. 3

PERFORMED WELL: Volumes of similar shapes. Nearly all candidates found the correct linearfactor; most then continued to calculate the correct answer, but some simply multiplied 750by the linear factor.

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Page nine

6. The diagram below shows the position of three towns.

Lowtown is due west of Midtown.

The distance from

• Lowtown to Midtown is 75 kilometres.

• Midtown to Hightown is 110 kilometres.

• Hightown to Lowtown is 85 kilometres.

Hightown

MidtownLowtown

85 km 110 km

75 km

Is Hightown directly north of Lowtown?

Justify your answer.

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PERFORMED WELL: Converse of Pythagoras’ Theorem: Most candidates scored three of fourmarks in this question. Where marks were dropped it was usually for poorly communicatedresponses, eg for not stating explicitly that 1102¹852+752, so the triangle is not right-angledetc.

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Page ten

7. An ornament is in the shape of a cone with diameter 8 centimetres and height15 centimetres.

The bottom contains a hemisphere made of copper with diameter7·4 centimetres. The rest is made of glass, as shown in the diagram below.

15 cm

glass

copper

7·4 cm

8 cm

Calculate the volume of the glass part of the ornament.

Give your answer correct to 2 significant figures. 5

PERFORMED WELL: Volume of a composite solid involving a cone and a hemisphere. Mostcandidates scored three or more marks in this question. Where marks were dropped it wasusually for incorrect rounding (the final answer was often rounded to two decimal placesrather than two significant figures), using an incorrect radius for the cone and/or thehemisphere, or finding the volume of the sphere and then not halving it.

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Page eleven

8. Simplify n nn

5

2

× 10

2.

9. Express7

5

3- x =-5, x = 0x + x

as a single fraction in its simplest form.

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DEMANDING Simplify an expression involving indices. Most candidates managed tocancel the constants, but many did not correctly deal with the indices. 5n3 was a commonanswer.

DEMANDING: Subtract algebraic fractions. Many candidates gained the first two marks butfailed to subtract correctly for the third mark. A final numerator of 4x + 15 was common.Some candidates arrived at the correct answer and then proceeded to cancel an x on thenumerator with an x on the denominator.

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Page twelve

10. In a race, boats sail round three buoys represented by A, B, and C in thediagram below.

North

North

60 º

B

A

C

8 km

11 km

13 km

B is 8 kilometres from A on a bearing of 060º.

C is 11 kilometres from B.

A is 13 kilometres from C.

(a) Calculate the size of angle ABC.

(b) Hence find the size of the shaded angle.

Total marks

3

2

5

DEMANDING(b): Calculate the size of an angle. Many candidates did not realise that angleABN was 120 degrees. A common response was to divide the answer to part (a) by 2 thensubtract from 180 degrees.

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Page thirteen

11. Change the subject of the formula s = ut + 1 at2

2 to a.

12. Solve the equation 11cos x° - 2 = 3, for 0 < x <360.

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DEMANDING: Change the subject of a formula. This question was poorly attempted.Candidates made a variety of confused responses, particularly in trying to deal with the t2.Many divided by t and then found the square root. Some thought that the square applied tothe a as well as the t. Many candidates did not multiply all terms by 2 when dealing with the½; many did not multiply by 2 at all. Some treated the ut term and the ½ in the same way.

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Page fourteen

13. The picture shows the entrance to a tunnel which is in the shape of part of acircle.

The diagram below represents the cross-section of the tunnel.

• The centre of the circle is O.

• MN is a chord of the circle.

• Angle MON is 50º.

• The radius of the circle is 7 metres.

Calculate the area of the cross-section of the tunnel.

[END OF QUESTION PAPER]

M

50º

O

7 m7 m

N

5

DEMANDING: Calculate the area of a composite shape involving a sector of a circle anda triangle. There were a variety of responses to this question. The majority picked up someor all of the marks but many candidates only calculated the area of the triangle or the area ofone of the sectors. Some used A=1/2bh to calculate the area of the triangle after having usedlaborious methods to calculate the base and height.

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Page fifteen

ADDITIONAL SPACE FOR ANSWERS

Section 1: Comments on the Assessment

Summary of the Course assessmentThe course assessment was found to be accessible to the vast majority of candidates.

Feedback suggested that it was set at a level similar to Intermediate 2 and Credit Level, andgave candidates a good opportunity to demonstrate the spread and depth of their knowledgeof the subject at this level. It was a good reflection of what had appeared in model andpractice papers.

The course assessment performed as expected except for Question 13 in Paper 1, whichcandidates found more difficult than was intended. This affected the stronger candidates lessthan the others.

Section 2: Comments on candidate performance

Summary of the Candidate PerformanceThe mean mark for Paper 1 was 20∙6 out of 40 ie 51∙5%. The mean mark for Paper 2 was32∙4 out of 50 ie 64∙8%. The mean mark overall was 53 out of 90 ie 58∙9%.

¨ The majority of candidates made a good attempt at all questions apart from questions10, 11(b) and 13 in Paper 1 and question 11 in Paper 2.

¨ Some candidates scored very high marks. Others however, scored very low marks andwere perhaps inappropriately presented at this level.

¨ Most candidates wrote clearly, showed all appropriate working and stated correct unitsfor their answers where appropriate.

¨ The number of candidates who failed to achieve full marks in some questions in Paper 1because of an inability to carry out straightforward calculations was disappointing.

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ADDITIONAL SPACE FOR ANSWERS

Section 5: Advice to centres for preparation offuture candidatesCentres deserve credit for the preparation of candidates for the National 5 Mathematicscourse assessment. Candidates were well-prepared in dealing with most questions andworking was usually displayed clearly.

The following advice that may help candidates pick up more marks:

¨ A mark is available for stating correct units in one question in the course assessment.Candidates should state the correct units for their answers to all appropriate questions toensure that they gain full credit in the question in which the mark for units is available.

¨ In Paper 1, poor number skills cost many candidates valuable marks. Centres shouldconsider how best to maintain and practice number skills in preparation for the non-calculator paper in the course assessment.

¨ When finding the equation of a straight line, candidates at this level should give theequation in its simplest form in terms of the given variables, eg C=15F+125.

¨ Centres should note that the use of functional notation is not restricted to linearfunctions.

¨ In questions that involve angles in a diagram, candidates should write the sizes of anyangles they use, in the diagram. This allows the marker to follow the candidate’sworking, and increases the opportunity for marks to be awarded.

¨ Centres should consider how best to practise problem solving skills, which candidatesrequire to tackle questions which involve some reasoning in the course assessment.

The SQA website contains the Marking Instructions for the 2014 course assessment. Allthose teaching National 5 Mathematics, and candidates undertaking the course, will findfurther advice and guidance in these detailed Marking Instructions.