broughton high school · 2018 paper 2 question 16 4 marks - answer: yes. he is correct. the...

BROUGHTON HIGH SCHOOL

MATHEMATICS FACULTY

National 5 Mathematics

Past Papers Booklet

(By Assessment Standard)

Updated September 2019

Unit 1Applications 1∙3 – Percentages & Fractions

Relationships 1∙4 – Pythagoras, Similarity & Angles

Expressions & Formulae 1∙4 – Volume of 3D Shape & Circles

Unit 2Expressions & Formulae 1∙2 – Expanding, Factorising & Completing the Square

Applications 1∙1 – Trig in Triangles

Relationships 1∙1 – Equations, Inequations, Simultaneous Equations & Change The

Subject

Unit 3Applications 1∙4 – Statistics

Applications 1∙2 – Vectors

Expressions & Formulae 1∙3 – Algebraic Fractions

Expressions & Formulae 1∙1 – Surds, Indices & Scientific Notation

Unit 4Relationships 1∙2 – Graphs of Quadratic Functions

Relationships 1∙3 – Quadratic Equations

Relationships 1∙5 – Trig Graphs & Trig Equations

National 5 Maths Past Paper Questions

Applications 1∙3

Specimen Paper 1 Question 1

2 marks - Answer: 5

37


3 marks - Answer: 85∙2 miles


3 marks - Answer: £387∙50

2014 Paper 1 Question 1

2 marks - Answer: 27

25


3 marks - Answer: 600 000





133


3 marks - Answer: £253628∙16


3 marks - Answer: £350



13


3 marks - Answer: 27∙25 g


2 marks - Answer: 9

42


2 marks - Answer:


3 marks - Answer: £1369






2 marks - Answer:




3 marks - Answer: £23·85


Relationships 1∙4


a) 1 mark - Answer: r - 5

b) 3 marks - Answer: 10∙6 cm


3 marks - Answer: 4∙15 litres


4 marks - Answer: 18 cm


3 marks - Answer: 3072 cm3


4 marks - Answer: No, c2 ≠ a2 + b2 so therefore the triangle is not right angled.


3 marks - Answer: 39o




4 marks - Answer: 1∙99 m




3 marks - Answer: £4∙95


4 marks - Answer: 11∙4 cm


3 marks - Answer: x = 6∙5




3 marks - Answer: No. 425 ≠ 484.


4 marks - Answer: 42∙∙4 cm






4 marks - Answer: Yes. He is correct. The umbrella is 85 cm long and the space is 90 cm long.


a) 3 marks - Answer: LSF = so large volume should be 1944 cm3. So, they are not similar shapes.



4 marks - Answer: Angle ABC is a right angle. So yes, B is due East of A.




a) 3 marks - Answer: 990 cm 2

b) 2 marks - Answer: 126·1o


4 marks - Answer: 25·6 cm


Expressions & Formulae 1∙4




a) 3 marks - Answer: 1535∙8 cm2



5 marks - Answer: 4180 mm3




3 marks - Answer: 125·6 cm


5 marks - Answer: 29 900 cm3




3 marks - Answer: 2x3 – 5x2 -10x + 3


3 marks - Answer: x3 – 3x2 – 6x + 8


2 marks - Answer: 3 (x – 4) (x + 4)


2 marks - Answer: (x + 4)2 – 23


a) 2 marks - Answer: y = (x - 4)2 + 3

b) 3 marks - Answer: parabola passing through (0, 19) and (8, 19) with minimum turning point at (4, 3)


2 marks - Answer: 6x2 – 13x - 5


2 marks - Answer: (x – 7)2 – 5


3 marks - Answer: 2x3 – 5x2 – 10x + 3


3 marks - Answer: 5x2 – 2x - 11


3 marks - Answer: 2x3 + 3x2 - 38x - 15


2 marks - Answer: (x + 5)2 - 40


Applications 1∙1




a) 4 marks - Answer: 29∙0o

b) 2 marks - Answer: 249∙0o




a) 3 marks - Answer: 84∙8o

b) 2 marks - Answer: 155∙2o


5 marks - Answer: 151∙3 m2


3 marks - Answer: 0∙78 km


4 marks - Answer: 1039∙2 cm2




3 marks - Answer: 78∙2o






3 marks - Answer: 413 m




4 marks - Answer: 282∙1o


5 marks - Answer: 420∙3 cm2


2 marks - Answer: 1224·0 cm 2


3 marks - Answer: 46·4o


5 marks - Answer: 154·6 m


Relationships 1∙1


3 marks - Answer: m

p2


a) 1 mark - Answer: 3f + 4r = 185

b) 1 mark - Answer: 2f + 3r = 130

c) 3 marks - Answer: A restricted pass costs £20. A full pass costs £35.


a) 2 marks - Answer:

b) 2 marks - Answer: (3, 0)

3

4


3 marks - Answer: 2

)(2

t

utsa


3 marks - Answer: x = 7, y = -2


a) 1 mark - Answer: 5a + 2c = 158∙25

c) 4 marks - Answer: An adult ticket costs £22∙50 and a child tickets costs £15∙25.

b) 1 mark - Answer: 3a + 2c = 98


3 marks - Answer: x > -5


2 marks - Answer: a = 7


3 marks - Answer: y = 2x + 9


3 marks - Answer:t

pLk

4

2




c) 4 marks - Answer: cloak 1∙5 m2 , dress = 2∙2 m2

a) 1 mark - Answer: 2c + 3d = 9∙6

b) 1 mark - Answer: 3c + 4d = 13∙3


3 marks - Answer: x < 5


3 marks - Answer: 4

2tFcb


3 marks - Answer: y = -2x + 4


3 marks - Answer: (2∙5, 5∙5)


2 marks - Answer:5

3


3 marks - Answer: x = , y = -1


3 marks - Answer: x =


a) 3 marks - Answer: P = d + 2

b) 1 mark - Answer: £9∙50


3 marks - Answer: x > 6


2 marks - Answer: (0, -4)




2 marks - Answer: – 40


3 marks - Answer:


c) 4 marks - Answer: Cement = 20 kg, Gravel = 25 kg

a) 1 mark - Answer: 7c + 3g = 215

b) 1 mark - Answer: 5c + 4g = 200


Applications 1∙4


a) 3 marks - Answer: y = 2x + 1

b) 1 mark - Answer: 17


a) 3 marks - Answer: Mean = 21, SD = 2∙1

b) 2 marks - Answer: Machine A on average packs more sprouts into each (higher mean).

Machine A packs a more consistent number of sprouts into each bag (lower SD).


a) 3 marks - Answer: C = 15F + 125

b) 1 mark - Answer: 725 calories


a) i) 1 mark - Answer: 56∙5

ii) 3 marks - Answer: 2∙4

b) 1 mark - Answer: No, she is less consistent as the standard deviation has increased.




a) 3 marks - Answer: Median = 19∙5, SIQR = 4∙5

b) 2 marks - Answer: On average the second round’s scores are higher (higher mean),

The second round’s cores are more consistent (lower SD).


a) 3 marks - Answer: W = 20a + 40

b) 1 mark - Answer: 280 kg


a) 4 marks - Answer: Mean = 13 minutes, SD = 5∙7 minutes

b) 2 marks - Answer: Sophie had the longer waiting time on average as she had the higher mean.

Sophie had the more consistent waiting times as she had the lower standard

deviation.




4 marks - Answer: a = 3, b = 2


a) 4 marks - Answer: Mean = 126, Standard Deviation = 4∙05

b) 2 marks - Answer: In general, the number of customers was higher on Saturday

In general, the number of customers was less varied on Saturday


a) 3 marks - Answer: 2·25

b) 2 marks - Answer: In general the temperatures in Grantford are lower (lower mean).

In general, the Temperatures in Endoch are more consistent (lower SD).


a) 3 marks - Answer: F = -3E + 18·5

b) 1 mark - Answer: 15·2 km/l


Applications 1∙2




a) 1 mark - Answer: b – a

b) 1 mark - Answer: 2 (b – a)


2 marks - Answer:

3

10

4


2 marks - Answer: B (8, 4, 10) , C (4, 0, 10)




2 marks - Answer:

4

3


3 marks - Answer:

2

1


a) 1 mark - Answer: (8, 4, 0)

b) 3 marks - Answer: 7




1 mark - Answer: v – u


2 marks - Answer: B (0, 6, 6) and C (3, 3, 9)


2 marks - Answer:


a) 1 mark - Answer: d - c

b) 2 marks - Answer: cd2

1

2

3




2 marks - Answer: u - w


2 marks - Answer: B = (4, 8, 5) , C = (6, 8, 0)


a) 1 mark - Answer:

b) 2 marks - Answer:




2 marks - Answer: A (3, 0, 0) and B (3, 3, 8)




3 marks - Answer: )4)(2(

22

xx

x


3 marks - Answer: 5n4


3 marks - Answer: )5(

154

xx

x


3 marks - Answer: 5x

x


3 marks - Answer: 10s


3 marks - Answer: x =8

5


)1)(2(

78

xx

x3 marks - Answer:


2 marks - Answer: 2

23

a

a


a) 1 mark - Answer:

b) 3 marks - Answer:2

52

x

x

)52)(52( xx


3 marks - Answer:3(n + 2)

n


3 marks - Answer:


3 marks - Answer:


3 marks - Answer:




2 marks - Answer: 3

62


a) 2 marks - Answer: x-1 + x0

b) 1 mark - Answer: 6

11


2 marks - Answer: 1∙65 x 109




3 marks - Answer: 2




a) 3 marks - Answer: 1∙1 x 1012 km3

b) 2 marks - Answer: 50 times bigger


2 marks - Answer: 5

52


2 marks - Answer: 8 x 10-9 g


3 marks - Answer: 4

1

n


2 marks - Answer: 3

1

x


2 marks - Answer:


2 marks - Answer: p8


3 marks - Answer: 1∙094 x 1012 km3


3 marks - Answer:


2 marks - Answer: 2·88 x 107 kg


3 marks - Answer:

THE FOLLOWING

TOPICS ARE

NOT IN

THE PRELIM


Relationships 1∙2


a) 2 marks - Answer: y = (x - 4)2 + 3

b) 3 marks - Answer: parabola passing through (0, 19) and (8, 19) with minimum turning point at (4, 3)


2 marks - Answer: k = -4


2 marks - Answer: k = -4


a) 4 marks - Answer: 6 seconds

b) 3 marks - Answer: No. It has a maximum height of 64 metres.




a) i) 1 mark - Answer: a = -2

b) 1 mark - Answer: x = 2

a) ii) 1 mark - Answer: b = -4


3 marks - Answer:


a) 1 mark - Answer: a = 5

b) 2 marks - Answer: b = 4


3 marks - Answer:


ii) 1 mark - Answer: b = 20

a) 1 mark - Answer: x = 4

b) i) 1 mark - Answer: a = -4


Relationships 1∙3


3 marks - Answer: x = -5, x =2

3


3 marks - Answer: p > 3

1


a) i) 1 mark - Answer: 2x + 3


a) ii) 2 marks - Answer: 4x2 + 44x – 153 = 0


2 marks - Answer: b2 – 4ac = 53, so they are real and distinct


a) 1 mark - Answer: (2x +1) (x + 8)

b) 3 marks - Answer: x2 - 2x – 8 = 0

c) 3 marks - Answer: 12 cm and 9 cm


3 marks - Answer: x = -3∙1 , y = 0∙6


2 marks - Answer: x = 3 , x = 8


2 marks - Answer: No real roots.


a) i) 2 marks - Answer: (x – 3)2 – 90

b) 4 marks - Answer: d = 3, e = 10

ii) 1 mark - Answer: x = 3


a) 1 mark - Answer: 4 m

b) 4 marks - Answer: 3·4 seconds


3 marks - Answer: -3·2, 0·2


Relationships 1∙5


a) 2 marks - Answer: a = 3 because 2 and -4 are six apart and 3 is half of 6.

b = -1 because the graph of y = 3 cos x has been moved down by 1.

b) 4 marks - Answer: x = 70∙5o , 289∙5o


3 marks - Answer: x = 63o, 297

o


2 marks - Answer: cos 100o, cos 90o, cos 300o


2 marks - Answer: sin2 x


2 marks - Answer: a = 3, b = -40


2 marks - Answer: a = 4, b = 3


3 marks - Answer: 102∙5o, 282∙5o


a) 1 mark - Answer: 51∙5 m

b) 1 mark - Answer: 17 m

c) 3 marks - Answer: 21∙4 o

and 335∙9o


2 marks - Answer: a = 5 , b = 4


1 mark - Answer:


2 marks - Answer: sin2 xo


3 marks - Answer: x = 8∙2, x = 171∙8


2 marks - Answer: (135, -3)


3 marks - Answer: 101·5o and 258·5o


2 marks - Answer: 1 + 2 sin x cos x

broughton high school · 2018 paper 2 question 16 4 marks - answer: yes. he is correct. the...

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