Auchmuty High School Mathematics Department
2016 National 5 Maths Revision Sheet
The following questions have been chosen as the likelihood of questions similar to
them appearing in this year’s exam is higher than normal.
It is important you understand this is NOT a definitive list. Other topics/questions will
appear in your exam, some of these questions may not and that it is IMPOSSIBLE to
actually predict a maths exam paper.
It is in your interest, however, to ensure you are able to answer as many of the
following types of question as possible.
Ideally you should have attempted these questions before you attend the study days
for maths on the 10th & 11th of May in order to seek help for any you could not do.
Auchmuty High School Mathematics Department
2016 National 5 Maths Revision Sheet
Paper 1 Non – Calculator
Fractions - multiply/divide
(2)
Answer: 4
Fractions - BODMAS
(3)
Answer:
53
20
or 2
13
20
Brackets
(3)
Answer: 4𝑥 3 − 16𝑥 2 + 19𝑥 − 6
Vectors 3D Coordinates
(2)
Answer: M (0,2,0), N (7,4,4)
Auchmuty High School Mathematics Department
2016 National 5 Maths Revision Sheet
Vectors – Alternative vector pathways
(1,2)
Answer: (a) u + v
(b) 2u – 2v
Angles in a Circle
(3)
Answer: 26
Straight Lines – rearrange an equation to find a gradient.
(1,2)
1
Answer: (a) m = − 3
(b) (0,4)
Auchmuty High School Mathematics Department
2016 National 5 Maths Revision Sheet
Straight Lines – Scattergraphs
(3)
3
4
Answer:𝑦 − 30 = (𝑥 − 17) 𝑂𝑅 4𝑦 = 3𝑥 − 21
Surds – Multiplying and simplifying
(2)
Answer:15√2
Auchmuty High School Mathematics Department
2016 National 5 Maths Revision Sheet
Surds – multiply out brackets and simplify
4 3 (2 6  3 )
(3)
Answer:24√2 − 12
Indices
Simplify and write your final answer with a positive power
( y 4 ) 3 X y 2
Answer:
(3)
1
𝑦 10
Indices - brackets
(2,1)
Answer:(a) 𝑥 3 + 1 (b) 65
Completing the square
(2,3)
Answer: (a) 𝑦 = (𝑥 − 3)2 + 5 (b) U-shaped parabola with TP at (3,5) and y-intercept at (0,14)
Auchmuty High School Mathematics Department
2016 National 5 Maths Revision Sheet
Trig Graphs
(1)
Answer: 30
Trig Graphs - again
(2)
Answer: a is the amplitude – i.e. half of difference between max and min values, i.e. 6 ÷ 2 = 3
B is -2 as the graph of y=3cosx has been moved down by 2 places, i.e. starts at 1 and not 3.
Auchmuty High School Mathematics Department
2016 National 5 Maths Revision Sheet
Quadratics – y=kx2
(2)
Answer: k = -3
Area of a Triangle
(3)
Answer: 40cm2
Sine Rule/Cosine Rule: non-calc
(3)
4
8
Hint: Start with 𝑠𝑖𝑛𝐵 = 𝑠𝑖𝑛150
Auchmuty High School Mathematics Department
2016 National 5 Maths Revision Sheet
Paper 2 - Calculator Allowed
Percentages – Compound
(4)
Answer: 590
Algebraic fractions – Add/Subtract
(3)
𝑥−13
Answer: (𝑥+2)(𝑥−3)
Algebraic Fractions – factorise then cancel down
(3)
Answer:
3𝑥
𝑥+5
Circles – Arc length/Area of a Sector
(2,2)
Answer: (a) 2289.6cm2 (b) 222.4cm
Auchmuty High School Mathematics Department
2016 National 5 Maths Revision Sheet
Pythagoras – Converse
(3)
Answer: 𝑁𝑜. 1602 ≠ 1442 + 702
Volume
(5)
Answer: 6900cm2 (i.e. 6900ml)
Auchmuty High School Mathematics Department
2016 National 5 Maths Revision Sheet
Volume – working backwards
(3,2)
Answer: (a) 1180cm3 (b) 7.7cm
Quadratic Formula
(4)
Answer: x = 5.4, x = -0.4
Auchmuty High School Mathematics Department
2016 National 5 Maths Revision Sheet
Standard Deviation
(4,2)
Answer: (a) 2
(b) Lower mean under new coach – scoring less goals on average.
Higher S.D under new coach – No. of goals more varied.
Simultaneous equations – with a wee story
(1,1,3)
Answer: (a) 3c + 2d = 33 (b) 4c + 3d = 47 (c) CD - £5, DVD- £9
Auchmuty High School Mathematics Department
2016 National 5 Maths Revision Sheet
Simultaneous equations – to find a point of intersection
(4)
Answer: (1,5)
Change the subject of a formula
(3)
Answer: d 
5
ac
Pythagoras in a Circle
(4)
Answer: 0.46m
Auchmuty High School Mathematics Department
2016 National 5 Maths Revision Sheet
Similar Areas
(3)
Answer: 20cm2
Similar Volumes
(3)
Answer: 7.6 Litres
Percentages – Working Backwards
(3)
Answer: 840g
Auchmuty High School Mathematics Department
2016 National 5 Maths Revision Sheet
Sine Rule/Cosine Rule: calc
(3)
Answer: 30.6 degrees
Solve a trig equation - Basic
(3)
Answer: x  76.0,256.0
Auchmuty High School Mathematics Department
2016 National 5 Maths Revision Sheet
Solve a trig equation - from a graph
(2,4)
Answer: (a) a is the amplitude – i.e. half of difference between max and min values, i.e. 4 ÷ 2 = 2
B is -1 as the graph of y=2sinx has been moved down by 1 place, i.e. starts at 1 and not 2.
(b) x = 30, x = 150
Quadratics – Roots & Turning Points
(3,1,2)
Answer: (a) A (-1,0) B (3,0) (b) x = 1 (c) 4
Auchmuty High School Mathematics Department
2016 National 5 Maths Revision Sheet
Quadratics – Roots
(3)
Answer: 8 seconds
Discriminant
(3)
Hint: Show the discriminant < 0
Discriminant
(3)
Answer: p < 0.25