X100/12/11
NATIONAL
QUALIFICATIONS
WEDNESDAY, 20 MAY
9.00 AM – 10.30 AM
MATHEMATICS
2015 HIGHER
Paper 1
(Non-calculator)
Read carefully
Calculators may NOT be used in this paper.
Section A – Questions 1–20 (40 marks)
Instructions for completion of Section A are given on Page two.
Section B (30 marks)
Full credit will be given only where the solution contains appropriate working.
Answers obtained by readings from scale drawings will not receive any credit.
Write your answers clearly in the spaces in the answer booklet provided. Additional space for
answers is provided at the end of the answer booklet. If you use this space you must clearly
identify the question number you are attempting.
Use blue or black ink.
Before leaving the examination room you must give your answer booklet to the Invigilator; if you do
not, you may lose all the marks for this paper.
HTP *X100/12/11* ©
,Read the questions for Section A and record your answers on the grid on Page three of the
answer booklet.
1. The answer to each question is either A, B, C or D. Decide what your answer is, then
fill in the appropriate bubble (see sample question below).
2. There is only one correct answer to each question.
Do NOT use gel pens.
Sample Question
A curve has equation y = x3 – 4x.
What is the gradient at the point where x = 2?
A 1
B 8
C 0
D –4
The correct answer is B—8. The answer B bubble has been clearly filled in (see below).
Changing an answer
If you decide to change your answer, cancel your first answer by putting a cross through it
(see below) and fill in the answer you want. The answer below has been changed to D.
If you then decide to change back to an answer you have already scored out, put a tick (3)
to the right of the answer you want, as shown below:
or
[X100/12/11] Page two
, FORMULAE LIST
Circle:
The equation x2 + y2 + 2gx + 2fy + c = 0 represents a circle centre (–g, –f) and radius g2 + f 2 − c .
The equation (x – a)2 + (y – b)2 = r2 represents a circle centre (a, b) and radius r.
Scalar Product: a.b = |a||b| cos q, where q is the angle between a and b
a1 b1
or a.b = a1b1 + a2b2 + a3b3 where a = a2 and b = b2 .
a b
3 3
Trigonometric formulae: sin (A ± B) = sin A cos B ± cos A sin B
cos (A ± B) = cos A cos B sin A sin B
±
sin 2A = 2sin A cos A
cos 2A = cos2 A – sin2 A
= 2cos2 A – 1
= 1 – 2sin2 A
Table of standard derivatives:
f(x) f ′(x)
sin ax a cos ax
cos ax –a sin ax
Table of standard integrals:
f(x) ∫ f (x)dx
sin ax − a1 cos ax + c
cos ax − a1 sin ax + c
[Turn over
[X100/12/11] Page three
NATIONAL
QUALIFICATIONS
WEDNESDAY, 20 MAY
9.00 AM – 10.30 AM
MATHEMATICS
2015 HIGHER
Paper 1
(Non-calculator)
Read carefully
Calculators may NOT be used in this paper.
Section A – Questions 1–20 (40 marks)
Instructions for completion of Section A are given on Page two.
Section B (30 marks)
Full credit will be given only where the solution contains appropriate working.
Answers obtained by readings from scale drawings will not receive any credit.
Write your answers clearly in the spaces in the answer booklet provided. Additional space for
answers is provided at the end of the answer booklet. If you use this space you must clearly
identify the question number you are attempting.
Use blue or black ink.
Before leaving the examination room you must give your answer booklet to the Invigilator; if you do
not, you may lose all the marks for this paper.
HTP *X100/12/11* ©
,Read the questions for Section A and record your answers on the grid on Page three of the
answer booklet.
1. The answer to each question is either A, B, C or D. Decide what your answer is, then
fill in the appropriate bubble (see sample question below).
2. There is only one correct answer to each question.
Do NOT use gel pens.
Sample Question
A curve has equation y = x3 – 4x.
What is the gradient at the point where x = 2?
A 1
B 8
C 0
D –4
The correct answer is B—8. The answer B bubble has been clearly filled in (see below).
Changing an answer
If you decide to change your answer, cancel your first answer by putting a cross through it
(see below) and fill in the answer you want. The answer below has been changed to D.
If you then decide to change back to an answer you have already scored out, put a tick (3)
to the right of the answer you want, as shown below:
or
[X100/12/11] Page two
, FORMULAE LIST
Circle:
The equation x2 + y2 + 2gx + 2fy + c = 0 represents a circle centre (–g, –f) and radius g2 + f 2 − c .
The equation (x – a)2 + (y – b)2 = r2 represents a circle centre (a, b) and radius r.
Scalar Product: a.b = |a||b| cos q, where q is the angle between a and b
a1 b1
or a.b = a1b1 + a2b2 + a3b3 where a = a2 and b = b2 .
a b
3 3
Trigonometric formulae: sin (A ± B) = sin A cos B ± cos A sin B
cos (A ± B) = cos A cos B sin A sin B
±
sin 2A = 2sin A cos A
cos 2A = cos2 A – sin2 A
= 2cos2 A – 1
= 1 – 2sin2 A
Table of standard derivatives:
f(x) f ′(x)
sin ax a cos ax
cos ax –a sin ax
Table of standard integrals:
f(x) ∫ f (x)dx
sin ax − a1 cos ax + c
cos ax − a1 sin ax + c
[Turn over
[X100/12/11] Page three
