Exam (elaborations)
Pearson Edexcel International GCSE Further Pure Mathematics PAPER 2 QP JUNE 2024
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Pearson Edexcel International GCSE Further Pure Mathematics PAPER 2 QP JUNE 2024
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Further Pure Mathematics
🟐 🟐
PAPER 2
Pearson Edexcel International GCSE Further Pure Mathematics PAPER 2 QP JUNE 2024
Instructions
•• Use black ink or ball-point pen.
Fill in the boxes at the top of this page with your name,
centre number and candidate number.
•• Answer all questions.
Without sufficient working, correct answers may be awarded no marks.
• Answer the questions
– there may in thethan
be more space spaces
youprovided
need.
• Anything you write on the formulae page will gain NO credit.
You must NOT write anything on the formulae page.
Information
•• The total mark for this paper is 100.
The marks for each question are shown in brackets
– use this as a guide as to how much time to spend on each question.
Advice
•• Read each question carefully before you start to answer it.
Check your answers if you have time at the end.
Turn over
P76508A
©2024 Pearson Education Ltd.
F:1/1/1/1/1/
, International GCSE in Further Pure Mathematics Formulae sheet
Mensuration
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Surface area of sphere = 4πr2
Curved surface area of cone = πr slant height
4
Volume of sphere = πr3
3
Series
Arithmetic series
Sum to n terms, Sn
n
2a (n 1)d
2
Geometric series
a(1 rn )
Sum to n terms, Sn
(1 r)
a
Sum to infinity, S r <1
DO NOT WRITE IN THIS AREA
1 r
Binomial series
n(n 1) n(n 1) (n r 1)
(1 x)n 1 nx x2 xr for x < 1, n
2! r!
Calculus
Quotient rule (differentiation)
d f ( x) f' ( x)g( x) f( x)g' ( x)
dx g( x) [g( x)]2
Trigonometry
Cosine rule
In triangle ABC: a2 = b2 + c2 – 2bc cos A
sin θ
tan θ
DO NOT WRITE IN THIS AREA
cosθ
sin(A + B) = sin A cos B + cos A sin B sin(A – B) = sin A cos B – cos A sin B
cos(A + B) = cos A cos B – sin A sin B cos(A – B) = cos A cos B + sin A sin B
tan A tan B tan A tan B
tan( A B) tan( A B)
1 tan A tan B 1 tan A tan B
Logarithms
log x
loga x b
logb a
2
■■■■
, Answer all ELEVEN questions.
Write your answers in the spaces provided.
DO NOT WRITE IN THIS AREA
You must write down all the stages in your working.
1 f(x) 6x3 13x2 ax 10 where a is a constant
Given that 3x 2 is a factor of f(x)
(a) show that a 21
(2)
(b) Hence show algebraically that the curve y f(x) has only one intersection with the
x-axis.
(4)
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(Total for Question 1 is 6 marks)
3
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, 2 The quadratic equation 3x2 5x 1 0 has roots and
Without solving the equation,
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form a quadratic equation with integer coefficients, that has roots and
2 2 (8)
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