surname names
Number Number
Further Pure Mathematics
■ ■
PAPER 1R
Pearson Edexcel International GCSE Further Pure Mathematics PAPER 1R QP MAY 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
P74099A
©2024 Pearson Education Ltd.
F:1/1/1/1/1/
, International GCSE in Further Pure Mathematics Formulae sheet
DO NOT WRITE IN THIS AREA
Mensuration
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
DO NOT WRITE IN THIS AREA
Sum to infinity, S r <1
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
DO NOT WRITE IN THIS AREA
tan θ
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 Without using a calculator, solve the inequality 50 x 18 6x 5
Give your answer in an exact form with a rationalised denominator.
Show your working clearly.
(4)
............................................................................................................................. .....................................................................................................................
.................................................................................................................................. ................................................................................................................
....................................................................................................................................... ...........................................................................................................
............................................................................................................................................ ......................................................................................................
DO NOT WRITE IN THIS AREA
............................................................................................................................. .....................................................................................................................
............................................................................................................................. .....................................................................................................................
............................................................................................................................. .....................................................................................................................
.................................................................................................................................. ................................................................................................................
....................................................................................................................................... ...........................................................................................................
............................................................................................................................................ ......................................................................................................
................................................................................................................................................. .................................................................................................
......................... ............................................................................................................................. ............................................................................................
............................................................................................................................. .....................................................................................................................
DO NOT WRITE IN THIS AREA
.................................................................................................................................. ................................................................................................................
....................................................................................................................................... ...........................................................................................................
............................................................................................................................................ ......................................................................................................
................................................................................................................................................. .................................................................................................
......................... ............................................................................................................................. ............................................................................................
............................................................................................................................. .....................................................................................................................
(Total for Question 1 is 4 marks)
3
■■■■ Turn over
, 2 Given that
1 5
1 x x2 ...
DO NOT WRITE IN THIS AREA
3 36
is the binomial expansion, in ascending powers of x, of 1 Ax
n
where A and n are rational numbers,
(a) find the value of A and the value of n
(6)
(b) Hence find the value of the coefficient of x3
p
Give your answer in the form where p is a prime number and q is an integer.
q (2)
............................................................................................................................. .......................................................................................... ...........................
............................................................................................................................. ............................................................................................... ......................
DO NOT WRITE IN THIS AREA
............................................................................................................................. .....................................................................................................................
............................................................................................................................. .....................................................................................................................
.................................................................................................................................. ................................................................................................................
....................................................................................................................................... ...........................................................................................................
............................................................................................................................................ ......................................................................................................
................................................................................................................................................. .................................................................................................
......................... ............................................................................................................................. ............................................................................................
............................................................................................................................. .....................................................................................................................
.................................................................................................................................. ................................................................................................................
DO NOT WRITE IN THIS AREA
............................................................................................................................. ................................................................................................................ .....
............................................................................................................................. .....................................................................................................................
............................................................................................................................. .....................................................................................................................
............................................................................................................................. .....................................................................................................................
............................................................................................................................. .....................................................................................................................
.................................................................................................................................. ................................................................................................................
....................................................................................................................................... ...........................................................................................................
4
■■■■
Number Number
Further Pure Mathematics
■ ■
PAPER 1R
Pearson Edexcel International GCSE Further Pure Mathematics PAPER 1R QP MAY 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
P74099A
©2024 Pearson Education Ltd.
F:1/1/1/1/1/
, International GCSE in Further Pure Mathematics Formulae sheet
DO NOT WRITE IN THIS AREA
Mensuration
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
DO NOT WRITE IN THIS AREA
Sum to infinity, S r <1
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
DO NOT WRITE IN THIS AREA
tan θ
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 Without using a calculator, solve the inequality 50 x 18 6x 5
Give your answer in an exact form with a rationalised denominator.
Show your working clearly.
(4)
............................................................................................................................. .....................................................................................................................
.................................................................................................................................. ................................................................................................................
....................................................................................................................................... ...........................................................................................................
............................................................................................................................................ ......................................................................................................
DO NOT WRITE IN THIS AREA
............................................................................................................................. .....................................................................................................................
............................................................................................................................. .....................................................................................................................
............................................................................................................................. .....................................................................................................................
.................................................................................................................................. ................................................................................................................
....................................................................................................................................... ...........................................................................................................
............................................................................................................................................ ......................................................................................................
................................................................................................................................................. .................................................................................................
......................... ............................................................................................................................. ............................................................................................
............................................................................................................................. .....................................................................................................................
DO NOT WRITE IN THIS AREA
.................................................................................................................................. ................................................................................................................
....................................................................................................................................... ...........................................................................................................
............................................................................................................................................ ......................................................................................................
................................................................................................................................................. .................................................................................................
......................... ............................................................................................................................. ............................................................................................
............................................................................................................................. .....................................................................................................................
(Total for Question 1 is 4 marks)
3
■■■■ Turn over
, 2 Given that
1 5
1 x x2 ...
DO NOT WRITE IN THIS AREA
3 36
is the binomial expansion, in ascending powers of x, of 1 Ax
n
where A and n are rational numbers,
(a) find the value of A and the value of n
(6)
(b) Hence find the value of the coefficient of x3
p
Give your answer in the form where p is a prime number and q is an integer.
q (2)
............................................................................................................................. .......................................................................................... ...........................
............................................................................................................................. ............................................................................................... ......................
DO NOT WRITE IN THIS AREA
............................................................................................................................. .....................................................................................................................
............................................................................................................................. .....................................................................................................................
.................................................................................................................................. ................................................................................................................
....................................................................................................................................... ...........................................................................................................
............................................................................................................................................ ......................................................................................................
................................................................................................................................................. .................................................................................................
......................... ............................................................................................................................. ............................................................................................
............................................................................................................................. .....................................................................................................................
.................................................................................................................................. ................................................................................................................
DO NOT WRITE IN THIS AREA
............................................................................................................................. ................................................................................................................ .....
............................................................................................................................. .....................................................................................................................
............................................................................................................................. .....................................................................................................................
............................................................................................................................. .....................................................................................................................
............................................................................................................................. .....................................................................................................................
.................................................................................................................................. ................................................................................................................
....................................................................................................................................... ...........................................................................................................
4
■■■■
