FP1 Further Pure
Mathematics Advanced
Level 2024-2025 Practice
Test
, surname names
Number Number
Further Mathematics
■ ■
Advanced
PAPER 3A: Further Pure Mathematics 1
Candidates may use any calculator permitted by Pearson regulations. Calculators
must not have the facility for symbolic algebraic manipulation, differentiation and
integration, or have retrievable mathematical formulae stored in them.
Instructions
•• Use black ink or ball-point pen.
•
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
Fill in the
centre boxesand
number at the top of this
candidate page with your name,
number.
• Answer all questions and ensure that your answers to parts of questions are
•
clearly labelled.
Answer the questions in the spaces provided
•
– there may be more space than you need.
You should show sufficient working to make your methods clear.
•
Answers without working may not gain full credit.
Inexact answers should be given to three significant figures unless otherwise stated.
Information
•• A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
•
There are 10 questions in this question paper. The total mark for this paper is 75.
The
– usemarks
this asfor each as
a guide question
to howare shown
much timeintobrackets
spend on each question.
Advice
• Read each question carefully before you start to answer it.
•• Try to answer every question.
Check your answers if you have time at the end. Turn over
P75686RA
©2024 Pearson Education Ltd.
F:1/1/1/1/1/1/
, 1. (a) Given that
y ln 3 x2
DO NOT WRITE IN THIS AREA
complete the table with the value of y corresponding to x = 3, giving your answer to
4 significant figures.
x 2 2.5 3 3.5 4 4.5 5
y 1.946 2.225 2.725 2.944 3.146 3.332
(1)
In part (b) you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
(b) Use Simpson’s rule with all the values of y in the completed table to estimate, to 3
significant figures, the value of
DO NOT WRITE IN THIS AREA
5ln 3 x2 dx
2
(3)
(c) Using your answer to part (b) and making your method clear, estimate the value of
ln 3 x dx
5
2
2
(1)
DO NOT WRITE IN THIS AREA
2
■■■■
, Question 1 continued
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(Total for Question 1 is 5 marks)
3
■■■■ Turn over
Mathematics Advanced
Level 2024-2025 Practice
Test
, surname names
Number Number
Further Mathematics
■ ■
Advanced
PAPER 3A: Further Pure Mathematics 1
Candidates may use any calculator permitted by Pearson regulations. Calculators
must not have the facility for symbolic algebraic manipulation, differentiation and
integration, or have retrievable mathematical formulae stored in them.
Instructions
•• Use black ink or ball-point pen.
•
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
Fill in the
centre boxesand
number at the top of this
candidate page with your name,
number.
• Answer all questions and ensure that your answers to parts of questions are
•
clearly labelled.
Answer the questions in the spaces provided
•
– there may be more space than you need.
You should show sufficient working to make your methods clear.
•
Answers without working may not gain full credit.
Inexact answers should be given to three significant figures unless otherwise stated.
Information
•• A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
•
There are 10 questions in this question paper. The total mark for this paper is 75.
The
– usemarks
this asfor each as
a guide question
to howare shown
much timeintobrackets
spend on each question.
Advice
• Read each question carefully before you start to answer it.
•• Try to answer every question.
Check your answers if you have time at the end. Turn over
P75686RA
©2024 Pearson Education Ltd.
F:1/1/1/1/1/1/
, 1. (a) Given that
y ln 3 x2
DO NOT WRITE IN THIS AREA
complete the table with the value of y corresponding to x = 3, giving your answer to
4 significant figures.
x 2 2.5 3 3.5 4 4.5 5
y 1.946 2.225 2.725 2.944 3.146 3.332
(1)
In part (b) you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
(b) Use Simpson’s rule with all the values of y in the completed table to estimate, to 3
significant figures, the value of
DO NOT WRITE IN THIS AREA
5ln 3 x2 dx
2
(3)
(c) Using your answer to part (b) and making your method clear, estimate the value of
ln 3 x dx
5
2
2
(1)
DO NOT WRITE IN THIS AREA
2
■■■■
, Question 1 continued
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(Total for Question 1 is 5 marks)
3
■■■■ Turn over
