surname names
Number Number
Paper
Further Mathematics
� �
Advanced
PAPER 2: Core Pure Mathematics 2
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
• If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
centre number and candidate 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.
• There are 9 questions in this question paper. The total mark for this paper is 75.
– 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
,1. In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
Given that
z 2 2 3i and w 1 3i
show that
z z
(a)
w w (3)
(b) arg(zw) arg (z) arg(w)
(3)
,Question 1 continued
(Total for Question 1 is 6 marks)
, 2. An archer shoots an arrow towards a target.
In a model
• the arrow is a particle
• the flight path of the arrow is a straight line
• the target is part of a plane
Relative to a fixed origin O
• the arrow is fired from the point with position vector 3i 5j 2k
• the plane containing the target has equation 2x 4 y z 3
Use the model to answer parts (a) to (d).
(a) Determine the shortest distance that the arrow must travel to reach the plane.
(2)
The arrow hits the target at the point with position vector 6i 2j k
(b) Determine a vector equation of the flight path of the arrow.
(2)
(c) Determine the acute angle that the flight path of the arrow makes with the target.
Give your answer to the nearest degree.
(2)
(d) Determine the distance travelled by the arrow.
(1)
(e) Comment on whether the actual distance travelled by the arrow is likely to match
the answer to part (d), giving a reason for your answer.
(1)
Number Number
Paper
Further Mathematics
� �
Advanced
PAPER 2: Core Pure Mathematics 2
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
• If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
centre number and candidate 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.
• There are 9 questions in this question paper. The total mark for this paper is 75.
– 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
,1. In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
Given that
z 2 2 3i and w 1 3i
show that
z z
(a)
w w (3)
(b) arg(zw) arg (z) arg(w)
(3)
,Question 1 continued
(Total for Question 1 is 6 marks)
, 2. An archer shoots an arrow towards a target.
In a model
• the arrow is a particle
• the flight path of the arrow is a straight line
• the target is part of a plane
Relative to a fixed origin O
• the arrow is fired from the point with position vector 3i 5j 2k
• the plane containing the target has equation 2x 4 y z 3
Use the model to answer parts (a) to (d).
(a) Determine the shortest distance that the arrow must travel to reach the plane.
(2)
The arrow hits the target at the point with position vector 6i 2j k
(b) Determine a vector equation of the flight path of the arrow.
(2)
(c) Determine the acute angle that the flight path of the arrow makes with the target.
Give your answer to the nearest degree.
(2)
(d) Determine the distance travelled by the arrow.
(1)
(e) Comment on whether the actual distance travelled by the arrow is likely to match
the answer to part (d), giving a reason for your answer.
(1)
