Prove that
å (r
r =1
n
2
- r -1 =
)
1 (n - 2)n(n + 2) . 3
(5)
2.
1 f ( x ) = ln x - 1 - . x
(a) Show that the root a of the equation f(x) = 0 lies in the interval 3 < a < 4 .
(2)
(b) Taking 3.6 as your starting value, apply the Newton-Raphson procedure on...
Edexcel Maths Fp2 Paper WITH MARKING
SCHEME 2024
by jayantnain |
Paper Reference(s)
6667
Edexcel GCE
Further Pure Mathematics FP1 Advanced Level
Specimen Paper Time: 1 hour 30 minutes
Materials required for examination Answer Book (AB16) Graph Paper (ASG2) Mathematical Formulae
(Lilac) Items included with question papers Nil
Candidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation
and/or integration. Thus candidates may NOT use calculators such as the Texas Instruments TI-89, TI-92,
Casio CFX-9970G, Hewlett Packard HP 48G.
Instructions to Candidates In the boxes on the answer book, write the name of the examining body
(Edexcel), your centre number, candidate number, the unit title (Further Pure Mathematics FP1), the paper
reference (6667), your surname, initials and signature. When a calculator is used, the answer should be
given to an appropriate degree of accuracy. Information for Candidates A booklet Mathematical Formulae
and Statistical Tables is provided. Full marks may be obtained for answers to ALL questions. This paper
has eight questions. Advice to Candidates You must ensure that your answers to parts of questions are
clearly labelled. You must show sufficient working to make your methods clear to the Examiner. Answers
without working may gain no credit.
(a) Show that the root a of the equation f(x) = 0 lies in the interval 3 < a < 4 .
(2)
(b) Taking 3.6 as your starting value, apply the Newton-Raphson procedure once to f(x) to obtain a second
approximation to a. Give your answer to 4 decimal places. (5) 3. Find the set of values of x for which 1 x > .
x -3 x -2
(7)
4.
f ( x ) º 2 x 3 - 5 x 2 + px - 5, p ? ℝ . The equation f (x) = 0 has (1 2i) as a root. Solve the equation and
determine the value of p. (7)
5.
(a) Obtain the general solution of the differential equation dS - 0.1S = t. dt
(6) (b) The differential equation in part (a) is used to model the assets, £S million, of a bank t years after it
was set up. Given that the initial assets of the bank were £200 million, use your answer to part (a) to
estimate, to the nearest £ million, the assets of the bank 10 years after it was set up. (4)
,2
, 6.
The curve C has polar equation
r 2 = a 2 cos 2q , -p p £q £ . 4 4
(a) Sketch the curve C. (2) (b) Find the polar coordinates of the points where tangents to C are parallel to
the initial line. (6) (c) Find the area of the region bounded by C. (4)
7.
Given that z = -3 + 4i and zw = -14 + 2i, find (a) w in the form p + iq where p and q are real, (4) (b) the
modulus of z and the argument of z in radians to 2 decimal places (4) (c) the values of the real constants m
and n such that mz + nzw = -10 - 20i .
(5)
3
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