A document featuring exam questions and worked solutions for A-level Maths is invaluable. It offers vital practice opportunities, enhances understanding through step-by-step explanations, aids in error identification and correction, familiarizes students with exam formats, comprehensively covers sy...
YEAR 12 MATHEMATICS
- Chapters 1&2-
6&7 Statistcs-
(45 Minutes)
NAME: __________________
Worked Solutions TEACHER: _______________
SCK -
MARKS: ____
45 /453
43
.
Candidates may use any calculator allowed by the regulations of the
Joint Council for Qualifications. Calculators must not have the facility
for symbolic algebra manipulation, differentiation and integration, or
have retrievable mathematical formulae stored in them.
Instructions
● Use black ink or a ball-point pen.
● If pencil is used for diagrams / sketches / graphs it must be dark (HB or B).
● Fill in the boxes at the top of this page with your name,
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.
● Answers should be given to three significant figures unless otherwise stated.
Information
● A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
43
● There are 7 questions in this question paper. The total mark for this paper is e
45.
● 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.
● Try to answer every question.
● Check your answers if you have time at the end.
, Statistics
Discrete distributions
For a discrete random variable X taking values xi with probabilities P(X = xi )
Expectation (mean): E(X ) = μ = Σxi P(X = xi )
Variance: Var(X ) = σ 2 = Σ(xi – μ)2 P(X = xi ) = Σ x2i P(X = xi ) – μ 2
For a function g(X ): E(g(X )) = Σg(xi ) P(X = xi )
The probability generating function of X is GX (t) = E(t X ) and
E(X ) = G′X (1) and Var(X ) = G′′X (1) + G′X (1) – [G′X (1)]2
For Z = X + Y, where X and Y are independent: GZ (t) = GX (t) × GY (t)
Discrete distributions
Standard discrete distributions:
Distribution of X P(X = x) Mean Variance P.G.F.
n x
x p (1 – p)
n –x
Binomial B(n, p) np np(1 – p) (1 – p + pt)n
λx
Poisson Po(λ) e− λ λ λ eλ(t –1)
x!
Geometric Geo( p) 1 1− p pt
p(1 – p)x –1
on 1, 2, . . . p p2 1 − (1 − p )t
r
Negative binomial x − 1 r r r (1 − p ) pt
r − 1 p (1 – p)
x –r
on r, r + 1, . . . p p2 1 − (1 − p )t
4
Continuous distributions
For a continuous random variable X having probability density function f
For independent random variables X and Y
E(XY ) = E(X )E(Y ), Var(aX ± bY ) = a2 Var(X ) + b2 Var(Y )
24 Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Mathematics and Further Mathematics
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