Download S1 Scheme of Work

YEAR 12 S1
Specification
Reference
1. Mathematical models in
probability and statistics
Heinemann Chapter 1

Section 1:1 and 1:2
- Read Chapter 1
- Use this for discussion
The basic ideas of mathematical
modelling as applied in probability
and statistics
2. Representation and summary of
data


Histograms, stem and leaf
diagrams, box plots.
Measures of location – mean,
median and mode.
Heinemann Chapter 2
Section 2:1 – 2:4
- Exercise 2A
Section 2:5 – 2:8
- Exercise 2B
Heinemann Chapter 3
Section 3:1 – 3:5
- Exercise 3A
Notes/Extra Material
Revision Exercise 1
Use to compare distributions. Back-toback stem and leaf diagrams may be
required. (Section 2:4)
Interpret measures of location and
dispersion. (Section 4:4)
Data may be discrete, continuous, grouped
or ungrouped. Use of coding. (Section
3:5)



Measures of dispersion –
variance, standard deviation,
range and interpercentile ranges.
Skewness.
Concepts of outliers.
Heinemann Chapter 4
Section 4:1 – 4:3
- Exercise 4A
(also see Section 3:4 for further work on
interpercentiles)
Section 4:4
- Exercise 4A
3. Probability
Heinemann Chapter 5



Elementary probability.
Sample space.
Complementary events.
Section 5:1 – 5:2 & 5:6
- Exercise 5A
- Exercise 5D

Conditional Probability
Section 5:4
- Exercise 5B


Exclusive events
Independence of two events.
Section 5:5
- Exercise 5C

Sum and product laws.
Section 5:3
- Exercise 5A
Section 5:4
- Exercise 5B
Revision Exercise 5E
Simple interpolation may be required.
(Section 3:3 – 3:4)
Any rule to identify outliers will be specified
in the question.
Revision Exercises 2, 3 and 4
Understanding and use of;
P(A’) = 1 – P(A) (Section 5:2)
P(A  B) = P(A) + P(B) – P(A  B)
(Section 5:3)
P(A  B) = P(A) x P(B/A) (Section 5:4)
For independence (Section 5:5)
P(B/A) = P(B)
P(A/B) = P(A)
P(A  B) = P(A) x P(B)
Use of tree diagrams and Venn diagrams.
(throughout Chapter 5)
Sampling with and without replacement.
(Section 5:5)
Revision Exercise 5
4. Correlation and regression
Heinemann Chapter 6


Correlation
Scatter diagrams.
Section 6:1 – 6:2
- Exercise 6A


Linear Regression.
Explanatory (independent) and
response (dependent) variables.
Applications and interpretations
Heinemann Chapter 7


The product moment correlation
coefficient, its use interpretation
and limitations.
Section 7:1 – 7:4
- Exercise 7A
Section 6:3 – 6:4
- Exercise 6A
Heinemann Chapter 8

The concept of a discrete random
variable
The probability function and the
cumulative distribution function for
a discrete random variable.
Section 8:1 – 8:3
- Exercise 8A
Mean and variance of a discrete
random variable
Section 8:4
- Exercise 8B
Section 8:5
- Exercise 8C


The discrete uniform distribution
Use to make predictions within the range of
values of the explanatory variable and the
dangers of extrapolation. (Section 7:4)
Use of coding may be required. (Section
6:3)
Revision Exercises 6 & 7
5. Discrete random variables

Calculation of the equation of a linear
regression line using the method of least
squares. Scatter diagrams may be
required to be drawn. (Chapter 7)
Section 8:6
- Exercise 8D
Simple uses of the probability function p(x)
where p(x) = P(X=x). (Section 8:1 – 8:2)
Use of the cumulative distribution function
F(x) = P(X  x) =  p(x) (Section 8:3)
Use of E(X), E(X2) for calculating the
variance of X. (Section 8:4)
Knowledge and use of (Section 8:5)
E(aX + b) = aE(X) + b
Var (aX + b) = a2 Var (X)
Including the mean and variance of the
discrete uniform distribution. (Section 8:6)
Revision Exercise 8
6. The Normal Distribution
Heinemann Chapter 9

Section 9:1 – 9:2
- Exercise 9A
The Normal distribution including
the mean, variance and use of
tables of the cumulative
distribution function.
Knowledge of the shape and symmetry of
the distribution is required. (Section 9:1)
Questions may involve the solution of
simultaneous equations.
Revision Exercise 9