Maths YMA01 — specification explorer

1. Mathematical models in probability and statistics

• 1.1The basic ideas of mathematical modelling as applied in probability and statistics.S1
  3 resources

1. Representation and summary of data

• 2.1Histograms, stem and leaf diagrams, box plots. Using histograms, stem and leaf diagrams and box plots to compare distributions. Back-to-back stem and leaf diagrams may be required. Drawing of histograms, stem and leaf diagrams or box plots will not be the direct focus of examination questions.S1
  7 resources
• 2.2Measures of location – mean, median, mode. Calculation of mean, mode and median, range and interquartile range will not be the direct focus of examination questions. Students will be expected to draw simple inferences and give interpretations to measures of location and dispersion. Significance tests will not be expected. Data may be discrete, continuous, grouped or ungrouped. Understanding and use of coding.S1
  8 resources
• 2.3Measures of dispersion – variance, standard deviation, range and interpercentile ranges. Simple interpolation may be required. Interpretation of measures of location and dispersion.S1
  5 resources
• 2.4Skewness. Concepts of outliers. Students may be asked to illustrate the location of outliers on a box plot. Any rule to identify outliers will be specified in the question.S1
  6 resources

1. Probability

• 3.1Elementary probability.S1
  5 resources
• 3.2

  Sample space. Exclusive and complementary events. Conditional probability.:

  • Understanding and use of P(A′) = 1 − P(A), P(A ∪ B) = P(A) + P(B) − P(A ∩ B), P(A ∩ B) = P(A) P(B | A).

  S1
  7 resources
• 3.3

  Independence of two events.:

  • P(B|A) = P(B), P(A|B) = P(A), P(A ∩ B) = P(A) P(B).

  S1
  3 resources
• 3.4Sum and product laws. Use of tree diagrams and Venn diagrams. Sampling with and without replacement.S1
  8 resources

1. Correlation and regression

• 4.1Scatter diagrams. Linear regression. Calculation of the equation of a linear regression line using the method of least squares. Students may be required to draw this regression line on a scatter diagram.S1
  9 resources
• 4.2

  Explanatory (independent) and response (dependent) variables. Applications and interpretations.:

  • Use to make predictions within the range of values of the explanatory variable and the dangers of extrapolation. Derivations will not be required. Variables other than x and y may be used. Linear change of variable may be required.

  S1
• 4.3The product moment correlation coefficient, its use, interpretation and limitations. Derivations and tests of significance will not be required.S1
  5 resources

1. Discrete random variables

• 5.1The Normal distribution including the mean, variance and use of tables of the cumulative distribution function. Knowledge of the shape and the symmetry of the distribution is required. Knowledge of the probability density function is not required. Derivation of the mean, variance and cumulative distribution function is not required. Interpolation is not necessary. Questions may involve the solution of simultaneous equations.S1
  6 resources
• 5.2

  The probability function and the cumulative distribution function for a discrete random variable.:

  • Simple uses of the probability function p(x) where p(x) = P(X = x). Use of the cumulative distribution function: F(x₀) = P(X x₀) = ∑p(x). x x₀

  S1
  3 resources
• 5.3

  Mean and variance of a discrete random variable.:

  • Use of E(X), E(X²) for calculating the variance of X. Knowledge and use of E(aX + b) = aE(X) + b, Var(aX + b) = a² Var(X).

  S1
  4 resources
• 5.4The discrete uniform distribution. The mean and variance of this distribution.S1
  3 resources