Maths for Computing

Be able to apply matrix methods.

Matrices: method of representing ordered data, relationship with computer program variable arrays, index notation.

Operations: add, subtract, scalar multiplication, multiply two matrices, inverse, transpose.

Techniques: solving simultaneous linear equations, vector transformation and rotation, maps and graphs.

Assessment Criteria

• 1.1

  Show how matrices can be used to represent ordered data

• 1.2

  Perform add, subtract and scalar multiplication operations on a matrix.

• 1.3

  Multiply two matrices.

• 1.4

  Find the inverse and transpose of a matrix.

• 1.5

  Apply matrix techniques to solve simultaneous linear equations.

Be able to apply sequences and series, probability and recursion

Sequences and series: nth term of a sequence, generation of recurrence relationship, arithmetic and geometric sequences and series, sum to n terms of an arithmetic and geometric series, sum to infinity of a geometric series, Σ notation.

Probability: events e.g. union, intersection, complementary, mutually exclusive, independent, space diagrams e.g. sum of scores when two dice are thrown, visualising events using Venn diagrams, tree diagrams.

Recursion: series e.g. Fibonacci, factorial, natural numbers, termination condition, recursive algorithms e.g. factorial, quicksort, binary search

Assessment Criteria

• 2.1

  Apply sequence and series techniques to solve problems.

• 2.2

  Apply probability and recursion techniques to solve problems.

Be able to apply number systems

Number systems: binary, octal, denary and hexadecimal, conversion between number systems, basic operations e.g. addition, division, multiplication, subtraction on number systems.

Uses in computing: ASCII code (binary), MIME (hex), file permissions in Unix (octal), IP addressing, subnet addressing, subnet masking, class addressing, domain routing, etc.

Assessment Criteria

• 3.1

  Explain how number systems are used in computing.

• 3.2

  Perform basic operations on number systems.

• 3.3

  Perform conversion operations between number systems.

Be able to interpret data.

Gathering data: methods of gathering quantity data e.g. measurements, questionnaires, surveys, extraction of required information from raw data, limitations of data gathered.

Representing data: comparing data sets using back-to-back stem and leaf diagrams e.g. pulse rates of students before and after exercise, mean, median, mode, interquartile ranges, histograms, variance, standard deviation.

Interpreting data: e.g. analysing summary data, proving hypotheses, identifying trends and patterns.

Assessment Criteria

• 4.1

  Gather data for a defined purpose.

• 4.2

  Interpret trends and patterns in data.