# Sequences

## 4 files09/06/2016

(a) Term-to term rules and position-to-term rules (both linear and non-linear)

(b) Finding the nth term of linear sequences.

(c) Finding nth term of an oscillating sequence (e.g. 100th term of 6, 4, 1, 6, 4, 1, 6, ...) with application to last digit of powers (e.g. 3^100)# Number Theory

## 5 files30/11/2016

(a) Understand key terms such as perfect square, integer, positive integer, non-negative integers.

(b) Prime factorise a number and use to find the LCM, HCF of two numbers. Understand when numbers are 'coprime'.

(c) Know the divisibility laws from 3 to 11 and be able to break down into multiple divisibility rules for larger numbers. Use these rules to mentally prime factorise numbers rapidly and have a sense if a number is prime. (d) Find factors of a number using its prime factorisation (e.g. is 20 a factor of 2^{4}x 3 x 5^{3}?) and determine the number of factors of a number.

Extension: (i) Reason about divisibility on each side of an equation and of terms, and find integer solutions to linear equations (i.e. linear Diophantine equations).

(ii) Further uses of prime factorisations: (1) Squares and cubes (2) Trailing zeroes.# Area & Perimeter

## 4 files05/01/2017

(a) Find the perimeter and area of rectilinear shapes.

(b) Find the area of a triangle, trapezium, parallelogram.

(c) Find the area and circumference/perimeter of circles and fractions of circles (e.g. 1/2, 1/4).

(d) Appreciate strategies to find areas of composite shapes, by (i) adding areas (ii) subtracting areas, including appreciation of the 'frame' method and (iii) cutting/reforming areas.

(e) Appreciate that triangles have the same area if their base and height are the same, and compare sizes of triangles by considering the proportion of base/height.

(f) Find what fraction of a shape is shaded by splitting into congruent shapes.