Numbers

4

Write numbers in standard form.

Understand upper and lower bounds

Use index notation and the index laws with negative and fractional powers (e.g. 4^-2 or 16^½)

Use algebraic methods to convert a recurring decimal to a fraction.           

Calculations

4

Recognise and use reciprocals.  

Use a calculator efficiently (see ‘Know Your Calculator’).

Algebra

4

Remember and use the index laws in algebra (e.g. x⁴ ÷ x² = x²  or x^-½ = ¹/_Öx ).

Square a linear expression such as (2x + 3)²,

Expand and simplify expressions such as (x – 1)(x + 4).

Establish identities such as a² – b² = (a + b)(a – b).       

Solve inequalities in two variables.

Change the subject of a formula.

Find the next term and the nth term of quadratic sequences (e.g. for 3, 9, 19, 33, ... the nth term is 2n² + 1).

Plot the graph of the inverse of a linear function.

Remember simple properties of quadratic functions.         

Plot graphs of simple quadratic and cubic functions, (e.g. y = x²,  y = 3x² + 4,  y = x³).

Shape, space and measures      

4

Show that two or more triangles are congruent.        

Explain why the perpendicular from the centre of a circle to the chord bisects the chord.

Understand the effects of enlargement on the area and volume of shapes.

Find points that divide a line in a given ratio.

Calculate the length of the line AB, given the coordinates of points A and B.

Remember that measurements given to the nearest whole unit may be inaccurate by up to one half of the unit in either direction.

Understand and use measures of speed (and other compound measures such as density or pressure).

Know and use the formulae for length of arcs and area of sectors of circles.

Begin to use sine, cosine and tangent in right-angled triangles to solve problems (trigonometry).

Discuss the difference between practical demonstration and proof.

Handling data

4

Identify possible sources of bias in surveys and plan how to minimise it.

Produce cumulative frequency tables and draw cumulative frequency graphs.           

Estimate the median, quartiles and interquartile range from a cumulative frequency graph.