How each topic is examined in 4WM1H/01

Decimals

Converting recurring decimals to fractions with algebra (for example 0.45 recurring = 5/11), writing fractions as recurring decimals, and knowing which fractions terminate (denominators whose only prime factors are 2 and 5).

Fractions and percentages

Calculations with mixed numbers showing every step (for example 3⅔ × 2 4/7), fraction-of-an-amount problems worked backwards, writing one quantity as a percentage of another, and ordering fractions, decimals and percentages.

Ratio, proportion and money

In Unit 1 this is everyday number: money, time and metric units, and currency conversion with an exchange rate. Ratio sharing and proportion are tested in Unit 2.

Surds and powers

Simplifying surds such as √72 = 6√2, adding and expanding surds, rationalising denominators, negative, zero and fractional indices, index laws with algebra, and writing numbers as a power of 2 or 3.

Degree of accuracy

Rounding to significant figures, estimating by rounding to 1 significant figure, error intervals, and upper and lower bounds in calculations, including division (largest ÷ smallest).

Set language, notation and Venn diagrams

Listing members of sets, n(A), complements, set-builder notation, shading regions, and two- and three-set Venn diagram problems in context.

Algebraic manipulation

Expanding two or three brackets, factorising (including ax² + bx + c and the difference of two squares), simplifying and adding algebraic fractions, substitution and completing the square, including the form a − b(x + c)².

Linear equations

Equations with brackets, fractions or the unknown in a denominator, and forming equations from angles, perimeters and costs.

Linear graphs

Gradient from two points, the equation of a line through two points, parallel and perpendicular lines (often in the form ay = bx + c), midpoints and distance–time graphs.

Quadratic equations and graphs

Solving by factorising, by the formula (to 2 decimal places or 3 significant figures) and by completing the square (exact answers with surds), problems in context, turning points, cubic tables of values and recognising cubic, reciprocal, sine, cosine and tangent graphs.

Compound measures

Speed, density and pressure (the pressure formula is given), with unit changes such as km/h to m/s, minutes to hours and cm² to m².

Geometry of shapes

Angles with parallel lines, triangles and quadrilaterals, the exterior angle of a triangle, isosceles triangles, and giving the correct geometric reason.

Perimeter, area and sectors

Trapezia, circles, semicircles and composite shapes, area unit conversion, arc length, sector area and perimeter, and the area of a segment (degrees only, no radians).

Pythagoras' theorem and trigonometry

Finding missing sides and angles in right-angled triangles, distances between coordinates, and angles of elevation and depression.

Advanced trigonometry

The sine rule (including the obtuse case), the cosine rule for sides and angles, area = ½ab sin C, Pythagoras in 3D and the angle between a line and a plane.

Graphical representation of data

Histograms with unequal class widths (frequency = frequency density × class width, and estimates from part of a class) and two-way tables.

Probability

Probability tables that add to 1, relative and expected frequency, sample spaces, tree diagrams, independent events, selections without replacement, “at least one” and conditional probability from Venn diagrams and tables.