MATSEC SEC Mathematics study plan

Apply the four operations correctly to integers, fractions, decimals and percentages, including mixed numbers and negative numbers, without a calculator.

Convert fluently between fractions, decimals and percentages, and order a mixed list of such values from smallest to largest.

Use the laws of indices for positive, negative and zero powers, and express numbers in standard form and back again.

Solve problems involving ratio and direct proportion, including sharing an amount in a given ratio and scaling recipes or maps.

Simplify algebraic expressions by collecting like terms, expanding single and double brackets, and factorising common factors and quadratics.

Rearrange formulas to change the subject, including cases where the subject appears twice.

Solve linear equations and simultaneous linear equations by elimination and by substitution, and check solutions by substitution.

Construct and solve inequalities, and represent their solution sets on a number line.

Generate and use the nth term of linear and simple quadratic sequences, and identify whether a sequence is arithmetic, geometric or neither.

Plot and interpret straight-line graphs, calculate gradient and intercept, and find the equation of a line from two points or from a graph.

Solve quadratic equations by factorising and by using the quadratic formula, and sketch the corresponding parabola showing intercepts and turning point.

Set up and solve word problems by forming an equation or a pair of simultaneous equations from the given information.

Use Pythagoras' theorem and the trigonometric ratios to find missing sides and angles in right-angled triangles, choosing the correct ratio each time.

Compute the area and perimeter of triangles, parallelograms, trapezia and compound shapes, and the circumference and area of circles and sectors.

Calculate the volume and surface area of prisms, cylinders, pyramids, cones and spheres, keeping units consistent.

Convert between units of length, area and volume, including metric-imperial equivalents where they are given.

State and use the angle facts for straight lines, triangles, parallel lines, polygons and circles, giving a reason for every step.

Apply the conditions for congruent and similar triangles, and use similarity ratios to find unknown lengths and areas.

Perform constructions and loci accurately with ruler and compasses, including perpendicular bisectors, angle bisectors and simple loci.

Describe and perform transformations of shapes: reflection, rotation, translation and enlargement, including fractional and negative scale factors.

Read and interpret scales on maps and drawings, and solve bearings problems by drawing and by calculation.

Calculate the mean, median, mode and range for raw and grouped data, and explain how an outlier or a grouped estimate affects each measure.

Construct and interpret bar charts, pie charts, histograms with unequal class widths and cumulative frequency curves.

Compute probabilities for single and combined events using sample space diagrams, tree diagrams and Venn diagrams, including conditional cases.

Interpret scatter graphs, describe correlation, and draw and use a line of best fit to make predictions, commenting on reliability.

Compare two data sets using averages and measures of spread, and justify which average is most appropriate in a given context.

Distinguish between experimental and theoretical probability, and estimate probability from relative frequency data.

Critique misleading graphs and statistical claims, identifying the specific feature that distorts the message.

Complete two full past-paper-style papers under strict timing, allocating roughly one minute per mark and leaving time to check.

Mark both papers against a mark scheme and classify every lost mark as method, accuracy, misread or time.

Re-work every incorrect question from scratch without looking at the original attempt, then re-test those topics.

Memorise and rehearse a final revision card of formulas and angle reasons that are not given in the exam.