Botswana BGCSE General Mathematics 1236 study plan
Botswana BGCSE General Mathematics 1236 · Give each week a clear focus.
8 weeks · About 6 hours per week
Number and Numeration (including fractions, decimals, percentages, ratio, proportion, indices and standard form)
Convert fluently between fractions, decimals and percentages, including recurring decimals and values greater than 1
Solve ratio and direct/inverse proportion problems, including sharing a quantity in a given ratio and scaling recipes
Apply percentage change, profit and loss, simple interest and discount to multi-step word problems
Estimate answers before calculating and correct every error in a timed set within 5 minutes of finishing
Your checkpoint
A 30-question calculator-free numeration paper completed in 45 minutes at 80% or better, with a written error log naming the cause of each mistake
Number and Numeration (including fractions, decimals, percentages, ratio, proportion, indices and standard form) & Sets, Functions and Relations
Apply the laws of indices to simplify products, quotients and powers of powers, including zero and negative indices
Express numbers in standard form and multiply or divide two numbers given in standard form
Use set notation (element of, subset, union, intersection, complement) to list and describe sets
Shade and interpret two-set and three-set Venn diagrams, including problems containing a 'neither' region
Your checkpoint
A one-page notation and formula sheet written from memory, plus 20 mixed indices, standard form and set questions scored at 85% or better
Sets, Functions and Relations
Distinguish a relation from a function using mapping diagrams and the vertical line test
Evaluate f(x) for given inputs and find the inverse of simple linear functions
Plot linear and quadratic graphs from a table of values and read off intercepts and turning points
State the domain and range of a function shown as a graph or a set of ordered pairs
Your checkpoint
Five hand-drawn graphs with their tables of values and a 15-question functions test scored at 80% or better
Algebra (expressions, equations, inequalities, sequences and graphs)
Expand brackets and factorise quadratic expressions of the form x squared plus bx plus c
Solve linear equations and linear inequalities, showing the solution set on a number line
Solve simultaneous linear equations by both elimination and substitution
Generate and continue arithmetic and geometric sequences and find the nth term of an arithmetic sequence
Your checkpoint
A 40-minute timed algebra paper scored at 75% or better, with all working shown
Geometry (angles, polygons, circles, constructions, transformations and vectors) & Mensuration (length, area, surface area and volume of plane and solid figures)
Calculate unknown angles in polygons and in parallel-line configurations, giving a reason for each step
Apply circle theorems, including angle in a semicircle, cyclic quadrilateral and tangent-radius, to find unknown angles
Construct an angle bisector and a perpendicular bisector using only ruler and compasses
Compute the perimeter and area of triangles, parallelograms, circles and composite shapes
Your checkpoint
A folder of six accurate constructions with construction arcs visible, plus 20 geometry and mensuration questions scored at 80% or better
Mensuration (length, area, surface area and volume of plane and solid figures) & Statistics and Probability (data handling, averages, display of data, chance)
Calculate the surface area and volume of prisms, cylinders, cones and spheres
Convert between units of length, area and volume, including cubic centimetres to litres
Compute the mean, median, mode and range from raw data and from a frequency table
Draw and interpret bar charts, pie charts and frequency polygons from a given data set
Your checkpoint
A one-page data project: collect 30 data points, present them in a frequency table and a suitable chart, and compute all four averages with one sentence of interpretation
Statistics and Probability (data handling, averages, display of data, chance) & Trigonometry (right-angled triangles, sine and cosine rules, bearings)
Assign probabilities from equally likely outcomes and apply the complement rule
Use sample space diagrams and tree diagrams to find the probability of two combined events
Apply Pythagoras' theorem and the sine, cosine and tangent ratios to find missing sides and angles in right-angled triangles
Solve two-dimensional problems involving angles of elevation and depression
Your checkpoint
A 25-question probability and right-triangle trigonometry test scored at 80% or better, with diagrams drawn for every word problem
Trigonometry (right-angled triangles, sine and cosine rules, bearings) & Number and Numeration (including fractions, decimals, percentages, ratio, proportion, indices and standard form) & Algebra (expressions, equations, inequalities, sequences and graphs)
Apply the sine rule, the cosine rule and the area formula half a b sine C to non-right-angled triangles
Solve three-figure bearing problems using clear sketches and, where required, a scale drawing
Redo ten questions each from the two lowest-scoring topics in earlier tests until both reach 90%
Complete a full past-paper-style mock under timed exam conditions without notes
Your checkpoint
A completed 2.5-hour mock paper with section scores recorded and an overall score of 70% or better
Milestones
Week 2: Score 80% or better on a 25-question mixed paper covering fractions, percentages, ratio, indices, standard form and sets, without a calculator
Week 4: Score 75% or better on a 40-question paper covering domains 1 to 3, and complete the algebra section within 40 minutes
Week 6: Produce all six constructions accurately and score 80% or better on a 30-question geometry, mensuration and statistics paper
Week 8: Complete the full mock paper within 2.5 hours and score 70% or better overall, with no domain below 60%