Botswana BGCSE General Mathematics 1236 study guide
Botswana BGCSE General Mathematics 1236 · Work through your exam, one topic at a time.
The Botswana General Certificate of Secondary Education (BGCSE) is the school-leaving qualification awarded by the Botswana Examinations Council (BEC) at the end of senior secondary schooling. General Mathematics, subject 1236, is one of the subjects examined within that certificate. The Botswana BGCSE General Mathematics 1236 study guide has 7 sections and about 2,353 words.
01Number and Numeration
You need fluent, accurate work with integers, fractions, decimals and percentages, and the ability to move between them: 0.35 = 35% = 7/20. Revise the four operations on fractions (common denominators for addition and subtraction; cancel diagonally before multiplying), rounding to a given number of decimal places or significant figures, and estimation to check answers.
337 words, about 2 min02Sets, Functions and Relations
Know the language: element, subset, universal set (xi), complement (A'), union (A union B), intersection (A intersect B), empty set and set-builder notation. A set with n elements has 2^n subsets.
324 words, about 2 min03Algebra
Be fluent in simplifying expressions by collecting like terms, multiplying out brackets (including double brackets), and factorising: common factors, difference of two squares (a^2 - b^2 = (a-b)(a+b)) and quadratic trinomials. Handle algebraic fractions by finding a common denominator and cancelling only factors, never terms.
322 words, about 2 min04Geometry
Learn angle facts and use them in chains of reasoning: angles on a straight line (180 degrees), at a point (360 degrees), vertically opposite, and in parallel lines (alternate, corresponding and co-interior angles). Triangle angle sum is 180 degrees; the exterior angle equals the sum of the two opposite interior angles.
346 words, about 2 min05Mensuration
Know the area formulas for rectangles, triangles (half base times height), parallelograms, trapeziums (half the sum of parallel sides times height) and circles (pi r^2), and the circumference formula C = 2 pi r. For sectors, arc length = (theta/360) x 2 pi r and sector area = (theta/360) x pi r^2.
351 words, about 2 min06Statistics and Probability
Be able to read and draw bar charts, pie charts, line graphs, histograms and scatter diagrams. For pie charts, each category's angle = (frequency / total) x 360 degrees.
357 words, about 2 min07Trigonometry
In right-angled triangles use Pythagoras and SOHCAHTOA: sin theta = opposite/hypotenuse, cos theta = adjacent/hypotenuse, tan theta = opposite/adjacent. Find sides by multiplying, and angles by using the inverse functions.
316 words, about 2 min