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BGCSE Mathematics

Every topic on the syllabus, worked examples, and past-paper style questions with mark-earning steps shown.

Topic 1

Number & Numeration

Types of number

Every number you'll work with in BGCSE Maths belongs to one or more number sets, and exam questions often hinge on knowing which set a number belongs to. Natural numbers are the counting numbers (1, 2, 3…). Integers extend that to include zero and negatives. Rational numbers are anything that can be written as a fraction — including terminating and recurring decimals. Irrational numbers cannot: π and √2 are the classic examples.

Real numbers Rational Integers Natural 1, 2, 3… ½, 0.75 π, √2
Every natural number is also an integer; every integer is also rational — but not every real number is rational.

Prime factorisation

Any whole number greater than 1 can be broken down into a unique product of prime numbers — this is the foundation for finding HCF (Highest Common Factor) and LCM (Lowest Common Multiple), both of which show up regularly in exam questions on fractions and ratio.

  • To find the HCF of two numbers, list the prime factors each number shares, and multiply them together.
  • To find the LCM, take every prime factor that appears in either number, using the highest power of each.
Worked example Find the HCF and LCM of 60 and 84.

60 = 2² × 3 × 5
84 = 2² × 3 × 7

HCF = 2² × 3 = 12 (the factors common to both)
LCM = 2² × 3 × 5 × 7 = 420 (every factor, highest power)

Rounding and significant figures

Botswana exam papers frequently ask for an answer "correct to 3 significant figures" rather than a fixed number of decimal places — the two are easy to confuse. Significant figures count from the first non-zero digit, regardless of where the decimal point falls, so 0.004512 to 2 s.f. is 0.0045, while 4512 to 2 s.f. is 4500.

Topic 2

Algebra

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Topic 3

Geometry

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Topic 4

Mensuration

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Topic 5

Trigonometry

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Topic 6

Statistics & Probability

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Topic 7

Graphs & Functions

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Flashcards

Key Terms

30 cards covering every topic below.

TermNatural numbers
DefinitionThe counting numbers: 1, 2, 3…
TermIntegers
DefinitionNatural numbers extended to include zero and negative numbers.
TermRational numbers
DefinitionAny number that can be written as a fraction — including terminating and recurring decimals.
TermIrrational numbers
DefinitionNumbers that cannot be written as a fraction — e.g. π and √2.
TermHCF (Highest Common Factor)
DefinitionThe largest number that divides exactly into two or more numbers.
TermLCM (Lowest Common Multiple)
DefinitionThe smallest number that two or more numbers divide into exactly.
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TermExpression
DefinitionA mathematical phrase with no equals sign, like 3x + 5 — it simplifies but doesn't "solve."
TermEquation
DefinitionA mathematical statement with an equals sign, like 3x + 5 = 20 — solved to find the value of the unknown.
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TermVertically opposite angles
DefinitionThe equal angles formed facing each other when two straight lines cross.
TermCorresponding angles
DefinitionEqual angles in the same position at each intersection when a line crosses two parallel lines (an "F" shape).
TermAlternate angles
DefinitionEqual angles on opposite sides of a line crossing two parallel lines (a "Z" shape).
TermCo-interior angles
DefinitionAngles on the same side of a line crossing two parallel lines, which add up to 180°.
TermEquilateral triangle
DefinitionA triangle with all three sides and all three angles equal (each 60°).
TermIsosceles triangle
DefinitionA triangle with two equal sides, and the two angles opposite those sides also equal.
TermRadius
DefinitionThe distance from the centre of a circle to its edge.
TermDiameter
DefinitionA straight line from edge to edge through the centre of a circle — twice the radius.
TermTangent
DefinitionA straight line that touches a circle at exactly one point.
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TermPerimeter
DefinitionThe total distance around the outside of a shape.
TermArea
DefinitionThe amount of space a shape covers.
TermVolume
DefinitionThe amount of space a 3D shape occupies, measured in cubic units.
TermSurface area
DefinitionThe total area of all the outer faces of a 3D shape.
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TermSOHCAHTOA
DefinitionA mnemonic for the three trig ratios: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.
TermHypotenuse
DefinitionThe longest side of a right-angled triangle, always opposite the right angle.
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TermMean
DefinitionThe sum of all values divided by how many there are.
TermMedian
DefinitionThe middle value once data is arranged in order (or the average of the two middle values).
TermMode
DefinitionThe value that appears most often in a data set.
TermProbability
DefinitionA number between 0 (impossible) and 1 (certain) describing how likely an event is.
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Termy = mx + c
DefinitionThe general equation of a straight line, where m is the gradient and c is the y-intercept.
TermGradient
DefinitionHow steep a line is, and whether it rises or falls left to right — calculated as "rise over run."
Termy-intercept
DefinitionThe point where a line crosses the y-axis, when x = 0.
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Number & Numeration

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Topic 2

AlgebraAlgebra

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Topic 3

GeometryGeometry

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Topic 4

MensurationMensuration

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Topic 5

TrigonometryTrigonometry

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Topic 6

Statistics & ProbabilityStatistics & Probability

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Topic 7

Graphs & FunctionsGraphs & Functions

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Mock Exams & Past Papers

Full Papers

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