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GABECE study materials
GABECE study resources

GABECE: Mathematics: Number, Algebra, Geometry and Statistics

GABECE · Work through your exam, one topic at a time.

All guide sections

Mathematics: Number, Algebra, Geometry and Statistics

The GABECE Mathematics paper tests number and numeration, algebraic processes, geometry and measurement, and statistics and probability. Paper 1 checks speed and accuracy; Paper 2 rewards correct method, clear working, and correct units, even when the final answer is wrong.

Core rules and concepts

  • Follow BODMAS: brackets, order, division and multiplication, addition and subtraction.
  • Integers: same signs multiply or divide to give positive; different signs give negative. Subtracting a negative is adding.
  • Fractions and decimals: use a common denominator; line up decimal points; know place value.
  • Percentage: part divided by whole times 100. For increase or decrease, find the change, divide by the original, then multiply by 100.
  • Ratio and proportion: simplify ratios; for direct proportion, both quantities increase together; for inverse proportion, one increases as the other decreases.
  • Algebra: collect like terms, expand brackets by multiplying every term, and solve linear equations by doing the same operation to both sides.
  • Geometry: angles on a straight line sum to 180 degrees; angles in a triangle sum to 180 degrees; polygon angle sum is (n minus 2) times 180 degrees; circle circumference is 2 pi r and area is pi r squared.
  • Measurement: convert units before calculating. 1 m = 100 cm, 1 m squared = 10,000 cm squared, and 1 litre = 1,000 cm cubed.
  • Statistics: mean is total divided by count; median requires ordered data; mode is the most frequent value.

Worked example

Solve 3(2x minus 1) = 4x + 9. Expand the bracket: 6x minus 3 = 4x + 9. Subtract 4x from both sides: 2x minus 3 = 9. Add 3 to both sides: 2x = 12. Divide by 2: x = 6. Check: left side is 3(12 minus 1) = 33; right side is 24 + 9 = 33. The check confirms the answer.

Traps that cost marks

  • Multiplying only the first term inside a bracket.
  • Forgetting to change signs when moving terms across the equals sign.
  • Using diameter instead of radius in circle formulas.
  • Mixing cm with cm squared or litres with cm cubed.
  • Rounding too early in a multi-step calculation.
  • Giving a numerical answer without units in measurement questions.