JHS Mathematics Summary Notes: Key Formulas, Rules, and Definitions for BECE

Subject: Mathematics | Level: JHS (Basic 7 – 9) | Type: Summary Notes / Revision Guide | Purpose: BECE Preparation

These summary notes cover the most important Mathematics formulas, rules, and definitions for the JHS BECE examination. Use them for quick revision. Always study the full lesson notes for deeper understanding.

Number and Numeration

HCF = Highest Common Factor (largest number that divides exactly into two or more numbers)
LCM = Lowest Common Multiple (smallest number that two or more numbers divide into exactly)
A prime number has exactly two factors: 1 and itself. First ten prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
To round: look at the next digit; if 5 or more, round up; if less than 5, leave unchanged
Standard form: A × 10ⁿ where 1 ≤ A < 10 and n is an integer (e.g. 3,400 = 3.4 × 10³)
Percentage increase = (Increase ÷ Original) × 100
Percentage decrease = (Decrease ÷ Original) × 100

Fractions and Decimals

To add/subtract fractions: find the LCM of the denominators first
To multiply fractions: multiply numerators, multiply denominators
To divide fractions: multiply by the reciprocal of the second fraction
To convert fraction to decimal: divide numerator by denominator
To convert decimal to fraction: write over appropriate power of 10 and simplify

Ratio and Proportion

Ratio a:b means for every a parts, there are b parts
To share GHS X in the ratio a:b: Total parts = a + b; First share = (a/(a+b)) × X
Direct proportion: as one quantity increases, the other increases at the same rate
Inverse proportion: as one quantity increases, the other decreases at the same rate

Algebra

Like terms: same variable and same power can be added or subtracted
To solve a linear equation: isolate the variable by performing the same operation on both sides
Always check your answer by substituting back into the original equation
Difference of two squares: a² – b² = (a + b)(a – b)
Perfect square: (a + b)² = a² + 2ab + b²
Quadratic formula: x = (-b ± √(b² – 4ac)) / 2a
When solving inequalities: if you multiply or divide by a negative number, reverse the inequality sign

Indices (Laws of Indices)

aᵐ × aⁿ = aᵐ⁺ⁿ (same base: add powers when multiplying)
aᵐ ÷ aⁿ = aᵐ⁻ⁿ (same base: subtract powers when dividing)
(aᵐ)ⁿ = aᵐⁿ (power of a power: multiply)
a⁰ = 1 (any non-zero number raised to the power 0 equals 1)
a⁻ⁿ = 1/aⁿ (negative index means reciprocal)
a^(1/n) = nth root of a

Geometry and Measurement

Angles

Angles on a straight line add up to 180°
Angles at a point add up to 360°
Vertically opposite angles are equal
Alternate angles (Z-angles) are equal (parallel lines)
Co-interior (C-angles) add up to 180°
Sum of interior angles of a polygon = (n – 2) × 180°, where n = number of sides

Triangles

Sum of angles in a triangle = 180°
Exterior angle of a triangle = sum of the two non-adjacent interior angles
Pythagoras theorem (right-angled triangle): a² + b² = c² where c is the hypotenuse

Area and Perimeter

Rectangle: Area = l × w; Perimeter = 2(l + w)
Triangle: Area = ½ × base × height
Circle: Area = πr²; Circumference = 2πr (use π = 22/7 or 3.14)
Trapezium: Area = ½(a + b)h where a and b are the parallel sides
Parallelogram: Area = base × height

Volume and Surface Area

Cuboid: Volume = l × w × h; Surface Area = 2(lw + lh + wh)
Cylinder: Volume = πr²h; Curved Surface Area = 2πrh; Total Surface Area = 2πr(r + h)
Cone: Volume = ⅓πr²h
Sphere: Volume = 4/3 πr³; Surface Area = 4πr²
Prism: Volume = Cross-sectional area × length

Statistics

Mean = Sum of all values ÷ Number of values
Median = Middle value when data is arranged in order; if even count, average the two middle values
Mode = The value that appears most frequently
Range = Highest value – Lowest value
To find mean from a frequency table: Mean = Σ(fx) ÷ Σf

Probability

Probability of an event = Number of favourable outcomes ÷ Total number of possible outcomes
Probability always lies between 0 (impossible) and 1 (certain)
P(A) + P(not A) = 1, so P(not A) = 1 – P(A)
For mutually exclusive events: P(A or B) = P(A) + P(B)
For independent events: P(A and B) = P(A) × P(B)

Vectors

A vector has both magnitude (size) and direction
Column vector: (x over y) means x units horizontally, y units vertically
To add vectors: add corresponding components
Magnitude of vector (x over y) = √(x² + y²)
Translation: every point moves the same distance in the same direction

Bearings

Bearings are measured clockwise from North
Always given as a three-digit number (e.g. 045°, 270°)
North = 000°, East = 090°, South = 180°, West = 270°

These summary notes are original content prepared by Education Always for BECE revision purposes only. They are not an official GES or WAEC document.

Related lessons: Browse the JHS Mathematics section for detailed lessons on each of these topics.