ZIMSEC O-Level Mathematics Revision & Mock Test

Learn: Fractions, decimals, percentages, ratio, standard form and indices.

Key rule: Use a common denominator; follow order of operations.

Worked example: 3/4 + 5/8 = 6/8 + 5/8 = 1 3/8.

Common mistake: Do not round too early.

Learn: Subsets, complements, unions, intersections and Venn diagrams.

Key rule: n(A union B)=n(A)+n(B)-n(A intersection B).

Worked example: 22+18-35 gives an intersection of 5.

Common mistake: Subtract the overlap once.

Learn: Profit, discount, tax, wages, hire purchase and interest.

Key rule: Simple interest I=PRT/100.

Worked example: $600 at 8% for 3 years earns $144; amount $744.

Common mistake: Interest and final amount are different.

Learn: Simplify, expand, factorise and solve equations, inequalities and sequences.

Key rule: Do the same operation to both sides.

Worked example: 3(x-2)=2x+5 gives x=11.

Common mistake: Watch signs when moving terms.

Learn: Angles, similarity, symmetry, bearings and circle theorems.

Key rule: Polygon interior sum=(n-2) x 180 degrees.

Worked example: A hexagon has interior sum 720 degrees.

Common mistake: Identify which angle rule applies.

Learn: Use sine, cosine and tangent in right triangles.

Key rule: SOH CAH TOA.

Worked example: Opposite 6 and adjacent 8 gives tan theta=0.75.

Common mistake: Label the triangle before choosing a ratio.

Learn: Perimeter, area, surface area and volume.

Key rule: Cylinder volume=pi r squared h.

Worked example: r=3 and h=5 gives 45pi cubic units.

Common mistake: Do not use diameter as radius.

Learn: Plot graphs, find gradients and model direct or inverse variation.

Key rule: For direct square variation y=kx squared.

Worked example: If y=20 at x=2, k=5; at x=3, y=45.

Common mistake: Not every direct variation is y=kx.

Learn: Tables, charts, mean, median, mode and range.

Key rule: Mean=total divided by frequency.

Worked example: 4,7,7,8,9 has mean 7.

Common mistake: Order data before finding the median.

Learn: Single and combined events, tables and tree diagrams.

Key rule: P(event)=favourable outcomes/total outcomes.

Worked example: 5 red, 3 blue, 2 green gives P(not blue)=7/10.

Common mistake: Use total outcomes as denominator.

Learn: Matrix operations, translation, reflection, rotation and enlargement.

Key rule: Add corresponding entries in equal-order matrices.

Worked example: [[2,1],[3,4]]+[[1,5],[0,2]]=[[3,6],[3,6]].

Common mistake: Matrix multiplication is not entry-by-entry.

Learn: Column vectors, addition, subtraction and scalar multiplication.

Key rule: Add corresponding components.

Worked example: (3,-1)+(-2,4)=(1,3).

Common mistake: Keep negative signs.

Learn: Gradient, midpoint, distance and straight-line equations.

Key rule: Midpoint=((x1+x2)/2,(y1+y2)/2).

Worked example: Midpoint of (-2,5) and (6,-3) is (2,1).

Common mistake: Average coordinates; do not subtract.

Learn: Units, scales, significant figures, bounds and error intervals.

Key rule: Nearest unit u means half u below and above.

Worked example: 8.4 cm nearest 0.1 has lower bound 8.35.

Common mistake: The upper bound is excluded.