Mathematics
Core concepts
Revise algebra, indices, logarithms, equations, and inequalities. Study trigonometry: sine, cosine, tangent rules, radian measure, and identities. Learn coordinate geometry, straight lines, circles, and conic sections. Understand differentiation and integration with applications to rates of change, maxima and minima, areas, and volumes. Study matrices, determinants, and their use in solving linear systems. Learn statistics: mean, median, mode, standard deviation, probability, and basic distributions. Understand complex numbers and their arithmetic.
Common traps
Questions often confuse the sine rule with the cosine rule, or degrees with radians. Watch for sign errors when differentiating or integrating. In statistics, distinguish population standard deviation from sample standard deviation. Ensure angles are in the correct unit before using trigonometric functions.
Worked example
Differentiate y = 3x² + 5x − 2. dy/dx = 6x + 5. Setting this to zero gives x = −5/6, which is the turning point. Rule of thumb: differentiate, set the derivative to zero, then check the second derivative to classify the point.
Study approach
Practise a mixed set of algebra, trigonometry, calculus, and statistics problems. Show every step and check units and signs.