Summary
Highlights
Before starting the exam, review multiplication tables as calculators are not allowed. Read questions carefully to understand the requirements, show all working steps for partial credit, and manage your time effectively by not dwelling on challenging questions, returning to them later if necessary.
Remember the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction) for calculation order. For adding/subtracting fractions, ensure denominators are the same. For multiplying fractions, multiply numerators and denominators directly. For division, multiply by the reciprocal of the second fraction. Also, correctly identify when terms can be cancelled in expressions, only during multiplication or division, not addition or subtraction.
When multiplying decimals, perform the multiplication as usual and then count the total number of decimal places in the original numbers to place the decimal point in the answer. For dividing decimals, convert them to fractions with common denominators or shift decimal points to make the divisor a whole number. When adding or subtracting decimals, align the decimal points before performing the operation.
To make 'x' the subject of an equation, isolate 'x' by moving other terms across the equals sign and performing inverse operations. Understand exponent rules: a square root is power of 1/2, a cube root is power of 1/3, and so on. When multiplying exponents with the same base, add the powers. When dividing, subtract the powers. Negative exponents indicate a reciprocal (e.g., x^-2 = 1/x^2).
To rationalize a denominator containing a square root (e.g., 2 / (√6 - 1)), multiply both the numerator and denominator by the conjugate of the denominator (e.g., √6 + 1). This eliminates the square root from the denominator.
Recall key geometry formulas: Perimeter is the sum of all sides. Area of a square is s², rectangle is length × breadth, triangle is ½ base × height (or ½ab sin C). For 3D shapes, volume of a cube is s³, cuboid is length × breadth × height. For a cylinder, volume is πr²h and total surface area is 2πrh + 2πr². For a sphere, volume is 4/3πr³ and surface area is 4πr². For a hemisphere, halve the sphere's volume and add the area of the circular base to half the sphere's surface area. For a pyramid, volume is 1/3 × base area × height, and total surface area is base area + ½ × base perimeter × slant length.
When converting from a big unit to a small unit, multiply (e.g., kg to g). When converting from a small unit to a big unit, divide (e.g., cents to dollars). For similar shapes, if lengths are in a ratio, areas are in the square of that ratio, and volumes are in the cube of that ratio. Ensure units are consistent during calculations.
Probability is the chance of an event occurring. The probability of an event not happening is 1 minus the probability of it happening. In probability trees, 'and' means multiply probabilities along a path, and 'or' means add probabilities of different paths.
Solve inequalities like normal algebraic equations. However, if you multiply or divide both sides by a negative number, remember to reverse the inequality sign.