Patterns, Algebra and Problem Solving
What the exam tests
Patterns, algebra and problem solving tests number sequences, simple algebraic expressions and equations, and word problems that must be translated into number sentences.
Core rules
- In a sequence, find the rule by comparing consecutive terms. A constant difference means add or subtract the same number each time.
- Use a letter for an unknown, for example let x be the number of boxes.
- Solve an equation by doing the same operation to both sides. Undo addition with subtraction, and multiplication with division.
- Form an equation from the words, then solve it and check the answer in the original problem.
- Show the operation signs and keep the equals sign balanced.
Worked example
Solve 3x + 7 = 25. Subtract 7 from both sides: 3x = 18. Divide both sides by 3: x = 6. Check: 3 × 6 + 7 = 18 + 7 = 25, which is correct.
Traps that cost marks
Do not guess the next term without finding the rule; a sequence can look simple but change. When solving, undo operations in reverse order: deal with the added 7 before dividing by 3. Do not drop the variable before the answer is found. In word problems, check the units and whether the question asks for the unknown or for a related total. Always substitute back to check.