National 5 Maths: Equations and Inequations in Context

Many of the longer questions on both National 5 Mathematics papers start from a paragraph of words rather than an equation. The course asks you to construct simultaneous equations from text and solve them algebraically or graphically, to work with linear equations and inequations whose coefficients are fractions, and to use reasoning skills: interpreting a situation, choosing a strategy and explaining a solution in context. This material trains those skills together.

The quiz has twelve questions. The first pair turns a description of cinema tickets into a pair of equations and then solves them. Others ask what the crossing point of two straight-line graphs represents, when two phone plans cost the same, how many 50p coins are in a jar of 30 coins worth £22, and which of two plumbers is cheaper for a longer job once their graphs have crossed. Two equations and two inequations have fractions to clear, one of them with a negative coefficient where the inequality sign has to be reversed. A taxi question asks for the greatest whole number of miles within a budget, and a reasoning question checks what happens to a price after a 20 per cent rise followed by a 20 per cent fall. The wrong options follow the usual slips: swapping the values, forgetting to reverse the sign, rounding the wrong way and working a second percentage from the original amount.

The flashcards cover forming equations from words, the elimination and substitution methods, the graphical solution as the point of intersection, clearing fractions with the lowest common multiple, reversing the inequality sign, checking an answer in the context, writing a concluding sentence, and deciding which of two pricing plans is cheaper.

The printable written work has eight longer problems to answer by hand: café prices and hotel prices from two statements each, an intersection of two lines with a comment on graphical accuracy, an equation and an inequation with fractions, two gym memberships compared over a year, two ways of giving a pay rise, and a pupil's mistake with a negative coefficient to find and correct. Each ends with a sentence in context, which is how the reasoning marks are earned.

In the oral practice exam an examiner asks one question at a time, describes each situation in words, asks you to explain what your answer means, and ends with brief feedback. The material suits S4 pupils preparing for National 5 and extends the category's practice on relationships.

• Construct a pair of simultaneous equations from a description and solve them
• Interpret the point of intersection of two straight-line graphs
• Solve linear equations with fractional coefficients
• Solve linear inequations, reversing the sign when multiplying or dividing by a negative number
• Compare two options in context and explain which is better and when
• Explain a solution and relate it to the context

Practice material written by Zestly, based on the National 5 Mathematics course specification (Qualifications Scotland, formerly SQA; version 3.0, May 2023), algebraic skills (linear equations and inequations, simultaneous equations constructed from text, graphical and algebraic solution) and reasoning skills.