Glossary of Exam Terminology
There are some terms and expressions that occur frequently in examination questions and that carry particular meanings and expectations during the marking process. The principal ones are briefly explained here with a view to helping students in their answering and to facilitating understanding of published marking schemes.
[Source: Department of Education and Science, Guidelines for Teachers – Junior Cert Maths]
To “construct” means to draw according to specific requirements, usually with instruments such as ruler, compass and protractor. Accurate measurements are required and construction lines such as arcs should be shown clearly. Free-hand drawings are not acceptable. The marking of constructions involves measuring of the candidate’s work by examiners. For each measurement, a small tolerance is allowed without penalty.
“Draw the graph…./ Graph….”
Graphs are likely to be required in questions on co-ordinate geometry, statistics and functions. Where relevant, they should be presented in solution boxes, in the spaces in which gridlines are provided – or, if necessary, on separate sheets of graph paper. They should be distinctly drawn and sufficiently large to ensure clarity. Axes should be perpendicular and clearly labelled. Appropriate scales should be chosen and indicated. Graduations should be marked clearly on both axes. Plotted points should be accurately positioned and identified. Where the points are to be joined, this should be done in the appropriate manner; for example, a smooth curve is necessary for a quadratic function whereas line segments are required for a trend graph.
It should be noted that an ogive (cumulative frequency curve) is a smooth curve. In examination answers it should always start on the X-axis, since its initial point will represent the value below which it is known there are no data.
“Estimate…./ Show how to calculate an approximate value of ….”
Questions involving estimation or approximation require candidates to use their own judgement regarding the level of rounding that is appropriate in order to a value close enough to the exact calculation to be useful. In a solution box, the layout of solutions may be prompted by the provision of appropriate blank spaces, and candidates should be alert to this source of guidance. Examiners will focus on the depth of understanding of the approximation process displayed by candidates as well as on their ability to perform the mechanical steps. This means that flexibility will be exercised in the marking of the numerical results presented and that usually a specific estimate will not be required for full marks. For example, two acceptable estimates of
as either approach is clearly a sound guide to arriving at the actual value (2.425307…).
Find the value of.
“Give your answer in the form….” “Express in the form”
For full credit, candidates must adhere closely to instructions of this type. For example, an answer of 1.87 will be penalised if the question requests a result to one place of decimals. In the same way, 25 will not suffice if candidates are told to give the answer in the form 5n.
The word “hence” is generally used to connect two tasks which the candidate is expected to perform, one after the other, with the outcome of the first helping the second. It points candidates to the method or approach which examiners expect. For example, consider:
It is important to note that when “hence” is used in this way, candidates may be penalised if the first result is not used in order to perform the second task.
More commonly, the phrase “hence, or otherwise” is used. This indicates that any approach of the candidate’s choosing can be taken to the second task. However, a helpful lead-in is always provided by the first part, and candidates usually fare better if they follow this rather than make a fresh start at the second part.
In accordance with the syllabus, the idea of proof will be addressed only in higher-level questions. Candidates may be required to prove the theorems marked with asterisks in the syllabus as well as “cuts” arising from the results (theorems and “facts”).
All the steps in proofs must be written down in logical order. Each assertion in the proof should be accompanied by a reason.
Proofs should be accompanied by diagrams, wherever they serve to clarify the argument being presented. However, it should be noted that information marked on diagrams will not be accepted as a substitute for written steps.
Normally, when students are asked to show a result, any correct mathematical method is awarded full marks assuming that it is properly applied. One exception is that measurement from diagrams using a ruler, protractor, or other instrument is not accepted unless this approach is specifically requested. In cases where a particular method is required, the question will give clear directions – for example, “Show, by calculation, that |ab|=|bc|” – and these directions must be followed.
Carry out a task such as removing brackets, multiplying, dividing and make sure the result is as simple as possible. For example ; Simplify (3+2i)(4-i) =12-3i+8i-2i2) is not finished. 14+5i is the simplified answer.
When a sketch is required, diagrams are not expected to conform to specific measurements. Examiners will be assessing candidates’ intuitive feel for the task at hand. For example, in sketching images of shapes under transformations, examiners will be looking for evidence that the shape has the correct orientation and is in roughly the correct location.
“Use your graph to show that….”
To earn full marks, candidates must display evidence that they have extracted their answers from their graphs. It is not acceptable to use other methods of arriving at the required results even if the alternative methods are mathematically correct and accurately applied.
For example, candidates who successfully solve the equation 2×2 – 3x – 5 = 0 using the quadratic formula cannot be awarded marks if the instruction given is “Use your graph to estimate the roots of the equation 2×2 – 3x – 5 = 0”.
Verifying a solution of an equation in algebra involves substituting the value into the given equation and showing that the result is a true statement. It is important to note that solving the equation is not acceptable if verification is sought.