IGCSE Mathematics 0580 · Exam traps · ~7 min read
Maths Exam Traps & Last-Night Checklist
The 30 mistakes that lose the most marks in IGCSE Maths, grouped by topic, plus command words, calculator habits and a checklist for the night before.
CalculatorNumberAlgebraGeometryTrigonometryStatisticsCommand words
RSby Riyaz Sir
mentorriyaz.in
mentorriyaz.in
No tag = Core (everyone)EXTENDED Extended onlyhighlight = comes up again and againHANDY worth memorisingTest yourself at the end
In 30 seconds
- Most lost marks are careless, not hard. The 30 traps below cause a huge share of them. Read each one and say the correct version out loud.
- Always show working. A wrong answer with a correct method still earns method marks. A bare wrong answer earns nothing.
- Last 10 minutes: check units, accuracy (3 significant figures) and that every part of every question has an answer.
1The 30 traps
Accuracy and calculator
Common mistakeRounding too early. Keep the full calculator value in the display and round only the final answer.
Common mistakeWrong accuracy. Unless told otherwise give 3 significant figures, angles to 1 decimal place and money to 2 decimal places, such as $4.50 and not $4.5.
Common mistakeCalculator in the wrong mode. Check it is in DEG (degrees), not RAD, before the paper starts.
Common mistakeFractions typed without brackets. (3 + 4) ÷ (2 + 5) is not 3 + 4 ÷ 2 + 5. Use brackets or the fraction key.
Common mistakeTime in decimals. 2.4 hours is 2 hours 24 minutes, not 2 hours 40 minutes.
Number
Common mistakePercentage change divided by the wrong value. Divide by the original, not the new value.
Common mistakeReverse percentages done forwards. If a price after a 20% rise is $60, the original is 60 ÷ 1.2 = $50. It is not 60 minus 20%.
Common mistakeAdding fractions top and bottom. 1/2 + 1/3 is 5/6 using a common denominator. It is not 2/5.
Common mistakeStandard form with the wrong first number. 12 × 10³ is not standard form. It must be 1.2 × 10⁴.
Common mistakeRatio with different units. Convert to the same unit before you simplify or share.
Algebra
Common mistake(x + 3)² is not x² + 9. It is x² + 6x + 9. Write the bracket twice.
Common mistake−3² and (−3)². On paper −3² = −9, but (−3)² = 9. On the calculator use brackets for negative numbers.
Common mistakeDividing both sides by x. It loses the solution x = 0. Factorise instead: x² = 5x gives x(x − 5) = 0.
Common mistakeInequalities. Flip the sign when you multiply or divide by a negative number.
Common mistakeSign errors when subtracting equations or brackets. −(x − 4) = −x + 4, and subtracting a negative term adds it.
Geometry and measures
Common mistakeBearings. Measure clockwise from North, use three figures, and draw the North line at the point you travel from.
Common mistakeScale factors. Area scales by k² and volume by k³, not by k.
Common mistakeAngle reasons. Name the full rule, such as "alternate angles are equal". "Z angles" earns nothing.
Common mistakeRadius and diameter mixed up. If you are given the diameter, halve it before using πr².
Common mistakeUnits. Area is in cm² and volume in cm³. Convert to the same units first: 1 m² = 10 000 cm² and 1 m³ = 1 000 000 cm³.
Trigonometry
Common mistakeWrong sides labelled. Mark the hypotenuse first, then the opposite and adjacent sides relative to the angle.
Common mistakePythagoras added when it should be subtracted. To find a shorter side use c² − a², not c² + a².
Common mistakeUsing sin when you needed sin⁻¹. To find an angle use sin⁻¹, cos⁻¹ or tan⁻¹ and check the answer is sensible.
Statistics and probability
Common mistakeHistograms. The vertical axis is frequency density, not frequency. Divide by the class width.
Common mistakeCumulative frequency. Plot at the upper boundary of each class and read the median at ½n.
Common mistakeMean from a frequency table. Divide by Σf (the total frequency), not by the number of rows.
Common mistakeMedian of unordered data. Always put the numbers in order first.
Common mistakeProbability above 1, or as a ratio. A probability is a fraction, decimal or percentage between 0 and 1.
Common mistakeTree diagrams. AND means multiply along the branches. OR means add the ends. Without replacement the denominators drop by 1.
Common mistakeDescribing correlation. Write the type and the context, for example "positive correlation: as hours of revision increase, the test score increases".
2Command words
What the question is really asking
| Word | What to do |
|---|---|
| Write down or state | give the answer only. No working is needed |
| Work out or calculate | show your working, then the answer |
| Show that | prove the given result. Every step must be visible |
| Explain or give a reason | give the rule or reason in words |
| Estimate | use rounded values, for example to 1 significant figure |
| Simplify | collect like terms, cancel fractions, give the shortest form |
| Factorise | write as a product, for example 2(x + 3) |
| Solve | find the value or values that make the equation true |
| Sketch | the shape and key points, not drawn to scale |
| Draw or construct | accurate, with ruler, compasses and protractor. Keep your construction arcs |
| Give your answer in terms of π | leave π in the answer, do not use 3.14 |
3Calculator habits
Use it well
- Use the answer memory (Ans) to keep full accuracy between steps, rather than retyping rounded numbers.
- Check the display after typing. Misread brackets and a missing minus sign are very common.
- Use the standard form key (× 10ˣ or EXP) for numbers like 3.2 × 10⁻⁴.
- Estimate first. Round everything to 1 significant figure and check your answer is in the right range.
Exam tipIf you are stuck, write the formula and substitute. Method marks are often half the marks on a question.
4The night before
Checklist
- Bag: black pens, pencils, a ruler, a protractor, compasses, an eraser and a calculator with fresh batteries.
- Revise: the formula sheet and this sheet. Do one short past paper question set. Learn nothing new.
- Sleep: aim for 8 hours. A rested brain beats one more hour of revision.
- In the exam: answer every question, and never leave a blank. A method mark is still a mark.
- Time: about one minute per mark. Move on from anything that takes too long, and come back to it.
5Test yourself
Test yourself — cover the answers first
Quick check
- What is 2.4 hours in hours and minutes?
- A sale price is $60 after a 20% reduction. What was the original price?
- What is the area scale factor if the length scale factor is 3?
- Expand (x + 3)².
- Solve x² = 5x.
- The bearing of B from A is 070°. What is the bearing of A from B?
- EXT What do you plot on the vertical axis of a histogram?
- EXT Where do you plot cumulative frequency points?
- How many cm³ are in 1 m³?
- What should the calculator angle mode be set to?
Show answers
- 2 hours 24 minutes
- $75 (60 ÷ 0.8)
- 9
- x² + 6x + 9
- x = 0 or x = 5
- 250°
- frequency density
- at the upper class boundary
- 1 000 000
- DEG
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