Most mistakes that look careless are habits. Of more than 1,400 mistake notes from our recorded lessons, about two in three belong to a mistake that came back more than once.
The one we see most is treating −32 and (−3)2 as the same number. It turned up in 10 of our 20 lesson reviews.
Statistics and percentages are the two biggest topics in our maths notes. Together they hold one note in five.
Almost one in four of our mistake notes come from Additional Mathematics lessons, where the same algebra habits return inside harder questions.
Every mistake on this page has a 2-minute check you can do at home. The quickest works for most of them: put the answer back into the question.
Why does my child keep making careless mistakes in maths?
Most careless mistakes are not random. In more than 1,400 mistake notes from our recorded lessons, the same slips came back again and again, such as a minus sign that disappears or a percentage taken of the wrong number. If a mistake repeats, it is not carelessness. It is a habit, and a habit can be fixed.
How often means how many of our 20 lesson reviews the mistake turned up in. Where two are level, the one with more separate notes comes first.
How we know
These notes come from Teacher Au’s own recorded lessons: group classes and one-to-one lessons, mostly Year 7 to Year 11, and Additional Mathematics. The recordings are reviewed in batches, and every place a student’s working went wrong is written down. Repeats of the same mistake are merged.
More than 1,400 mistake notes, from more than 1,200 recorded lessons taught between July 2023 and November 2026
More than 250 mistakes that came back again and again
More than 700 explanations that worked, logged from the same lessons
20 lesson reviews. Each mistake on this page says how many of the 20 it turned up in
No student names or schools are kept, and every example on this page is re-written with new numbers. This is one teacher’s lessons, not a national sample, so it shows what we see, not exam statistics. Last counted 6 November 2026.
Share of our maths mistake notes by topic, from more than 1,100 notes. Additional Mathematics is counted separately, in its own section below. The shares are rounded, so they add up to slightly more than 100%.
Share of our maths mistake notes, by topic
Topic
Share of notes
Statistics, probability and setsAverages, charts, Venn diagrams and chance
11%
Decimals and percentagesPercentage change, discounts, interest and tax
9%
Units, rounding and the calculatorRounding, significant figures, units and typing it in
8%
Angles, polygons and bearingsAngle facts, parallel lines, polygons and bearings
8%
Perimeter, area, volume and circlesPicking the right length, height or formula
7%
Powers, roots and standard formSquares, indices, roots, surds and standard form
7%
Graphs and functionsPlotting, gradient, straight lines and function notation
7%
Negative numbers and signsMinus signs, brackets and the order of operations
5%
QuadraticsExpanding, factorising and solving x2 equations
5%
Equations and inequalitiesSolving, rearranging and inequality signs
5%
Factors, primes, HCF and LCMTimes tables, factors, multiples and prime numbers
5%
FractionsAdding, dividing, simplifying and mixed numbers
5%
Pythagoras and trigonometryRight-angled triangles, sine, cosine and tangent
4%
Algebra basicsNotation, collecting terms and expanding brackets
4%
Reading the questionWord problems, exam wording and answering what was asked
3%
Similar shapes, transformations and vectorsScale factors, enlargements and vectors
3%
SequencesNumber patterns and the nth term
3%
Ratio, rate and proportionSharing in a ratio, speed and map scales
There are 31 marked mistakes below, in 12 topics. Most of these habits can show up in any year.
Show the ones we have seen in:
Why does my child keep getting negative numbers and signs wrong?
2 marked mistakes
A child who can do the arithmetic can still lose a minus sign when it sits in front of a square or a bracket. Both mistakes below are in our top ten.
1Year 7 to 11Negative numbersIGCSE 0580
Why does my child think −32 and (−3)2 are the same number?
Because the bracket decides what gets squared, and children read past it. (−3)2 means (−3) × (−3), which is 9. Without the bracket, −32 means −(3 × 3), which is −9. It often shows up when a child puts a negative number into a formula such as x2 − 4.
The question Find y when x = −3, for y = x2 − 4.
Your child’s working
x2=−32 = −9✗marked wrong
y=−9 − 4 = −13
Teacher’s note: no bracket, so the minus was not squared
The marked fix
x2=(−3)2✓
=(−3) × (−3) = 9✓
y=9 − 4 = 5✓correct
method marks secured ✓
Why it happens
The child assumes the minus sign is part of what gets squared. It only is when the bracket is there. Calculators follow the same rule, so typing −32 without a bracket gives −9.
How Teacher Au fixes it in class
He separates the two cases by the bracket. In one lesson, using −7, he put it like this: “the square belongs to the whole negative 7 with brackets; without brackets it only belongs to the 7.” He also tells students to type the bracket every time they square a negative number on the calculator.
A 2-minute check at home
Ask your child to type (−3)2 and then −32 into a calculator, and explain why one gives 9 and the other gives −9.
2Year 7 to 11Negative numbersIGCSE 0580
Why does my child write 5x − (2x − 3) as 3x − 3?
Because the minus sign in front of a bracket changes the sign of every term inside, not just the first one. So 5x − (2x − 3) becomes 5x − 2x + 3, which is 3x + 3. A child who changes only the first sign gets 3x − 3, and every line after that is built on it.
The question Expand and simplify 5x − (2x − 3).
Your child’s working
5x − (2x − 3)=5x − 2x − 3✗marked wrong
=3x − 3
Teacher’s note: this should be + 3
The marked fix
5x − (2x − 3)=5x − 2x + 3✓
=3x + 3✓correct
method marks secured ✓
Why it happens
The child sees the minus as belonging to the first term only. It really works like a hidden −1 that multiplies everything in the bracket.
How Teacher Au fixes it in class
He points out the invisible −1 in front of the bracket and multiplies it into each term in turn. When a student is unsure, he has them test the expansion with a small number they can work out by hand.
A 2-minute check at home
Ask your child to work out 10 − (3 + 2) twice: once doing the bracket first, once by removing the bracket. Both ways must give 5.
None of the mistakes in this section came up in lessons for the year you picked.
Sign slips that come back in every topic are often a foundation issue rather than carelessness. Our page on weak maths foundations explains what that looks like at home.
Why does my child keep getting fractions and percentages wrong?
3 marked mistakes
Percentages are where everyday maths meets the exam: discounts, price rises, interest and tax. Fractions and decimals sit underneath them. Together they make up about one in seven of our maths mistake notes.
3Year 7 to 10PercentagesIGCSE 0580
A bag costs RM80 after 20% off. Why does my child say it was RM96?
Because the 20% was taken of the wrong number. The discount was 20% of the original price, so RM80 is what is left: 80% of the original. Dividing 80 by 0.8 gives the original price, RM100. Taking 20% of RM80 and adding it back gives RM96, which is too small.
The question A bag costs RM80 after a 20% discount. What was the original price?
Your child’s working
20% of 80=16✗marked wrong
80 + 16=RM96
Teacher’s note: 20% of the wrong price
The marked fix
100% − 20%=80%✓
original=80 ÷ 0.8✓
=RM100✓correct
method marks secured ✓
Why it happens
The child applies the percentage to the number in front of them, instead of to the original price they are trying to find.
How Teacher Au fixes it in class
He makes students say what percentage the given price is before doing anything else: after a 20% discount, the sale price is 80% of the original. His rule: “Name the percentage first, then write the equation.” Then 0.8 × original = 80, so divide.
A 2-minute check at home
Ask your child to check the answer by taking 20% off it. RM96 minus 20% is RM76.80, not RM80, so RM96 cannot be right. RM100 minus 20% is RM80.
4Year 6 to 11 and Add MathsPercentagesIGCSE 0580
Why does my child divide by the new price to find a percentage increase?
Because the newest number feels like the one to use. Percentage change always compares the change with the original value. A price that rises from RM50 to RM60 has gone up by RM10, and 10 out of the original 50 is 20%. Dividing by 60 gives 16.7%, which is wrong.
The question A price rises from RM50 to RM60. Find the percentage increase.
Your child’s working
increase=60 − 50 = 10
10 ÷ 60≈0.167 = 16.7%✗marked wrong
Teacher’s note: 60 is the new price
The marked fix
increase=60 − 50 = 10✓
10 ÷ 50=0.2 = 20%✓correct
method marks secured ✓
Why it happens
The child picks whichever number came last, or the selling price, as the 100%. The original value is always the 100%.
How Teacher Au fixes it in class
He anchors every percentage change to the starting value: the original price is the 100%, so it always goes on the bottom of the fraction.
A 2-minute check at home
Ask your child: which price was there first? Divide the change by that one, never by the new price.
5Year 7, 9 and 10FractionsIGCSE 0580
Why does my child cross out numbers in a fraction like (6x + 3)/3?
Because “cancel” sounds like “cross out anything that matches”. Only a factor of the whole top and the whole bottom can cancel. In (6x + 3)/3 the 3 on top is added, so first take out the common factor: 3(2x + 1)/3 = 2x + 1. Crossing out the 3s gives 6x, which is wrong.
The question Simplify 6x + 336x plus 3, all over 3.
Your child’s working
6x + 336x plus 3, all over 3, with both 3s crossed out=6x✗marked wrong
Teacher’s note: you can’t cancel across a +
The marked fix
6x + 336x plus 3, all over 3=3(2x + 1)33 times 2x plus 1, all over 3✓
=2x + 1✓correct
method marks secured ✓
Why it happens
The child thinks cancelling means removing anything that appears on both the top and the bottom, rather than dividing the top and the bottom by the same number.
How Teacher Au fixes it in class
He puts a number in to show the cancelling fails, then factorises first. In one lesson he used d = 4 in (12d − 3)/3: the right value is 15, but crossing out the 3s gives 48. Written as 3(4d − 1)/3, the 3s cancel properly and leave 4d − 1.
A 2-minute check at home
Ask your child to put x = 1 into the fraction before and after simplifying. (6 + 3) ÷ 3 = 3, and 2x + 1 = 3 too, but 6x = 6. If the two values differ, the cancelling was not allowed.
None of the mistakes in this section came up in lessons for the year you picked.
If fraction slips keep coming back, they are often a hidden gap from earlier years. Our guide to hidden maths gaps shows how to spot one.
Why does my child mix up primes, factors, HCF and LCM?
3 marked mistakes
Whole-number skills look like primary school work, but they come back in IGCSE questions on prime factors, fractions and probability.
6Year 8 to 10HCF and LCMIGCSE 0580
Why is my child’s HCF bigger than the numbers they started with?
Because the powers were swapped. The highest common factor takes the lowest power of each shared prime, and the lowest common multiple takes the highest. For 24 = 23 × 3 and 36 = 22 × 32, the HCF is 22 × 3 = 12. Taking the highest powers gives 72, which is the LCM.
The question Find the HCF of 24 = 23 × 3 and 36 = 22 × 32.
Your child’s working
HCF=23 × 32✗marked wrong
=72
Teacher’s note: 72 can’t divide into 24
The marked fix
HCF=22 × 3✓
=12✓correct
method marks secured ✓
Why it happens
The word “highest” in highest common factor pulls the child towards the higher powers. The rule really is the opposite of what the name suggests.
How Teacher Au fixes it in class
He uses the names against themselves: “HCF, H stands for highest, the opposite is lowest”, and the same flip for LCM. In another class he showed why: a prime can only be in the HCF if every number has it, so you can only take as many as the number with the fewest.
A 2-minute check at home
Ask your child: can the HCF be bigger than the smaller number? It cannot, so an HCF of 72 for 24 and 36 means the powers were swapped.
7Year 7 to 10Prime numbersIGCSE 0580
Why does my child count 1 as a prime number?
Because the usual school phrase, “only divides by 1 and itself”, seems to fit 1. A prime number has exactly two different factors. The number 1 has only one factor, itself, so it is not prime. The primes up to 10 are 2, 3, 5 and 7: four of them, not five.
The question How many prime numbers are there from 1 to 10?
Your child’s working
primes1, 2, 3, 5, 7✗marked wrong
how many5
Teacher’s note: 1 has only one factor
The marked fix
primes2, 3, 5, 7✓
how many4✓correct
method marks secured ✓
Why it happens
The child learned a phrase rather than a definition. “Divides by 1 and itself” sounds true of 1, because 1 and itself are the same number.
How Teacher Au fixes it in class
He states the definition first, exactly two different factors, before any example. Students can then test numbers such as 1 for themselves.
A 2-minute check at home
Ask your child how many factors 1 has. If the answer is one, ask whether that fits “exactly two”.
8Year 7 to 10HCF and LCMIGCSE 0580
Two buses leave together. Why does my child use the HCF to find when they meet again?
Because both methods use the same numbers, and the child picks one without asking what the situation needs. Leaving together again means a time that is a multiple of both gaps, so it needs the lowest common multiple. Buses every 12 and 18 minutes next leave together after 36 minutes, not 6.
The question Bus A leaves every 12 minutes and Bus B every 18 minutes. They leave together at 8:00. When do they next leave together?
Your child’s working
HCF of 12 and 18=6✗marked wrong
next time8:06
Teacher’s note: 6 isn’t a multiple of 12
The marked fix
LCM of 12 and 18=36✓
next time8:36✓correct
method marks secured ✓
Why it happens
The child chooses by the word “common”, or by whichever method feels shorter, not by what the question describes.
How Teacher Au fixes it in class
He gives a decision rule: cutting or sharing out leads to factors, repeating or fitting together leads to multiples. His version for a rope question: “Cutting the rope makes pieces shorter. Shorter means factors.”
A 2-minute check at home
Ask: should the answer be bigger or smaller than the numbers in the question? Meeting again later means bigger, so it is the LCM.
None of the mistakes in this section came up in lessons for the year you picked.
Why does my child keep getting powers and standard form wrong?
2 marked mistakes
Powers look small on the page, so they are easy to misread, and the same small number comes back in area, quadratics and standard form.
9Year 7 to 9PowersIGCSE 0580
Why does my child write 52 = 10?
Because the small number is read as “times 2” instead of “multiply it by itself”. 52 means 5 × 5 = 25, and 23 means 2 × 2 × 2 = 8. The slip hides because 22 gives 4 either way, so a child can get some answers right by accident.
The question Work out 52 + 23.
Your child’s working
52=5 × 2 = 10✗marked wrong
23=2 × 3 = 6✗also wrong
10 + 6=16
Teacher’s note: the 2 means two 5s multiplied
The marked fix
52=5 × 5 = 25✓
23=2 × 2 × 2 = 8✓
25 + 8=33✓correct
method marks secured ✓
Why it happens
The child reads the power as a multiplier. It hides because some answers come out right by accident: 22 is 4 whether you square it or double it.
How Teacher Au fixes it in class
He has students restate the definition every time: squared means the number times itself, so 52 is five times five.
A 2-minute check at home
Ask your child to say 42 out loud as “four times four” and work it out. It is 16, not 8.
10Year 7Standard formIGCSE 0580
Why does my child add 3 × 104 and 4 × 103 and get 7 × 104?
Because the front numbers are added as if they were the same size. 3 × 104 is 30,000 and 4 × 103 is 4,000, so the total is 34,000, or 3.4 × 104. Before adding numbers in standard form, the powers of 10 must match. Multiplying works differently, which is why the habit is easy to pick up.
The question Work out 3 × 104 + 4 × 103. Give your answer in standard form.
Your child’s working
3 × 104 + 4 × 103=7 × 104✗marked wrong
Teacher’s note: the powers don’t match
The marked fix
4 × 103=0.4 × 104✓
3 × 104 + 0.4 × 104=3.4 × 104✓correct
method marks secured ✓
Why it happens
The child uses the multiplication habit, dealing with the front numbers and the powers separately, for addition, where it does not work.
How Teacher Au fixes it in class
He rewrites one number so both share 104: 4 × 103 becomes 0.4 × 104. In his words: “The value stays the same because I divide and multiply by 10 at the same time”.
A 2-minute check at home
Ask your child to write both numbers out in full, 30,000 + 4,000, and compare the total with their answer.
None of the mistakes in this section came up in lessons for the year you picked.
Why does my child keep making mistakes in algebra and equations?
2 marked mistakes
Most of IGCSE Maths is written in algebra, so a shaky step here shows up in every topic. Many slips that look careless are really unsteady algebra.
11Year 10InequalitiesIGCSE 0580
Why does my child get the inequality sign the wrong way round?
Because an inequality is treated exactly like an equation. That works until you multiply or divide by a negative number: then the sign must turn round. Solving 5 − 3x ≤ 17 means dividing by −3, so ≤ becomes ≥ and the answer is x ≥ −4, not x ≤ −4.
The question Solve 5 − 3x ≤ 17.
Your child’s working
−3x≤12
x≤−4✗marked wrong
Teacher’s note: dividing by −3 turns the sign
The marked fix
−3x≤12✓
x≥−4 (÷ by −3, sign turned)✓correct
method marks secured ✓
Why it happens
The child solves it like an equation and forgets the one rule that is different. Nothing on the page looks wrong, so the slip goes unnoticed.
How Teacher Au fixes it in class
He solves it, shows the wrong answer next to the right one, then tests a number from each. x = −5 fits the wrong answer, but 5 − 3 × (−5) = 20, and 20 ≤ 17 is false. x = −3 fits the right answer: 5 − 3 × (−3) = 14, and 14 ≤ 17 is true.
A 2-minute check at home
Ask your child to pick a number that fits their answer and put it back into the question. If the inequality comes out false, the sign needed turning round.
12Year 6 to 10AlgebraIGCSE 0580
Why does my child simplify 2x + 5 + 3x to 10x?
Because letters and numbers are treated as the same kind of thing. Only like terms can be added: 2x and 3x are both “lots of x”, so they make 5x. The 5 has no x, so it stays separate. The answer is 5x + 5, and putting x = 2 into both shows that 10x is wrong.
The question Simplify 2x + 5 + 3x.
Your child’s working
2x + 5 + 3x=10x✗marked wrong
Teacher’s note: the 5 has no x
The marked fix
2x + 3x=5x✓
2x + 5 + 3x=5x + 5✓correct
method marks secured ✓
Why it happens
The child treats every letter and number as the same kind of thing. We see it from the first algebra lessons right up to simultaneous equations in Year 10.
How Teacher Au fixes it in class
He asks a question a child can answer at once: “Two apples plus five oranges. Can I say I have seven apples?” The same picture is used again whenever the slip comes back in the lesson.
A 2-minute check at home
Ask your child to put x = 2 into the question and into their answer. Both must give the same number: here, 15.
None of the mistakes in this section came up in lessons for the year you picked.
If this sounds familiar, our page on weak algebra explains what to check first.
Why does my child struggle with quadratic equations?
2 marked mistakes
In quadratics a child often does the hard part correctly and then loses the answer on one rule.
13Year 8 to 11QuadraticsIGCSE 0580
x2 = 25. Why does my child only write x = 5?
Because the square root key gives one answer, so the child stops there. But (−5)2 is also 25, so x2 = 25 has two solutions: x = 5 and x = −5, written x = ±5. The negative one is only left out when the question rules it out, for example when x is a length.
The question Solve x2 = 25.
Your child’s working
x=√25root 25 = 5✗marked wrong
Teacher’s note: and −5?
The marked fix
x=±√25root 25✓
x = 5 or x = −5✓correct
method marks secured ✓
Why it happens
The child thinks of the square root as a calculator button that gives one answer.
How Teacher Au fixes it in class
He uses a class exercise where x = 4 and x = −4 both give y = 74 in y = 5x2 − 6, so working backwards from 74 must give x = ±4. Seeing two inputs land on the same answer makes the ± feel natural.
A 2-minute check at home
Ask your child: which number times itself makes 25? Then ask: is there a negative one too?
14Year 10QuadraticsIGCSE 0580
Why does my child solve x2 + x = 6 as x = 6 or x = 5?
Because the zero rule is used without the zero. If two numbers multiply to 0, one of them must be 0. If they multiply to 6, they could be almost anything. So the equation must equal 0 before factorising: x2 + x − 6 = 0 gives (x + 3)(x − 2) = 0, so x = −3 or x = 2.
The question Solve x2 + x = 6.
Your child’s working
x(x + 1)=6
x = 6 or x + 1 = 6✗marked wrong
x = 6 or x = 5
Teacher’s note: this only works when it equals 0
The marked fix
x2 + x − 6=0✓
(x + 3)(x − 2)=0✓
x = −3 or x = 2✓correct
method marks secured ✓
Why it happens
The rule “if a product is 0, one of the factors is 0” only works for 0. The child uses it for any number on the right.
How Teacher Au fixes it in class
He compares two products. If two numbers multiply to 4, there are endless pairs, so you learn nothing. If they multiply to 0, one of them has to be 0. That is why everything goes to one side before factorising.
A 2-minute check at home
Ask your child to put each answer back into the original equation. 62 + 6 is 42, not 6, so x = 6 cannot be right.
None of the mistakes in this section came up in lessons for the year you picked.
Why does my child get graph and function questions wrong?
2 marked mistakes
Graphs and functions reward reading the notation exactly as it is written. Both mistakes below come from reading too fast.
15Year 10 and 11FunctionsIGCSE 0580
Why does my child work out fg(1) in the wrong order?
Because fg is read from left to right, like a word. In fg(1), the function next to the 1 goes first: work out g(1), then put the answer into f. With f(x) = x + 3 and g(x) = 2x, g(1) = 2 and f(2) = 5. Doing f first gives 8, which is gf(1).
The question f(x) = x + 3 and g(x) = 2x. Find fg(1).
Your child’s working
f(1)=1 + 3 = 4✗marked wrong
g(4)=2 × 4 = 8
Teacher’s note: g is next to the 1, so g goes first
The marked fix
g(1)=2 × 1 = 2✓
f(2)=2 + 3 = 5✓
fg(1)=5✓correct
method marks secured ✓
Why it happens
The child reads fg from left to right like English, or treats the two letters as a multiplication.
How Teacher Au fixes it in class
He reads the letters from the inside out. With gf(4) in one lesson: “the f is closest to 4, so you compute f(4) first”. The letter closest to the number always goes first.
A 2-minute check at home
Ask your child which letter is written closest to the number in the bracket. That function goes first.
16Year 10Straight-line graphsIGCSE 0580
Why does my child say the gradient of 2y = 6x + 4 is 6?
Because the number in front of x is read off before the equation is in the form y = mx + c. The gradient is only the number in front of x once y is on its own. Dividing 2y = 6x + 4 by 2 gives y = 3x + 2, so the gradient is 3.
The question Find the gradient of the line 2y = 6x + 4.
Your child’s working
gradient=6✗marked wrong
Teacher’s note: y isn’t on its own yet
The marked fix
y=3x + 2 (everything ÷ 2)✓
gradient=3✓correct
method marks secured ✓
Why it happens
The child takes the first number they see next to x, without rearranging first.
How Teacher Au fixes it in class
The step he insists on: rearrange to y = mx + c first, dividing through by the number in front of y, and only then read the gradient.
A 2-minute check at home
Ask your child: is y on its own on one side? If not, the number in front of x is not the gradient yet.
None of the mistakes in this section came up in lessons for the year you picked.
Why does my child lose marks on area, perimeter and shape questions?
3 marked mistakes
Counted together, angles, area, trigonometry and similar shapes make up more than one in five of our maths mistake notes. Most slips below come from using a measurement that is on the diagram but is not the one the formula needs.
17Year 7 to 10Similar shapesIGCSE 0580
The lengths are 3 times bigger. Why does my child make the area 3 times bigger too?
Because one scale factor seems to apply to everything. When every length is multiplied by 3, the length and the width both grow, so the area grows by 3 × 3 = 9. A small rectangle of 5 cm2 becomes 45 cm2, not 15 cm2. For volume, the factor is cubed.
The question Two similar rectangles have lengths in the ratio 1 : 3. The small one has an area of 5 cm2. Find the area of the large one.
Your child’s working
5 × 3=15 cm2✗marked wrong
Teacher’s note: area needs 3 squared
The marked fix
area factor=32 = 9✓
5 × 9=45 cm2✓correct
method marks secured ✓
Why it happens
The child believes one scale factor applies to every measurement. Lengths use the factor, areas use its square and volumes use its cube.
How Teacher Au fixes it in class
He derives the rule from area = width × height. Scaling by 3 multiplies the width by 3 and the height by 3, so the area is multiplied by 32, and a square root takes you back.
A 2-minute check at home
Ask your child to draw a 1 by 1 square and a 2 by 2 square. How many small squares fit in the big one? Four, not two.
18Year 6 to 11Perimeter and circlesIGCSE 0580
Why does my child leave out the straight edge in the perimeter of a semicircle?
Because “perimeter” gets linked to the curved part only. Perimeter is the whole way round the outline, and a semicircle has a flat edge too: the diameter. For a diameter of 10 cm, the curve is 15.7 cm, so the perimeter is 15.7 + 10 = 25.7 cm, not 15.7 cm.
The question Find the perimeter of a semicircle with diameter 10 cm. Use π = 3.14.
Your child’s working
curve=½ × 3.14 × 10 = 15.7 cm
perimeter=15.7 cm✗marked wrong
Teacher’s note: and the straight edge?
The marked fix
curve=½ × 3.14 × 10 = 15.7 cm✓
straight edge=10 cm✓
perimeter=15.7 + 10 = 25.7 cm✓correct
method marks secured ✓
Why it happens
The child links “perimeter” with the curved part only, or works it out the way they would an area.
How Teacher Au fixes it in class
For perimeter, he walks round the edge and adds every curved and straight length, including any straight edge that only appears once a piece is cut out.
A 2-minute check at home
Ask your child to trace the outline with a finger and name each part they pass: one curve, one straight edge.
19Year 7, 8 and 10AreaIGCSE 0580
Why does my child use the slanted side to find the area of a parallelogram?
Because the slanted side is the length printed on the diagram. Area needs the perpendicular height: the distance straight up from the base, at 90°. A parallelogram with base 8 cm, slanted side 5 cm and height 4 cm has an area of 8 × 4 = 32 cm2, not 8 × 5 = 40 cm2.
The question A parallelogram has base 8 cm, slanted side 5 cm and perpendicular height 4 cm. Find its area.
Your child’s working
area=8 × 5 = 40 cm2✗marked wrong
Teacher’s note: 5 cm is the slope, not the height
The marked fix
area=base × height✓
=8 × 4 = 32 cm2✓correct
method marks secured ✓
Why it happens
The child uses whichever length is on the diagram. It rarely happens with rectangles, where the side is the height, so it appears once the sides start to slope.
How Teacher Au fixes it in class
Before any area formula, he has students draw the 90° drop from the top to the base. The height is that dotted line, not the sloping side.
A 2-minute check at home
Ask your child to draw the height as a dotted line with a small right-angle mark before working out any area.
None of the mistakes in this section came up in lessons for the year you picked.
Why does my child lose marks on rounding, units and the calculator?
2 marked mistakes
These marks are lost after the maths is done. The method can be right and the last line still wrong, because a number was rounded too soon or a unit was changed the wrong way.
20Year 8 to 11RoundingIGCSE 0580
Why is my child’s answer a little off, even with the right method?
Because a number was rounded in the middle of the working, and the small error grew through every later step. A circle with a circumference of 40 cm has a radius of 6.366… cm. Rounding it to 6.4 cm gives an area of 128.7 cm2, but keeping the full value gives 127.3 cm2.
The question A circle has a circumference of 40 cm. Find its area, correct to 1 decimal place.
Your child’s working
r=40 ÷ (2π) ≈ 6.4✗marked wrong
area=π × 6.42 ≈ 128.7 cm2
Teacher’s note: rounded too soon
The marked fix
r=40 ÷ (2π) = 6.36619… (keep it all)✓
area=π × 6.36619…2 ≈ 127.3 cm2✓correct
method marks secured ✓
Why it happens
Rounding each step feels neater, but the error is carried into every later step, and the final answer drifts away from the right one.
How Teacher Au fixes it in class
He shows one concrete case, this circle, where the rounded radius changes the area. His rule: “Whenever the final answer is not the radius, try to use as many decimal places as we can.”
A 2-minute check at home
Ask your child to keep the full number in the calculator, or use the Ans key, and round only on the last line.
21Year 9 and 10Time and speedIGCSE 0580
Why does my child write 2 hours 30 minutes as 2.3 hours?
Because the digits look right on the page. Time works in 60s, but decimals work in 10s. 30 minutes is half an hour, so 2 hours 30 minutes is 2.5 hours. A car that goes 150 km in that time averages 150 ÷ 2.5 = 60 km/h, not 65.2 km/h.
The question A car travels 150 km in 2 hours 30 minutes. Find its average speed.
Your child’s working
time=2.3hours✗marked wrong
speed=150 ÷ 2.3 ≈ 65.2 km/h
Teacher’s note: 30 minutes is 0.5 of an hour
The marked fix
time=2 + 30 ÷ 60 = 2.5 hours✓
speed=150 ÷ 2.5 = 60 km/h✓correct
method marks secured ✓
Why it happens
Time works in 60s and decimals work in 10s, and the digits 2 and 30 are right there to copy.
How Teacher Au fixes it in class
He explains that the digits after the point are a fraction of an hour, not minutes. In one lesson the time was 0.56 hours: 0.56 × 60 = 33.6 minutes, not 56 minutes.
A 2-minute check at home
Ask: how many minutes is 0.5 of an hour? Thirty. So 2.3 hours is not 2 hours 30 minutes. It is 2 hours 18 minutes.
None of the mistakes in this section came up in lessons for the year you picked.
Why does my child get statistics and probability questions wrong?
2 marked mistakes
Statistics, probability and sets make up the largest single topic in our maths notes, about one in nine. The mistakes there are spread across many small slips rather than a few big repeats, and these two are among the ones we see most.
22Year 9 to 11Sets and Venn diagramsIGCSE 0580
Why does my child count the middle of a Venn diagram twice?
Because the two circles are added without noticing that the overlap sits inside both. If 20 pupils like tea, 15 like coffee and 5 like both, then 20 + 15 counts those 5 twice. Taking them off once gives 30 pupils who like tea or coffee, not 35.
The question In a class, 20 pupils like tea, 15 like coffee and 5 like both. How many like tea or coffee?
Your child’s working
tea or coffee=20 + 15 = 35✗marked wrong
Teacher’s note: the 5 got counted twice
The marked fix
tea only=20 − 5 = 15✓
coffee only=15 − 5 = 10✓
tea or coffee=15 + 10 + 5 = 30✓correct
method marks secured ✓
Why it happens
The child adds the two circles without seeing that the pupils in the middle are inside both.
How Teacher Au fixes it in class
He labels every region first: both, tea only, coffee only, and outside. Then it is clear why the overlap is taken off once when you want one or the other.
A 2-minute check at home
Ask your child to fill in the middle of the Venn diagram first, then the “only” parts, then add up the regions.
23Year 8ProbabilityIGCSE 0580
Why does my child miss a case in “at least one” probability questions?
Because listing the cases by hand makes it easy to miss one. When a coin is tossed twice, “at least one head” includes head-head as well as head-tail and tail-head. The safe route is to take away the one outcome that is not wanted: 1 − P(tail, tail) = 1 − ¼ = ¾.
The question A coin is tossed twice. Find the probability of getting at least one head.
Your child’s working
outcomes wantedHT, TH✗marked wrong
P=2 out of 4 = ½
Teacher’s note: HH counts too
The marked fix
P(no heads)=P(TT) = ¼✓
P(at least one head)=1 − ¼ = ¾✓correct
method marks secured ✓
Why it happens
Listing by hand misses cases, and the quicker route, working out what is not wanted, does not occur to the child.
How Teacher Au fixes it in class
He looks at what is not wanted. In a lesson with red and blue counters he said: “at least one red means everything except blue-blue.” For two coins, that is everything except tail-tail.
A 2-minute check at home
Ask your child: which is the only outcome that is not “at least one head”? It is tail, tail. Everything else counts.
None of the mistakes in this section came up in lessons for the year you picked.
Why does my child lose marks even when they know the maths?
2 marked mistakes
Some marks are lost before any working starts, or on the very last line. The last line of a question says what to find, which units to use and how to round, and it is the line children read fastest.
24Year 9Reading the questionIGCSE 0580
Why does my child find x and stop, when the question asks for something else?
Because solving the equation feels like the end of the question. Often x is only a step. If a triangle’s angles are x, 2x and 3x, then 6x = 180 and x = 30, but the question asks for the largest angle, which is 3x = 90°. Writing 30° as the answer is wrong.
The question The angles of a triangle are x, 2x and 3x. Find the largest angle.
Your child’s working
x + 2x + 3x=180
6x=180
answerx = 30°✗marked wrong
Teacher’s note: the question wants 3x
The marked fix
6x=180✓
x=30✓
largest angle=3x = 90°✓correct
method marks secured ✓
Why it happens
Solving for x feels like finishing. We see the same stop with ratios, where x is found but not the share, and with coordinates, where x is found but not y.
How Teacher Au fixes it in class
The habit he builds is simple: before writing the final answer, re-read the last line of the question and check the answer matches what it asks for.
A 2-minute check at home
Ask your child to read the last line of the question again and point to the word that says what to find.
25Year 11Forming expressionsIGCSE 0580
Why does my child write “6 less than x” as 6 − x?
Because the words are written down in the order they are read. “6 less than x” starts with x and takes 6 away, so it is x − 6. The order matters: when x = 10, x − 6 is 4, but 6 − x is −4. The same trap appears in “subtract 4 from y”, which is y − 4.
The question Write an expression for “6 less than x”. Find its value when x = 10.
Your child’s working
6 less than x6 − x✗marked wrong
6 − 10=−4
Teacher’s note: start with x
The marked fix
6 less than xx − 6✓
10 − 6=4✓correct
method marks secured ✓
Why it happens
The child writes the numbers in the order they are read, but this phrase reads backwards from the algebra.
How Teacher Au fixes it in class
In class the trap gets named out loud: the phrase reads backwards from the algebra, so start with the thing that is being made smaller.
A 2-minute check at home
Ask: what is 6 less than 10? Your child will say 4. Now ask them to write the same thing with x in place of 10.
None of the mistakes in this section came up in lessons for the year you picked.
Why does my child keep losing marks in Additional Mathematics?
6 marked mistakes
Additional Mathematics (Cambridge 0606) is built on IGCSE algebra, so the old habits come back inside harder questions, and new ones appear. Almost one in four of our mistake notes come from Add Maths lessons. Here are six we see often.
26FunctionsAdd Maths 0606
Why does my child find the range of a function from the end values only?
Because the two ends of the domain look like the smallest and largest outputs, but a curve can dip lower in between. For f(x) = x2 − 2x + 5 on 0 ≤ x ≤ 5, the ends give 5 and 20, but the lowest point of the curve is 4, at x = 1. The range is 4 ≤ f(x) ≤ 20.
The question Find the range of f(x) = x2 − 2x + 5 for 0 ≤ x ≤ 5.
Your child’s working
f(0)=5
f(5)=20
range5 ≤ f(x) ≤ 20✗marked wrong
Teacher’s note: the curve dips to 4
The marked fix
f(x)=(x − 1)2 + 4✓
f(1)=4 (lowest point)✓
range4 ≤ f(x) ≤ 20✓correct
method marks secured ✓
Why it happens
The child treats the two ends of the domain as the smallest and largest values, without checking for a turning point in between.
How Teacher Au fixes it in class
He sketches the parabola, marks the turning point inside the domain, and reads the range from everything the graph passes through.
A 2-minute check at home
Ask your child to sketch the curve over the given domain before writing the range. Does it dip lower than either end?
Why does my child find only two answers to sin 2x = 0.5?
Because the range for x is used for 2x. If x runs from 0° to 360°, then 2x runs from 0° to 720°: two full turns. So 2x = 30°, 150°, 390° or 510°, and halving gives x = 15°, 75°, 195° and 255°. Solving in the original range finds only 15° and 75°.
The question Solve sin 2x = 0.5 for 0° ≤ x ≤ 360°.
Your child’s working
2x = 30° or 150°✗marked wrong
x = 15° or 75°
Teacher’s note: 2x goes up to 720°
The marked fix
0° ≤ 2x ≤ 720°✓
2x = 30°, 150°, 390°, 510°✓
x = 15°, 75°, 195°, 255°✓correct
method marks secured ✓
Why it happens
The child finds the solutions in the original range and halves them, so the second turn is never looked at.
How Teacher Au fixes it in class
He changes the range before solving. For sin 3x on 0° to 180° he said: “Since we have 3x, the domain for 3x is 0 to 540”.
A 2-minute check at home
Ask your child: how many answers should there be? For sin 2x between 0° and 360° there are usually four.
Why does my child get 0 for the distance travelled by a particle?
Because displacement and distance are treated as the same thing. A particle that goes out and comes back can end where it started, so its displacement is 0, but it still travelled. With v = 4 − 2t, the particle stops at t = 2, 4 m from the start, then comes back. The distance is 4 + 4 = 8 m.
The question A particle moves with velocity v = 4 − 2t m/s, starting from s = 0. Find the total distance travelled from t = 0 to t = 4.
Your child’s working
s=4t − t2
distance=s(4) = 16 − 16 = 0 m✗marked wrong
Teacher’s note: it turned back at t = 2
The marked fix
v = 0 when t = 2✓
s(2)=8 − 4 = 4 m✓
distance=4 + 4 = 8 m✓correct
method marks secured ✓
Why it happens
The child treats the change in position as the distance, and treats v = 0 as the end of the motion instead of the moment it turns round.
How Teacher Au fixes it in class
He draws the start and end points on a line: “Displacement is only the straight-line gap from start to end; if it returns, displacement is zero but distance is not.” Then he splits the journey at v = 0 and adds the two parts.
A 2-minute check at home
Ask your child: did the particle ever stop and turn round? If so, the journey must be split at that moment.
Why does my child use the sum formula when the question asks for one year’s value?
Because the sum and the nth term sit side by side in the formula list. “The salary in year 5” is one value, the 5th term. S5 adds up all five years. A salary that starts at RM30,000 and rises by RM2,000 a year is RM38,000 in year 5, while S5 gives RM170,000, the total paid.
The question A salary starts at RM30,000 and rises by RM2,000 each year. Find the salary in year 5.
Your child’s working
S5=525 over 2 × (60,000 + 8,000)✗marked wrong
=RM170,000
Teacher’s note: that’s all 5 years added up
The marked fix
5th term=30,000 + 4 × 2,000✓
=RM38,000✓correct
method marks secured ✓
Why it happens
The child mixes up a single term and the sum of the terms, because both formulas use the same letters.
How Teacher Au fixes it in class
He names the trap directly: Sn adds every year’s value together, but the question asks for the value in a single year.
A 2-minute check at home
Ask your child: does the question want one year, or the total of all the years?
Why does my child differentiate (3x + 1)5 as 5(3x + 1)4?
Because the bracket is treated as if it were a plain x. The inside, 3x + 1, has its own derivative, 3, and the answer must be multiplied by it. So the derivative of (3x + 1)5 is 5(3x + 1)4 × 3 = 15(3x + 1)4. Missing the × 3 spoils every later step.
The question Differentiate y = (3x + 1)5.
Your child’s working
dydxdy by dx=5(3x + 1)4✗marked wrong
Teacher’s note: × 3 for the inside
The marked fix
dydxdy by dx=5(3x + 1)4 × 3✓
=15(3x + 1)4✓correct
method marks secured ✓
Why it happens
The child brings the power down and stops, as if the bracket were a plain x.
How Teacher Au fixes it in class
He uses an onion picture: deal with the outer layer first, the power, and leave the inside alone. Then multiply by what the inside differentiates to.
A 2-minute check at home
Ask your child: after bringing the power down, did you multiply by the derivative of what is inside the bracket?
Because the calculator was left in degree mode. π/6 is an angle in radians, about 0.52 of a radian. In degree mode the calculator reads it as 0.52 of a degree, and the sine of that is tiny. In radian mode, sin(π/6) = 0.5. The wrong answer looks believable, so nothing warns the child.
The question Find sin(π/6).
Your child’s working
sin(π/6)≈0.0091(degree mode)✗marked wrong
Teacher’s note: check the D on the screen
The marked fix
sin(π/6)=0.5 (radian mode)✓
π/6 radians = 30°✓
sin 30° = 0.5✓correct
method marks secured ✓
Why it happens
The mode is not checked, and the wrong answer looks believable, so nothing on the screen warns the child.
How Teacher Au fixes it in class
The habit is to check the mode before any trigonometry, because this error gives no warning. For a radian question the screen should show R, not D. It matters on Paper 2, the calculator paper.
A 2-minute check at home
Ask your child to look for the small D or R on the calculator screen before every trigonometry question.
None of the mistakes in this section came up in lessons for the year you picked.
Is it carelessness or a gap? A 5-minute check at home
A careless slip is one your child can find and fix as soon as you point to the line. A gap is a mistake they cannot see, or one that comes back on a fresh question. If a mistake repeats, it is not carelessness. It is a habit, and the check below shows which one you are looking at.
Pick one wrong answer from a recent test or piece of homework.
Ask your child to point to the exact line where it went wrong, and say what they were thinking at that moment.
Cover the working and ask them to do the same question again, with one number changed.
If the same slip comes back, find it on this page and try the 2-minute check under it.
Write the slip in a short mistake list, and read the list before the next test.
Found and fixed straight away, it was a slip. Back again on the new question, it is a habit, and telling your child to be more careful will not shift it. Naming the exact step will.
Because a test shows up small habits that homework can hide. At home there is time to notice a lost minus sign or a misread question, and in a test there is not, so one slip early in a question carries into every later line. The fix is to find the habit, not to do more of the same questions.
Following a method when it is shown is not the same as using it alone on a question that looks new. In our lessons the marks are often lost at one step, such as a sign or the last line of the question. Practising that one step under time is what turns understanding into marks.
Name the mistake exactly, then practise the one step it lives in, not whole papers. Ask your child to check each answer by putting it back into the question, and to keep a short list of their own repeat mistakes to read before each test. Telling a child to be more careful rarely changes anything; naming the pattern does.
Because Add Maths puts IGCSE algebra inside longer questions, so a habit that cost one mark in IGCSE Maths can spoil a whole question. New traps appear too, such as solving sin 2x = 0.5 over the wrong range or forgetting the inside of a bracket in calculus. Paper 1 is a non-calculator paper, so the algebra has to be secure by hand.
In our own lessons, the mistake that came back most is treating −3² and (−3)² as the same number, which turned up in 10 of our 20 lesson reviews. Next is rounding in the middle of a calculation, in 9 of 20. After that come six mistakes that each turned up in 8 of 20: a minus sign before a bracket, finding an original price, area scale factors, inequality signs, percentage change and the perimeter of a semicircle.
Only if the practice targets the habit. Repeating papers without correcting the step that breaks can make the same mistake more automatic. Slow re-attempts of the exact step, with each answer tested by putting it back into the question, work better.
Find the one step before the exam does
Seeing one of these at home? Send Teacher Au a photo of the working. Teacher Au replies personally, usually the same day.
