Mnemonics for Maths and Reasoning Notes for SSC Exams
Rahul Kumar
SSC Exam Expert & Content Editor
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PDF Notes: Mnemonics for Maths and Reasoning Notes for SSC Exams
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Maths and Reasoning need rules that you must recall in a few seconds: the order of operations, the trigonometric ratios, the divisibility tests and the directions. These mnemonics for Maths and Reasoning for SSC give short tricks for each rule, with a worked example so that you can see how to use them.
Order of Operations: BODMAS
| Letter | Meaning | Order |
|---|---|---|
| B | Brackets | First |
| O | Of (for example, a fraction of a number) | Second |
| D | Division | Third |
| M | Multiplication | Fourth |
| A | Addition | Fifth |
| S | Subtraction | Last |
Example 1. Find 10 − 2 × 3. Multiplication comes before subtraction, so 10 − 6 = 4.
Trigonometry
| Trick | Meaning |
|---|---|
| SOH-CAH-TOA | Sin = Opposite / Hypotenuse, Cos = Adjacent / Hypotenuse, Tan = Opposite / Adjacent |
| All Silver Tea Cups (ASTC) | All ratios are positive in the first quadrant, Sin in the second, Tan in the third and Cos in the fourth |
| Pattern for the sin values | sin 0°, 30°, 45°, 60°, 90° = √0/2, √1/2, √2/2, √3/2, √4/2, which is 0, 1/2, 1/√2, √3/2, 1 |
The cos values go in the reverse order: 1, √3/2, 1/√2, 1/2, 0.
Divisibility Rules
| Divisor | Test |
|---|---|
| 2 | The last digit is even |
| 3 | The sum of the digits is divisible by 3 |
| 4 | The last two digits are divisible by 4 |
| 5 | The last digit is 0 or 5 |
| 6 | Divisible by both 2 and 3 |
| 8 | The last three digits are divisible by 8 |
| 9 | The sum of the digits is divisible by 9 |
| 11 | The difference between the sum of the digits at odd places and at even places is 0 or a multiple of 11 |
Example 2. Is 1234563 divisible by 3? The digit sum is 1 + 2 + 3 + 4 + 5 + 6 + 3 = 24, and 24 is divisible by 3. So yes.
Calendar
- "Thirty days hath September, April, June and November"; the others have 31 days except February.
- February has 28 days, and 29 days in a leap year.
- A year is a leap year if it is divisible by 4, but a century year must be divisible by 400. So 2000 was a leap year and 1900 was not.
Reasoning Tricks
| Topic | Trick |
|---|---|
| Letter positions | EJOTY: E = 5, J = 10, O = 15, T = 20, Y = 25 |
| Opposite letters | A and Z, B and Y ...: the positions of a letter and its opposite add up to 27 |
| Directions clockwise | "Never Eat Sour Worms": North, East, South, West |
| Blood relation basics | Father’s brother is the paternal uncle; mother’s brother is the maternal uncle (mama) |
Quick Tips
- Say the trick aloud and then solve one question with it.
- Write BODMAS and ASTC at the top of your rough sheet in the exam.
- Check divisibility with the digit sum before you divide.
- Use EJOTY to find the position of any letter quickly.
Quick Revision Points
- BODMAS: Brackets, Of, Division, Multiplication, Addition, Subtraction.
- SOH-CAH-TOA for the trigonometric ratios.
- ASTC: All Silver Tea Cups.
- A number is divisible by 9 if its digit sum is divisible by 9.
- EJOTY gives the letters at 5, 10, 15, 20 and 25.
Practice Questions With Answers
- What does the letter B in BODMAS stand for?
Answer: Brackets - Find the value of 10 − 2 × 3.
Answer: 4 - In SOH-CAH-TOA, what is sin?
Answer: Opposite / Hypotenuse - In which quadrant is cos positive and sin negative?
Answer: The fourth quadrant - In which quadrant is tan positive (and sin and cos negative)?
Answer: The third quadrant - What is the divisibility test for 9?
Answer: The sum of the digits is divisible by 9 - Is 1234563 divisible by 3?
Answer: Yes, the digit sum is 24 - How many days are there in September?
Answer: 30 - Is the year 1900 a leap year?
Answer: No, it is a century year that is not divisible by 400 - In which order do the directions go clockwise in "Never Eat Sour Worms"?
Answer: North, East, South, West
How to Practise This Chapter
Say each mnemonic aloud, write it once from memory and use it in a practice question the same day. Then test yourself with our practice papers and the previous year papers page. See all mnemonics on the Mnemonics page, and also read the MindMaps and Formula Guide pages. For more practice, read the Algebra and Trigonometry Formula Guide, the Alphabet Test and the Mathematics notes. The previous page is Mnemonics for Biology and the Human Body.
Frequently Asked Questions
What does BODMAS mean?
It is the order of operations: Brackets, Of, Division, Multiplication, Addition and Subtraction.
What is SOH-CAH-TOA?
It is a trick for the trigonometric ratios: sin is opposite over hypotenuse, cos is adjacent over hypotenuse and tan is opposite over adjacent.
What is ASTC?
All Silver Tea Cups tells you which ratios are positive in the four quadrants: All, Sin, Tan and Cos.
How do I check that a number is divisible by 9?
Add the digits, and if the sum is divisible by 9, then the number is also divisible by 9.
How do I check that a number is divisible by 11?
Find the difference between the sum of the digits at odd places and at even places. It must be 0 or a multiple of 11.
What is the rule of a leap year?
A year divisible by 4 is a leap year, but a century year must be divisible by 400.
What is EJOTY?
EJOTY are the letters at positions 5, 10, 15, 20 and 25 in the alphabet.
Which months have 30 days?
April, June, September and November.
Should I use mnemonics in the exam?
Yes. Write the key tricks like BODMAS and ASTC on your rough sheet at the start.
Is this useful for SSC exams?
Yes. Maths and reasoning questions need quick rules, and tricks help you recall them fast.
How many tricks should I learn each day?
Learn three to five tricks a day, and revise the older ones.
How often should I revise the tricks?
After 1 day, 3 days, 7 days and then once a month.
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Mnemonics for Biology and Human Body Notes for SSC Exams
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Mnemonics for Chemistry and the Periodic Table: Memory Tricks for Elements, Reactivity Series, Groups and Latin Symbols for SSC
Rahul Kumar
SSC Exam Expert & Content Editor
Rahul is a senior SSC exam strategist with 8+ years of experience helping aspirants crack CGL, CHSL and MTS exams. He writes in-depth notification breakdowns, exam pattern guides and preparation strategies.