Simplification
🔒 Log in to trackBODMAS, identity-based fractions, surds and indices, square/cube roots and approximation. These are the fastest marks in Tier 1 — usually 1–2 questions per shift — and the same skills (identities, surd handling) power the algebra questions.
One page per subtopic: detailed notes, every question type, formulas, tricks and practice sets.
Every formula on one printable page, grouped by subtopic.
5 exam-level questions worked step by step.
65 questions — untimed practice or a timed test with analysis.
Track record in the exam
Questions per shift in recent SSC CGL papers.
Test difficulty mix (65 questions)
Question patterns exams keep repeating
Taken from previous-year papers. If a pattern is marked "very common", expect to see it in your exam.
Mixed sums with 'of' and brackets
very commonA long sum with ÷, ×, brackets and the word 'of'.
Do brackets first, then 'of', then ÷ and ×, then + and −.
'Of' always comes before ÷ and ×.
Evaluate 64 ÷ 4 of 2 + 8 × 3.
'of' first: 4 of 2 = 8
64 ÷ 8 = 8
8 × 3 = 24
8 + 24 = 32
Cubes over squares: use the identity
very common"(15.2³ − 5.2³) ÷ (15.2² + 15.2 × 5.2 + 5.2²)"
Top is a³ − b³ and bottom is a² + ab + b². They cancel to leave a − b.
For a³ + b³ over a² − ab + b², the answer is a + b.
(15.2³ − 5.2³) ÷ (15.2² + 15.2 × 5.2 + 5.2²) = ?
Top is a³ − b³ with a = 15.2 and b = 5.2
Bottom is a² + ab + b², so it cancels
Answer = a − b = 15.2 − 5.2 = 10
Given x + 1/x, find the squares and cubes
very common"If x + 1/x = 4, find x³ + 1/x³."
For the square: (given)² − 2.
For the cube: (given)³ − 3 × (given).
If x + 1/x = 4, find x³ + 1/x³.
Cube the given: 4³ = 64
That equals x³ + 1/x³ + 3 × (x + 1/x)
So x³ + 1/x³ = 64 − 3 × 4
= 64 − 12 = 52
Powers with the same base
very common"2^(x+3) × 4^(x−1) = 128. Find x."
Write every number as a power of the same base (4 = 2², 128 = 2⁷).
Then make the powers equal.
Solve 2^(x+3) × 4^(x−1) = 128.
4 = 2², so 4^(x−1) = 2^(2x−2)
Add the powers: (x + 3) + (2x − 2) = 3x + 1
128 = 2⁷, so 3x + 1 = 7
x = 2
Remove roots from the bottom of a fraction
very common"1/(√4 + √3) + 1/(√3 + √2) + 1/(√2 + 1)"
Multiply top and bottom by the same numbers with the middle sign flipped.
In a chain, the middle terms cancel.
1/(√4 + √3) + 1/(√3 + √2) + 1/(√2 + 1) = ?
1/(√4 + √3) = √4 − √3 = 2 − √3 (bottom becomes 4 − 3 = 1)
Similarly: √3 − √2 and √2 − 1
Sum = (2 − √3) + (√3 − √2) + (√2 − 1)
Middle terms cancel: 2 − 1 = 1
Square root of a number with a root inside
common"Find √(11 + 6√2)."
Write it as a + 2√b.
Find two numbers that add to a and multiply to b; their square roots add up.
Find √(11 + 6√2).
6√2 = 2 × 3√2 = 2√18
Two numbers adding to 11 and multiplying to 18: 9 and 2
√(11 + 2√18) = √9 + √2
= 3 + √2
Square root, cube root and making a perfect square
very common"What is the least number to add to 1300 to make it a perfect square?"
Find the perfect squares just below and just above the number.
The gap to the next one is what you add.
Least number to add to 1300 to get a perfect square?
36² = 1296 (too small)
37² = 1369 (just above 1300)
1369 − 1300 = 69
Roots inside roots that never end
common"√(20 × √(20 × √(20 × ...)))"
Call the whole thing x.
The inside repeats, so replace it by x and solve.
√(20 × √(20 × √(20 × ...))) = ?
Let x = √(20 × x)
Square both sides: x² = 20x
Divide by x: x = 20
Quick estimates
very common"Find the approximate value of 29.9% of 1199.8 + 15.02 × 23.9."
Round every number to an easy one.
Calculate and pick the nearest option.
29.9% of 1199.8 + 15.02 × 23.9 ≈ ?
29.9% ≈ 30% and 1199.8 ≈ 1200, so 30% of 1200 = 360
15.02 × 23.9 ≈ 15 × 24 = 360
360 + 360 = 720