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Formulas & Tips

📈 Linear Equations (7th) Vedic

Formulas

ax + b = c → x = (c − b)/a
Two-step: undo +/− then ×/÷

Tips (Easy)

Gather x-terms on one side.
Plug back in to check.

Vedic

Sutras

Transpose & Adjust

Mental Rules

ax + b = c → x = (c − b)/a (done as one mental flow)

Quick Tricks

Cancel common factors in (c−b)/a to keep numbers small.

¼ Fractions (7th) Vedic

Formulas

(a/b)×(c/d)=(ac)/(bd)
(a/b)÷(c/d)=(a/b)×(d/c)

Tips (Easy)

Cancel before multiplying.
Keep-Change-Flip for division.

Vedic

Sutras

Vertically & Crosswise (for simple cancellations)

Mental Rules

Before multiplying, cancel common factors ‘crosswise’ to keep numbers small.

Quick Tricks

Cancel 2s/5s to end with neat 10s (decimal friendly).

📐 Algebraic Expressions (7th)

Formulas

a(b − c) = ab − ac
GCF: ax + ay = a(x + y)

Tips (Easy)

Circle like terms.
Factor GCF first when possible.

≶ Inequalities (7th)

Formulas

Multiply/divide by negative → flip sign

Tips (Easy)

Treat like equations until ×/÷ negative.
Combine like terms first.

％ Percent Problems (7th) Vedic

Formulas

Increase: ×(1 + p/100)
Decrease: ×(1 − p/100)

Tips (Easy)

% change = (new−old)/old.
Discounts multiply, don’t add.

Vedic

Sutras

Complementary % (near 100%)

Mental Rules

98% of N = N − 2% of N (use when % is close to 100%)

Quick Tricks

Chain discounts: multiply factors, e.g., 20% off then 10% off → ×0.8×0.9

🎲 Probability (7th) Vedic

Formulas

Independent: P(A∩B)=P(A)P(B)
Complement: P(Aᶜ)=1−P(A)

Tips (Easy)

Use complement for “at least one”.
Tree diagrams help.

Vedic

Sutras

Use the complement (quick mental path)

Mental Rules

P(≥1) = 1 − P(0) (often faster to compute)

Quick Tricks

Estimate first; check if your answer is reasonable (<1, ≥0).

📊 Statistics (7th)

Formulas

Mode = most common
Range = max − min

Tips (Easy)

Read histograms: tallest = most frequent.
Compare centers & spreads.

📏 Geometry (7th)

Formulas

Triangle: A=½bh
Circle: A=πr², C=2πr

Tips (Easy)

Height ⟂ base.
Use π≈3.14 unless told otherwise.

🧭 Graphing Equations (7th)

Formulas

m=(y₂−y₁)/(x₂−x₁)

Tips (Easy)

Pick clean points.
Negative slope → line falls to the right.

📐 Pythagorean Theorem (7th)

Formulas

a = √(c² − b²)

Tips (Easy)

Right triangles only.
Square before ops.

🧮 LCM and HCF (7th)

Formulas

Euclid’s algorithm (remainders)

Tips (Easy)

LCM for ‘line up’ problems.
HCF for equal groups.

^ Exponents and Powers (7th)

Formulas

a^m·a^n=a^(m+n)
a^m/a^n=a^(m−n)

Tips (Easy)

Same base only.
a^0=1 (a≠0).

📚 Decimals (7th)

Formulas

Multiply: total decimal places = sum of factors’ places

Tips (Easy)

Ignore decimals to multiply, then place the point.
Estimate to check.

📚 Systems of Equations (7th)

Formulas

Substitution: solve one for x/y
Elimination: add/sub equations to cancel

Tips (Easy)

Line up variables.
Multiply to line up coefficients.

📚 Scientific Notation (7th) Vedic

Formulas

(a×10^m)(b×10^n)=(ab)×10^(m+n)

Tips (Easy)

Multiply a’s, add exponents.

Vedic

Sutras

Place-value moves (mental)

Mental Rules

Shift decimal mentally first, then multiply small a,b.

Quick Tricks

Round a,b to 1 digit to estimate exponent result sanity check.

📚 Ratios and Rates (7th) Vedic

Formulas

a/b = c/d → ad = bc

Tips (Easy)

Cross-multiply to solve.
Keep units consistent.

Vedic

Sutras

Proportion by observation

Mental Rules

a/b ≈ c/d? Compare cross-products mentally for a quick check.

Quick Tricks

Scale small pairs to match one side first, then compare.

📚 Quadratics (7th) Vedic

Formulas

(x+p)(x+q)=x²+(p+q)x+pq

Tips (Easy)

Look for two numbers p,q.

Vedic

Sutras

By observation (pair-sum & product)

Mental Rules

Find p,q with sum=b and product=c to factor quickly (when a=1).

Quick Tricks

Keep factor pairs in a tiny table; spot the right pair fast.

📚 Proportions (7th) Vedic

Formulas

Scale up/down with same factor

Tips (Easy)

Use tables/graphs.
Keep units aligned.

Vedic

Sutras

Unitizing (per-one)

Mental Rules

Reduce to per-1 quickly to scale up/down mentally.

Quick Tricks

If both sides scale by k, proportions hold.

📚 Polynomials (7th)

Formulas

(ax+…)+(bx+…) = (a+b)x+…
(ax+…)-(bx+…) = (a−b)x+…

Tips (Easy)

Add/subtract coefficients for each power.
Watch signs.

📚 Number Systems (7th)

Formulas

|a| = distance from 0

Tips (Easy)

Absolute value is nonnegative.

📚 Angle Reasoning (7th)

Formulas

Vertical angles are equal
Linear pair sums to 180°

Tips (Easy)

Look for linear pairs.
Opposite angles match.

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