Exercise Solutions Available
Step-by-step answers for all textbook questions in this chapter
How to Revise Formulae
Do not only read formulae. Cover the page, write them from memory, and solve one sum for each formula. Keep a separate list for formulae you forget often.
Relations and Functions
| Concept | Reminder |
|---|---|
| Ordered pair | (x, y) where order matters. |
| Cartesian product | A x B = {(a, b): a in A, b in B} |
| Domain | Set of first elements or input values. |
| Range | Set of second elements or output values. |
| Function test | Every input must have exactly one output. |
Numbers and Sequences
| Concept | Formula or Rule |
|---|---|
| Euclid division lemma | a = bq + r, 0 <= r < b |
| HCF and LCM relation | HCF x LCM = product of two numbers |
| nth term of AP | a_n = a + (n - 1)d |
| Sum of first n terms | S_n = n/2 [2a + (n - 1)d] |
| Sum using first and last term | S_n = n/2 (a + l) |
Algebra
| Concept | Formula |
|---|---|
(a + b)^2 | a^2 + 2ab + b^2 |
(a - b)^2 | a^2 - 2ab + b^2 |
a^2 - b^2 | (a + b)(a - b) |
| Quadratic equation | ax^2 + bx + c = 0 |
| Quadratic formula | x = [-b +- sqrt(b^2 - 4ac)] / 2a |
| Discriminant | D = b^2 - 4ac |
Coordinate Geometry
| Concept | Formula | ||
|---|---|---|---|
| Distance | sqrt((x2 - x1)^2 + (y2 - y1)^2) | ||
| Midpoint | ((x1 + x2)/2, (y1 + y2)/2) | ||
| Slope | (y2 - y1) / (x2 - x1) | ||
| Area of triangle | `1/2 | x1(y2-y3) + x2(y3-y1) + x3(y1-y2) | ` |
Trigonometry
| Ratio | Meaning |
|---|---|
sin theta | Opposite side / Hypotenuse |
cos theta | Adjacent side / Hypotenuse |
tan theta | Opposite side / Adjacent side |
cosec theta | 1 / sin theta |
sec theta | 1 / cos theta |
cot theta | 1 / tan theta |
Trigonometric Identities
sin^2 theta + cos^2 theta = 11 + tan^2 theta = sec^2 theta1 + cot^2 theta = cosec^2 thetatan theta = sin theta / cos thetacot theta = cos theta / sin theta
Mensuration
| Shape | Formula |
|---|---|
| Cylinder curved surface area | 2 pi rh |
| Cylinder total surface area | 2 pi r(h + r) |
| Cylinder volume | pi r^2 h |
| Cone curved surface area | pi rl |
| Cone total surface area | pi r(l + r) |
| Cone volume | 1/3 pi r^2 h |
| Sphere surface area | 4 pi r^2 |
| Sphere volume | 4/3 pi r^3 |
| Hemisphere curved surface area | 2 pi r^2 |
| Hemisphere total surface area | 3 pi r^2 |
Statistics and Probability
| Concept | Formula |
|---|---|
| Mean | sum of observations / number of observations |
| Mean from frequency table | sum fx / sum f |
| Probability | number of favourable outcomes / total number of outcomes |
Last Week Formula Routine
1. Write all formulae from memory. 2. Mark the forgotten formulae in red. 3. Solve two textbook sums from each weak formula. 4. Reattempt one model paper formula question set. 5. Revise theorem statements with formulae.
Revision Checklist
- AP formulae memorised
- Algebra identities written correctly
- Coordinate formulae practised
- Trigonometric identities revised
- Mensuration units checked
- Statistics and probability formulae ready
Frequently Asked Questions
Write the formula sheet from memory every three days, then solve one example for each formula.