Core 4

Core 4

1. To multiply algebraic fractions: - Fully factorise all numerators and denominators - Cancel common factors - Multiply the numerators and multiply the denominators

2. To divide algebraic fractions: - Change to multiply and invert the last fraction - Follow multiplication rules

3. To add or subtract algebraic fractions: - Factorise the denominators - Express each term as a fraction whose denominator is the lowest common multiple of all the denominators - Add or subtract the fractions, writing a common denominator - Simplify the numerator, factorising if possible - Cancel common factors if possible

4. sink(x) differentiates to kcosk(x)

   • sink(x) integrates to (-1/k)cosk(x) +c

5. cosk(x) differentiates to -ksink(x)

   • cosk(x) integrates to (1/k)sink(x) +c

6. tank(x) differentiates to ksec^2(x)

   • sec^2k(x) integrates to (1/k)tank(x) +c

7. sin2A= 2sinAcosA

   • cos2A= 2cos^2A-1
     • tan2A= 2tanA/(1-tan^2A)

8. Must be in radians

   • tan(x) integrates to ln|sec(x)| +c
   • cot(x) integrates to ln|sin(x)| +c
   • cosec(x) integrates to -ln|cosec(x)+cot(x)| +c
   • sec(x) integrates to ln|sec(x)+tan(x)| +c

9. To differentiate a function defined parametrically: - Differentiate x with respect to t - Differentiate y with respect to t - Use a version of the chain rule

10. A scalar is a quantity that has magnitude only

    • E.g/ length, distance, speed and volume

11. A vector is a quantity that has magnitude and a direction

    • E.g/ displacement, velocity, acceleration, momentum