A level reminders

Differentiating sin(x) gives

• cos(x)

• -cos(x)

• cosec(x)

• cos2x

Differentiating e^2x gives:

• 0.5e^2x

• e^2x

• 2e^2x

• ln(2x)

cosec(x) is the same as

• 1/tan(x)

• 1/sin(x)

• 1/cos(x)

The integral of ln(x) is

• xln(x)

• 2xln(x)

• xln(x) - x

• ln(x) - x

To find the integral of ln(x) we use:

• The chain rule

• The quotient rule

• Integration by parts using ln(x) / 1

• First principles

e^4x = ....

[Multiple possible answers]

• (e^2x)²

• e^x x e^3x

• e^2x + e^2x

• e^12x / e^3x

• e^12x / e^8x

Factorise a^6y - 9

• (a⁶ - 3)(a^y + 3)

• (a^3y - 3)(a^3y + 3)

• (a^6y - 3)(a^y + 3)

To integrate cos²x

• Use the identities cos2x = cos²x - sin²x and cos²x + sin²x = 1

• Use a substitution such as u = cos(x)

• It is simply sin²x

To use the general form of the binomial expansion, (3 - 2x)ⁿ rearranges as:

• 0.5(6 - x)ⁿ

• 3(1 - 2x)ⁿ

• 1/3 (1 - 6x)ⁿ

• 3 (1 - 2x/3)ⁿ