Calculus - Algebra (4)

Question 1

If 9^2a+b = 27^2+2b, what is a?

Answer 1

1. 9 is 3^2 and 27 is 3^3. Replace these in the equation with brackets
2. Expand the exponent brackets
3. Get rid of the 3
4. Solve for b in terms of a

Question 2

When it says “exceeds”

Answer 2

Do a > sign

Question 3

Something with unknown powers

Answer 3

1. Simplify
2. Either substitute another number in for that one of use logs

Question 4

To find ‘K’ in a formula

Answer 4

Put it in either the quadratic formula or roots formula

Question 5

Roots?

Answer 5

> 0 = 2 Roots
= 0 = 1 Root
< 0 = No roots

Question 6

4log2(x) = 12

Answer 6

Can simplify the parts before & after the fraction. So log2(x) = 3

Question 7

If logs are zero or negative

Answer 7

Because the answer is undefined, it can’t be zero or -ve.

Question 8

K in an equation and they give you coordiates or when it crosses the graph, and asks for another intercept

Answer 8

Put x & y into the formula to find what K is.
Find what x can equal in the quadratic formula
Find the coordinates by the 1st equation

Question 9

When it says the x-intercepts are when x=2 & x=3

Answer 9

It would be (x-2)(x-3)=y or =0

Question 10

When a^x = b^x+1, making x the subject

Answer 10

1. Take the logs of both sides
2. Expand to xlogb + logb
3. Put all the x’s on one side
4. Factorise by taking the xs out
5. Divide the 2nd side by the first, leaving the x out

Question 11

When 1/x is in an equation

Answer 11

Multiply EVERYTHING by x

Question 12

Kinematics. When we get the time taken/speed, etc.

Answer 12

We can rearrange and use the v=d/t equation. To find where they meet, sub in the times.

Question 13

Trying to find x where all the denominators are x, or x+1, etc.

Answer 13

Make the denominators the same, this makes them disappear.