Maths Skills

Question 1

Percentage Change

Answer 1

(Actual change / over original x 100) OR (change in y / change in x)

% increase:
-E.g by 10% = x 1.1,

% decrease:
-E.g by 10% = x 0.9.

Question 2

Standard form

Answer 2

A x 10^n

-A has to be between 1 and 10.
-n has to be a whole number (positive or negative).

Positive - n tells us how many times you have to multiply by 10 (move decimal point to the right).
4 x 10^1 = 40 (4x 10)
4 x 10^2 = 400 (4 x 100)
4 x 10^3 = 4000 (4 x 1000)
4 x 10^4 = 40,000 (4 x 10,000)

Negative - n tells us how many times you have to divide by 10 (move decimal point to the left).
4 x 10^-1 = 0.4
4x 10^-2 = 0.04

Question 3

Significant figures and estimation

Answer 3

1sf, 2sf, 3sf etc…

-Decimals - after the decimal point, the first significant digit is the first non-zero. E.g 0.0005734 to 3sf = 0.000573

Question 4

Probability

Answer 4

0.01 = 1% probability
0.80 = 80% probability

Levels of significance:
-0.05 = a 5% probability the null hypothesis is correct (or 5% margin for error) - 95% certainty/confidence that it’s not due to chance and instead due to the variables under investigation - the default level of significance (between the other two levels of significance).
-0.10 = 10% margin for error - 90% certainty/confidence that it’s not due to chance - more lenient level of significance - prone to a type 1 error (false positive).
-0.01 = 1% margin for error - 99% certainty/confidence that it’s not due to chance - more stringent level of significance - hence used in medical research / drug testing - prone to a type 2 error (false negative).

Question 5

Algebra

Answer 5

a ∝ b (a is directly proportional to b)

a ∝ 1/b (a is inversely proportional to b)