Math Compilation

Question 1

What is the formula for finding a particular term of a binomial expansion?

Answer 1

nCr * a^n-r * x^r

Question 2

What is the remainder theorem?

Answer 2

If a function, f(x) is to be divided by (x-a), then f(a) is equal to the remainder, if any, gotten from the division.

Question 3

How does the factor theorem differ from the remainder theorem?

Answer 3

If f(a) = 0, then (x-a) is a factor of f(x)

Question 4

What is the formula for the sum of n terms of an AP?

Answer 4

S_n = n/2 * (2a + (n–1)d)

Question 5

What is the formula for the nth term (T_n) of an AP?

Answer 5

T_n = a + (n–1)d

Question 6

What is the formula for the sum of n terms of a GP?

Answer 6

S_n = a (rⁿ – 1) / (r – 1) OR
S_n = a (1 – rⁿ) / (1 – r)

Question 7

What is the formula for the nth term (T_n) of a GP?

Answer 7

T_n = ar^{(n– 1)}

Question 8

What is the formula for the sum to ∞ of a GP?

Answer 8

S^∞ = a/ (1 – r)

Question 9

In probability, if you have p (A ∪ B), what does that mean?

“A union B”

Answer 9

Or

Question 10

In probability, if you have p (A ∩ B), what does that mean?

“A intersection B”

Answer 10

And

Question 11

If you are asked to calculate the probability of A or B happening, what do you do?

Answer 11

p (A) + p (B)

Question 12

If you are asked to calculate the probability of A and B happening, what do you do?

Answer 12

p (A) * p (B)

Question 13

What do you do when you are told that two line equations intersect?

Answer 13

Solve them simultaneously

Question 14

How does the gradient of the normal to the curve at a point relate to the gradient of the tangent to the curve at that point?

Answer 14

m_Norm. = - 1 / m_Tan.

This also applies to the gradients of any 2 lines that are ⊥ to each other

Question 15

How do you find the coordinates of the midpoint btw two points on a line?

Answer 15

0.5(x₁ + x₂) , 0.5(y₁ + y₂)

Question 16

What is the quadratic formula?

Answer 16

[ -b ± √b² - 4ac ] / 2a

Question 17

What is the discriminant in the quadratic formula?

Answer 17

b² - 4ac

Question 18

What is the implication if the discriminant is equal to 0?

Answer 18

The quadratic equation has one real repeated root

Question 19

What is the implication if the discriminant is less than 0?

Answer 19

The quadratic equation has no real root or 2 complex roots

Question 20

What is the implication if the discriminant is greater than 0?

Answer 20

The quadratic equation has two distinct real roots

Question 21

How can you use the discriminant to check if a quadratic is factorisable?

Answer 21

If b² - 4ac is a perfect square , the quadratic is factorable