Cambridge IGCSE Further Mathematics: every topic, by paper

What does x ∈ A mean?

x is an element (member) of set A.

What do A ∪ B and A ∩ B mean?

A ∪ B: the union (elements in A or B or both). A ∩ B: the intersection (elements in both).

What does A′ mean?

The complement of A: elements in the universal set that are not in A.

What is f(x) notation?

A way of writing a function: f(x) = 3x + 2 means the output when x is input.

Find f(−2) for f(x) = x² − 3x.

4 + 6 = 10.

What is the domain of f(x) = 1/(x − 3)?

All real numbers except x = 3.

What is an asymptote?

A line that a graph approaches but never touches.

Give the asymptotes of y = 1/x.

x = 0 and y = 0.

Give the asymptotes of y = 1/(x − 2) + 3.

x = 2 and y = 3.

What is exponential growth?

A quantity multiplied by the same factor over equal time intervals, e.g. y = a × bˣ with b > 1.

A population of 500 grows by 8% a year. Write a formula for the population after t years.

P = 500 × 1.08ᵗ.

What is exponential decay?

A quantity multiplied by a factor between 0 and 1 over equal time intervals.

What is the nth term of 5, 9, 13, 17, …?

4n + 1.

What is the nth term of the geometric sequence 3, 6, 12, 24, …?

3 × 2ⁿ⁻¹.

Find the nth term of 2, 6, 12, 20, 30, …

n² + n.

State SOH CAH TOA.

sin = opp/hyp, cos = adj/hyp, tan = opp/adj.

State the sine rule.

a/sin A = b/sin B = c/sin C.

State the cosine rule.

a² = b² + c² − 2bc cos A.

Find the gradient of the line through (2, 3) and (6, 11).

8 ÷ 4 = 2.

Find the equation of the line through (1, 4) parallel to y = 3x − 2.

y = 3x + 1.

What is the gradient of a line perpendicular to y = −½x + 5?

2.

What is the probability of an event that is certain?

1.

What are mutually exclusive events?

Events that cannot happen at the same time: P(A or B) = P(A) + P(B).

What are independent events?

Events where one does not affect the other: P(A and B) = P(A) × P(B).