Maths Paper 1 and 2: Number Theory

Which of the following numbers is a prime number?

What is the Highest Common Factor (HCF) of 12 and 18?

Which of the following is an irrational number?

Simplify the following algebraic expression: $3x + 2y - x + 5y$

Solve the following linear equation for $x$: $2x + 5 = 11$

What is the solution set for the quadratic equation $x^2 - 5x + 6 = 0$?

Given the simultaneous equations $x + y = 5$ and $x - y = 1$, what are the values of $x$ and $y$?

A bag contains 5 red balls and 3 blue balls. If two balls are drawn at random without replacement, what is the probability that the first ball is red and the second ball is blue?

Solve for $x$: $5x - 3 = 12$.

Which type of triangle has all three sides of equal length?

What is the median of the following data set: 2, 5, 8, 11, 15?

A bag contains 3 red balls and 5 blue balls. If one ball is drawn at random, what is the probability that it is red?

What is the area of a circle with a radius of 7 cm? (Use $\pi = 3.14$)

Determine the next term in the following sequence: 1, 4, 9, 16, 25, ...

Given two events, A and B, where P(A) = 0.6, P(B) = 0.5, and P(A ∩ B) = 0.3, find P(A | B).

What transformation is represented by the mapping $(x, y) \rightarrow (-x, y)$?

Two dice are rolled. What is the probability that the sum of the numbers on the two dice is 7, given that at least one of the dice shows a 4?

Consider the recursively defined sequence: $a_1 = 1$, $a_{n+1} = a_n + 2n$ for $n \ge 1$. Find a closed-form expression for $a_n$.