TMUA · Paper 1: Applications of Mathematical Knowledge

Mathematical problem solving

16 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 16 questions

How many ordered pairs $(a, b)$ of positive integers satisfy $\frac{1}{a} + \frac{1}{b} = \frac{1}{6}$ ?
How many positive integers less than $100$ are multiples of $3$ or of $5$ but not of both?
What is the sum of the digits of the number $2^{10} \times 5^{7}$ ?
What is the remainder when $7^{100}$ is divided by $5$ ?
How many of the integers from $1$ to $1000$ inclusive are perfect squares or perfect cubes?
How many integers $x$ satisfy $∣ x - 3∣ + ∣ x + 2∣ \leq 7$ ?
A square is inscribed in a circle of radius $5$ (all four vertices lie on the circle). What is the area of the square?
Two fair six-sided dice are rolled. What is the probability that the sum of the scores is a prime number?
How many three-digit numbers have their digits in strictly increasing order from left to right (for example $138$ or $459$ )?
A right-angled triangle has shorter sides $6$ and $8$ . What is the radius of its inscribed circle?
What is the volume of a cone with base radius $3$ and slant height $5$ ?
What is the value of $k = 1 \sum 99 \frac{1}{k ( k + 1 )}$ ?
How many positive divisors does $360$ have?
How many real solutions does $x + 6 = x$ have?
The sum of the first $n$ terms of a sequence is $S_{n} = n^{2} + 4 n$ . What is the sum of the $11$ th to the $20$ th terms inclusive?
How many ordered pairs of integers $(x, y)$ satisfy $x^{2} - y^{2} = 45$ ?

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