TMUAQuestions

Every question from the released TMUA papers, 318 in all. Open one to answer it.

318 questions

Determine the number of stationary points on the curve with equation $y = 3 x^{4} + 4 x^{3} + 6 x^{2} - 5$ TMUA 2022 · Paper 1 · Question 1 · Save
Find the coefficient of the $x^{5}$ term in the expansion of $(1 + x)^{5} \times \sum_{i = 0}^{5} x^{i}$ TMUA 2022 · Paper 1 · Question 2 · Save
Consider the following statement about the positive integer $n$ if $n$ is prime, then $n^{2} + 2$ is not prime Which of the following is a counterexample to this statement? I $n = 2$ II $n = 3$ III $n = 4$ TMUA 2022 · Paper 1 · Question 3 · Save
The point $P$ has coordinates $(p, q)$ , and the equation of a circle is $x^{2} + 2 f x + y^{2} + 2 g y + h = 0$ where $f, g, h, p$ and $q$ are all real constants. Let $L$ be the distance between the centre of the circle and the point $P$ . Which one of the following is sufficient on its own to be able to calculate $L$ ?TMUA 2022 · Paper 1 · Question 4 · Save
A straight line $L$ passes through $(1, 2)$ . Let $P$ be the statement if the $y$ -intercept of $L$ is negative, then the $x$ -intercept of $L$ is positive. Which of the following statements must be true? I $P$ II the converse of $P$ III the contrapositive of $P$ TMUA 2022 · Paper 1 · Question 5 · Save
Consider the following claim: The difference between two consecutive positive cube numbers is always prime. Here is an attempted proof of this claim: I $(x + 1)^{3} = x^{3} + 3 x^{2} + 3 x + 1$ II Taking $x$ to be a positive integer, the difference between two consecutive cube numbers can be expressed as…TMUA 2022 · Paper 1 · Question 7 · Save
A selection, $S$ , of $n$ terms is taken from the arithmetic sequence $1, 4, 7, 10, \dots, 70$ . Consider the following statement: $()$ There are two distinct terms in $S$ whose sum is 74. What is the smallest value of $n$ for which $()$ is necessarily true?TMUA 2022 · Paper 1 · Question 8 · Save
Consider the following statement: $()$ For all real numbers $x$ , if $x < k$ then $x^{2} < k$ What is the complete set of values of $k$ for which $()$ is true?TMUA 2022 · Paper 1 · Question 9 · Save
Which of the following statements is/are true? I For all real numbers $x$ and for all positive integers $n, x < n$ II For all real numbers $x$ , there exists a positive integer $n$ such that $x < n$ III There exists a real number $x$ such that for all positive integers $n, x < n$ TMUA 2022 · Paper 1 · Question 10 · Save
[IMAGE_PLACEHOLDER] The diagram shows a kite $PQRS$ whose diagonals meet at $O$ . $OP = x$ $OQ = y$ $OR = x$ $OS = z$ Which of the following is necessary and sufficient for angle $SPQ$ to be a right angle?TMUA 2022 · Paper 1 · Question 11 · Save
Place the following integrals in order of size, starting with the smallest. $P = \int_{0}^{1} 2^{x} d x$ $Q = \int_{0}^{1} 2^{x} d x$ $R = \int_{0}^{1} (2)^{x} d x$ TMUA 2022 · Paper 1 · Question 12 · Save
Consider the statement $()$ about a real number $x$ : $()$ There exists a real number $y$ such that $x - x y + y$ is negative. For how many real values of $x$ is $()$ true?TMUA 2022 · Paper 1 · Question 13 · Save
Consider the two inequalities: $∣ x + 5∣ < ∣ x + 11∣$ $∣ x + 11∣ < ∣ x + 1∣$ Which one of the following is correct?TMUA 2022 · Paper 1 · Question 14 · Save
The real numbers $x, y$ and $z$ are all greater than 1, and satisfy the equations $lo g_{x} y = z and lo g_{y} z = x$ Which one of the following equations for $lo g_{z} x$ must be true?TMUA 2022 · Paper 1 · Question 15 · Save
In this question, $a_{1}, \dots, a_{100}$ and $b_{1}, \dots, b_{100}$ and $c_{1}, \dots, c_{100}$ are three sequences of integers such that $a_{n} \leq b_{n} + c_{n}$ for each $n$ . Which of the following statements must be true? I…TMUA 2022 · Paper 1 · Question 16 · Save
Consider the following statements about integers $x$ and $y$ : P: $x^{2} + y^{2}$ is divisible by 4. Q: $x$ and $y$ are both even integers. Which one of the following is true?TMUA 2022 · Paper 1 · Question 17 · Save
A triangle has sides $x^{2} - x y + y^{2}, x^{2} + x y + y^{2}$ and $x^{2} + y^{2}$ . Which of the following describes the largest angle of the triangle?TMUA 2022 · Paper 1 · Question 18 · Save
Consider the statement $()$ about a real number $x$ . $()$ $(∣ x ∣ - 1) (∣ x ∣ - 2) \geq 0$ What is the largest possible range of values of $x$ for which $()$ is false?TMUA 2022 · Paper 1 · Question 19 · Save
Let $lo g_{b} x = y$ . Consider the following statements: I $lo g_{x} x^{y} = x$ II $lo g_{x} lo g_{y} y^{x} = x$ III $lo g_{y} lo g_{x} b = - 1$ Which of these statements is/are true for all permissible real numbers $x, y$ and $b$ ?TMUA 2022 · Paper 1 · Question 20 · Save
Determine the number of stationary points on the curve with equation $y = 3 x^{4} + 4 x^{3} + 6 x^{2} - 5$ TMUA 2022 · Paper 2 · Question 1 · Save

20 of 318Show 20 more

TMUA/Questions

TMUAQuestions