Question bank

TMUA-P1-MM1-001

The equation $x^2 + kx + 9 = 0$ has two equal real roots. What is the sum of all possible values of $k$?

TMUA-P1-MM1-002

Simplify $\dfrac{2^3 \times 2^5}{2^4}$.

TMUA-P1-MM1-003

Simplify $\sqrt{50} + \sqrt{18}$, giving your answer in the form $a\sqrt{b}$ with $b$ square-free.

TMUA-P1-MM1-004

Solve $x^2 - 5x + 6 = 0$.

TMUA-P1-MM1-005

Write $x^2 + 6x + 5$ in the form $(x + a)^2 + b$. What is the value of $b$?

TMUA-P1-MM1-006

Let $f(x) = 3x - 7$. What is the value of $f(5)$?

TMUA-P1-MM1-007

Evaluate $\left(\dfrac{27}{8}\right)^{-2/3}$.

TMUA-P1-MM1-008

Rationalise the denominator of $\dfrac{6}{\sqrt{5} - 1}$, giving your answer in its simplest form.

TMUA-P1-MM1-009

The equation $kx^2 + 4x + 1 = 0$, with $k \neq 0$, has two equal real roots. What is the value of $k$?

TMUA-P1-MM1-010

The line $y = 2x + 1$ meets the curve $y = x^2 + 1$ at two points. What is the sum of the $x$-coordinates of these point…

TMUA-P1-MM1-011

How many integers $x$ satisfy $(x - 1)(x - 5) < 0$?

TMUA-P1-MM1-012

Which of the following is a factor of $2x^3 + x^2 - 5x + 2$?

TMUA-P1-MM1-013

Let $f(x) = \sqrt{5 - 2x}$ with domain restricted to real numbers. What is the largest integer $x$ in the domain of $f$?

TMUA-P1-MM1-014

Find the sum of all real solutions of $|3x - 4| = 11$.

TMUA-P1-MM1-015

What is the smallest integer $x$ satisfying $-2x + 7 < 13$?

TMUA-P1-MM1-016

The polynomial $P(x) = x^3 + px^2 + qx - 12$ is divisible by both $(x - 1)$ and $(x + 3)$. What is the value of $p$?

TMUA-P1-MM1-017

The line $y = 3x + k$ is tangent to the curve $y = x^2 + 2x + 1$. What is the value of $k$?

TMUA-P1-MM1-018

How many integers $x$ with $-5 \le x \le 5$ satisfy $\dfrac{x + 2}{x - 3} > 0$?

TMUA-P1-MM1-019

What is the product of all real solutions of $|2x + 1| = |x + 4|$?