Question bank

TMUA-P1-MM3-001

In an arithmetic sequence the 3rd term is $11$ and the 8th term is $31$. What is the first term?

TMUA-P1-MM3-002

What is the gradient of the straight line passing through $(1, 2)$ and $(5, 10)$?

TMUA-P1-MM3-003

What is the centre of the circle $(x - 3)^2 + (y + 2)^2 = 25$?

TMUA-P1-MM3-004

What is the gradient of a line perpendicular to $y = 3x - 7$?

TMUA-P1-MM3-005

Find the equation of the line through $(2, 5)$ parallel to $y = 4x - 1$.

TMUA-P1-MM3-006

The circle $x^2 + y^2 - 6x + 4y - 3 = 0$ has radius $r$. What is $r$?

TMUA-P1-MM3-007

$AB$ is a diameter of a circle with centre $O$, and $C$ lies on the circle. If angle $CAB = 34^\circ$, what is angle $CB…

TMUA-P1-MM3-008

$O$ is the centre of a circle and $A, B$ lie on the circle with angle $AOB = 100^\circ$. What is angle $OAB$?

TMUA-P1-MM3-009

A circle has centre $O(0, 0)$ and the point $P(6, 4)$ lies on it. Find the equation of the tangent to the circle at $P$.

TMUA-P1-MM3-010

The line $y = x + 1$ crosses the circle $x^2 + y^2 = 25$ at two points. What is the length of the chord joining them?

TMUA-P1-MM3-011

A cyclic quadrilateral has two opposite angles $(3x + 20)^\circ$ and $(x + 40)^\circ$. What is the larger of these two a…

TMUA-P1X-MM3-01

What is the centre of the circle $(x + 4)^2 + (y - 5)^2 = 36$?

TMUA-P1X-MM3-02

The circle $x^2 + y^2 + 8x - 6y + 9 = 0$ has radius $r$. What is $r$?

TMUA-P1X-MM3-03

The circle $x^2 + y^2 = 25$ passes through $P(3, 4)$. Find the equation of the tangent to the circle at $P$.

TMUA-P1X-MM3-04

A cyclic quadrilateral has two opposite angles $(2x + 10)^\circ$ and $(3x + 15)^\circ$. What is the larger of these two…

TMUA-P1X-MM3-05

The line $y = 2x + k$ with $k > 0$ is tangent to the circle $x^2 + y^2 = 20$. What is $k$?