GCE Advanced Level (Sri Lanka) · Combined Mathematics

Pure Maths: Coordinate Geometry, Vectors and Counting

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

Practise Pure Maths: Coordinate Geometry, Vectors and Counting now

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All 48 questions

The point $P (2, 3)$ lies outside the circle with centre $(- 1, - 1)$ and radius $3$ . Find the length of a tangent from $P$ to the circle.
A bag contains 5 red and 7 blue balls. Two balls are drawn without replacement. Find the probability that both are red.
Find the radius of the circle $x^{2} + y^{2} - 8 x - 10 y + 16 = 0$ .
Find the $y$ -intercept of the line through $(- 3, - 9)$ and $(- 1, - 7)$ .
In how many ways can $5$ different books be arranged in a row on a shelf if two particular books must be together?
Find the radius of the circle $x^{2} + y^{2} + 8 x + 8 y - 17 = 0$ .
Find the $y$ -intercept of the line through $(- 2, 0)$ and $(0, - 4)$ .
Find $a \cdot b$ for $a = 0 i + 0 j - 3 k$ and $b = 3 i + 4 j + 5 k$ .
In how many ways can $6$ different books be arranged in a row on a shelf if two particular books must be together?
Find the coordinates of the centre of the circle $x^{2} + y^{2} + 8 x + 2 y + 8 = 0$ .
The point $P (5, 11)$ lies outside the circle with centre $(0, - 1)$ and radius $5$ . Find the length of a tangent from $P$ to the circle.
In how many ways can $7$ different books be arranged in a row on a shelf if two particular books must be together?
Find the radius of the circle $x^{2} + y^{2} - 6 x - 8 y + 16 = 0$ .
Find the $y$ -intercept of the line through $(- 2, 2)$ and $(- 1, - 2)$ .
Find $a \cdot b$ for $a = - 4 i + 3 j - 4 k$ and $b = 4 i + 0 j + 3 k$ .
Find the coordinates of the centre of the circle $x^{2} + y^{2} + 6 x - 10 y - 30 = 0$ .
Find the $y$ -intercept of the line through $(- 1, 5)$ and $(3, 1)$ .
In how many ways can a committee of 4 be chosen from 7 people?
Find the $y$ -intercept of the line through $(1, - 5)$ and $(5, - 1)$ .
Find the magnitude of $4 i + 4 j + 7 k$ .
A bag contains 6 red and 3 blue balls. Two balls are drawn without replacement. Find the probability that both are red.
The point $P (2, 6)$ lies outside the circle with centre $(- 1, 2)$ and radius $3$ . Find the length of a tangent from $P$ to the circle.
A bag contains 3 red and 6 blue balls. Two balls are drawn without replacement. Find the probability that both are red.
Find the coordinates of the centre of the circle $x^{2} + y^{2} + 6 x - 10 y + 25 = 0$ .
The point $P (0, 8)$ lies outside the circle with centre $(- 3, 4)$ and radius $4$ . Find the length of a tangent from $P$ to the circle.
Find the magnitude of $6 i + 2 j + 3 k$ .
Find the coordinates of the centre of the circle $x^{2} + y^{2} - 2 x - 8 y + 1 = 0$ .
Find the $y$ -intercept of the line through $(- 3, - 7)$ and $(0, - 4)$ .
Find the magnitude of $1 i + 2 j + 2 k$ .
Find the radius of the circle $x^{2} + y^{2} - 4 x - 4 y - 8 = 0$ .
Find $a \cdot b$ for $a = - 2 i + 5 j - 2 k$ and $b = 5 i + 1 j + 5 k$ .
In how many ways can a committee of 2 be chosen from 7 people?
Find the coordinates of the centre of the circle $x^{2} + y^{2} + 4 x + 10 y - 7 = 0$ .
Find the $y$ -intercept of the line through $(- 1, - 7)$ and $(0, - 5)$ .
Find the magnitude of $2 i + 3 j + 6 k$ .
In how many ways can $4$ different books be arranged in a row on a shelf if two particular books must be together?
Find the coordinates of the centre of the circle $x^{2} + y^{2} - 8 x + 4 y - 44 = 0$ .
The point $P (6, 11)$ lies outside the circle with centre $(1, - 1)$ and radius $5$ . Find the length of a tangent from $P$ to the circle.
Find the radius of the circle $x^{2} + y^{2} - 4 x + 4 y - 28 = 0$ .
The point $P (6, 4)$ lies outside the circle with centre $(3, 0)$ and radius $3$ . Find the length of a tangent from $P$ to the circle.
Find the $y$ -intercept of the line through $(2, 8)$ and $(3, 11)$ .
Find $a \cdot b$ for $a = 3 i - 2 j + 4 k$ and $b = 2 i + 0 j + 2 k$ .
Find the radius of the circle $x^{2} + y^{2} + 6 x - 10 y - 30 = 0$ .
Find the $y$ -intercept of the line through $(- 3, 11)$ and $(- 1, 3)$ .
Find the radius of the circle $x^{2} + y^{2} - 4 x - 2 y - 4 = 0$ .
Find $a \cdot b$ for $a = 1 i - 3 j + 1 k$ and $b = - 3 i - 4 j + 4 k$ .
Find the radius of the circle $x^{2} + y^{2} - 4 x - 8 y - 5 = 0$ .
The point $P (1, 6)$ lies outside the circle with centre $(- 2, 2)$ and radius $4$ . Find the length of a tangent from $P$ to the circle.

Pure Maths: Coordinate Geometry, Vectors and Counting

Practise Pure Maths: Coordinate Geometry, Vectors and Counting now

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