Maths - Geometry

621 Words3 Pages
Geometry and trigonometry Topic assessment 1. Describe fully the curve whose equation is [pic]. [2] 2. Show that the line y = 3x – 10 is a tangent to the circle [pic]. [4] 3. The equation of a circle is [pic] i) Find the coordinates of the centre C of the circle, and the radius of the circle. [3] ii) Show that the point P (4, -5) lies on the circle. [1] iii) Find the equation of the tangent to the circle at the point P. [4] 4. AB is the diameter of a circle. A is (1, 3) and B is (7, -1). i) Find the coordinates of the centre C of the circle. [2] ii) Find the radius of the circle. [2] iii) Find the equation of the circle. [2] iv) The line y + 5x = 8 cuts the circle at A and again at a second point D. Calculate the coordinates of D. [4] v) Prove that the line AB is perpendicular to the line CD. [3] 5. Find the angle ( and the length x in the triangle shown below. [7] 6. Andrew walks 5 km on a bearing of 140°, and then walks 3 km on a bearing of 025°. (i) How far is Andrew from his starting point? [3] (ii) On what bearing should Andrew walk to get back to his starting point? [4] 7. A belt is wrapped around a cylinder of radius 2.5 m as shown. Find the length of the belt. [5] 8. Find the perimeter and area of the shaded sections of these shapes. (i) [7] (ii) [7] Total 60 marks Geometry and trigonometry Solutions to Topic assessment 1. The curve is a circle, centre O and radius 2. [2] 2. Substituting [pic] into [pic] gives [pic] Since the equation has a repeated root, the line meets the circle just once, and so the line is a tangent to the circle. [4]

More about Maths - Geometry

Open Document