Maths Non Calc Paper free essay sample

The radius of the base of a cylinder is x cm. The height of the cylinder is 9. 5 cm longer than the radius of its base. The area of the curved surface of the cylinder is equal to the total surface area, 33p cm2, of the toy. (c)Calculate the height of the cylinder. cm (6 marks) ————————————————————————————————————————— Question 3 A tent has a groundsheet as its horizontal base. The shape of the tent is a triangular prism of length 8 metres, with two identical half right-circular cones, one at each end. The vertical cross-section of the prism is an isosceles triangle of height 2. metres and base 3. 6 metres. (a)Calculate the area of the groundsheet. Give your answer, in m2, correct to one decimal place. (3 marks) (b)Calculate the total volume of the tent. Give your answer, in m2, correct to one decimal place. (4 marks) ————————————————————————————————————————— Question 4 A sphere has a radius of 5. 4 cm. A cone has a height of 8 cm. The volume of the sphere is equal to the volume of the cone. Calculate the radius of the base of the cone. Give your answer, in centimetres, correct to 2 significant figures. (3 marks) ————————————————————————————————————————— Question 5 A cylinder has a height of 24 cm and a radius of 4 cm. Work out the volume of the cylinder. Give your answer correct to 3 significant figures. cm3 (2 marks) ————————————————————————————————————————— Question 6 AB is parallel to CD Angle ACB = angle CBD = 90 °. Prove that triangle ABC is congruent to triangle DCB. (3 marks) ————————————————————————————————————————— Question 7 The diagram represents a large cone of heig ht 6 cm and base diameter 18 cm. The large cone is made by placing a small cone A of height 2 cm and base diameter 6 cm on top of a frustum B. Calculate the volume of the frustum B. Give your answer in terms of p. . (4 marks) ————————————————————————————————————————— Question 8 Triangle PQR is isosceles with PQ = PR. X is a point on PQ. Y is a point on PR. PX = PY. Prove that triangle PQY is congruent to triangle PRX. (3 marks) ————————————————————————————————————————— Question 9 The diagram shows a trapezium. The measurements on the diagram are in centimetres. The lengths of the parallel sides are x cm and 20 cm. The height of the trapezium is 2x cm. The area of the trapezium is 400 cm2. (a)Show that x2 + 20x = 400 2 marks) (b)Find the value of x. Give your answer correct to 3 decimal places. . (3 marks) ————————————————————————————————————————— Question 10 The diagram shows a sector of a circle, centre O. The radius of the circle is 9 cm. The angle at the centre of the circle is 40 °. Find the perimeter of the sector. Leave your answer in terms of p. . cm (4 marks) ——————————————————————— Ã¢â‚¬â€Ã¢â‚¬â€Ã¢â‚¬â€Ã¢â‚¬â€Ã¢â‚¬â€Ã¢â‚¬â€Ã¢â‚¬â€Ã¢â‚¬â€Ã¢â‚¬â€Ã¢â‚¬â€Ã¢â‚¬â€Ã¢â‚¬â€Ã¢â‚¬â€Ã¢â‚¬â€Ã¢â‚¬â€Ã¢â‚¬â€Ã¢â‚¬â€ Question 11 In triangle ABC, AC = 8 cm, CB = 15 cm, Angle ACB = 70 °. (a)Calculate the area of triangle ABC. Give your answer correct to 3 significant figures. .. cm2 (2 marks) X is the point on AB such that angle CXB = 90 °. (b)Calculate the length of CX. Give your answer correct to 3 significant figures. . cm (4 marks) ————————————————————————————————————————— Question 12 ABCDEF is a regular hexagon with sides of length 3 cm. PAB, QBC, RCD, SDE, TEF and UFA are equilateral triangles of length 3 cm. Calculate the total area of the shaded shape. Give your answer correct to 3 significant figures. cm2 (4 marks) ————————————————————————————————————————— Question 13 ABCD is a quadrilateral. K is the midpoint of AB. L is the midpoint of BC. M is the midpoint of CD. N is the midpoint of AD. (a)Find, in terms of a, b and c, the vectors. . . . . (4 marks) (b)Write down two geometrical facts about the lines KN and LM which could be deduced from your answers to part (a). (2 marks) ————————————————————————————————————————— Question 14 This is a sketch of the curve with equation y = f(x). The only maximum point of the curve y = f(x) is A(3, 6). Write down the coordinates of the maximum point for curves with each of the following equations. (i)y = f(x + 2) (. , . ) (ii)y = f(x) + 4 (. , . ) (iii)y = f(-x) (. , . ) (3 marks) ————————————————————————————————————————— Question 15 A greenhouse consists of a pyramid on top of a prism. The cross section of the prism and the base of the pyramid is a regular octagon. Each side of the octagon is 0. 80 m long. The height of the prism is 1. 73 m. The height of the pyramid is 0. 68 m. Calculate the volume of the greenhouse. Give your answer correct to 3 significant figures. Volume = m3 (7 marks) ————————————————————————————————————————— Question 16 OAB is a triangle. P is the mid-point of OA. B is the mid-point of OC. . (2 marks) (b)Use vectors to show that AC is parallel to PB. (3 marks) The length of PB is 8 cm. (c)Write down the length of AC. . cm (1 mark) ———————————————————————————————â€⠀Ã¢â‚¬â€Ã¢â‚¬â€Ã¢â‚¬â€Ã¢â‚¬â€Ã¢â‚¬â€Ã¢â‚¬â€Ã¢â‚¬â€Ã¢â‚¬â€Ã¢â‚¬â€ Question 17 a)Find an expression for the area, in cm2, of this trapezium. Give your answer in the form ax2 + bx + c, where a, b and c are integers. Area = cm2 (3 marks) The trapezium is cut from a square of side (2x + 5) cm. On the diagram, the shaded region is the area of the square that is left. (b)Show that the area of the shaded region is (22 + 11x + 21) cm2. (3 marks) The area of the shaded region is 42 cm2. (c)Form and solve a quadratic equation to find the value of x. x = (3 marks) ————————————————————————————————————————— Question 18 The pyramid Cheops in Egypt is a square based pyramid. The length of a side of the square is 230 metres. The vertical height of the pyramid is 146 metres. Both measurements are correct to the nearest metre. (a)Calculate the difference between the upper bound and the lower bound of the volume of the pyramid. Give your answer correct to 3 significant figures. .. m3 (3 marks) The length of a side of a square based pyramid is x metres. The vertical height is y metres. Both measurements are correct to the nearest metre. (b)Find an expression for the difference between the upper bound and he lower bound of the volume of the pyramid. Give your answer in its simplest form. . (3 marks) ——————————————————————————————————————— —— Question 19 The diagram shows a sector OAB of a circle of centre O. The radius of the circle is 12 cm. Angle AOB = 171 °. (a)Calculate the area of the sector AOB. Give your answer correct to 3 significant figures. cm2 (3 marks) OA and OB are joined to make a cone. (b)Calculate the vertical height, in centimetres, of the cone. Give your answer correct to 3 significant figures. . cm (6 marks)