Paper 1 Questions www.mathsrevision.com Credit Level If you can do these questions without looking at the answers then you are well on the way to passing the exam. (Click to start) Paper 1 Questions Credit Level www.mathsrevision.com Two yachts leave from harbour H. N Bearing 072° Yacht A sails on a bearing of 072° for 30 kilometres and stops. 72° Yacht B sails on a bearing of 140° for 50 kilometres and stops. 68° How far apart are the two yachts when they have both stopped? Do not use a scale drawing. h Bearing 140° 140° SAS Cosine Rule h = a +b -2 × abcos(h)° 2 2 2 h = 30 +50 -2×30 ×50cos68° = 47.7km 2 2 Paper 1 Questions www.mathsrevision.com Credit Level A mug is in the shape of a cylinder with diameter 10 cms and height 14 cms. a) Calculate the volume of the mug. b) 600 mls of coffee are poured in. Calculate the depth of the coffee in the cup. Volume r 2 h Volume 52 14 1100 mls Let height be h cms 600 5 h 2 600 h 52 h 7.64 cms Paper 1 Questions www.mathsrevision.com Credit Level The number of diagonals, d, in a polygon with n sides is given by the formula: n(n -3) d= 2 A polygon has 20 diagonals. How many sides does it have? What are we trying to find ? n n(n -3) 20 = 2 40 =n(n -3) n2 -3n - 40 = 0 n -8n +5 = 0 Polygon has 8 sides 40 =n2 -3n n = 8 or n = -5 Paper 1 Questions Credit Level www.mathsrevision.com In the diagram Angle STV = 34° Angle VSW = 25° Angle SVT = Angle SWV = 90° ST = 13.1 centimetres Calculate the length of SW SV sin34° = 13.1 SV =13.1 × sin34° = 7.33 cm SW cos25° = SV SW = 7.33×cos25° = 6.64 cm Paper 1 Questions www.mathsrevision.com Credit Level The area of triangle ABC is 38 square centimeters. AB is 9 centimetres and BC is 14 centimetres. Calculate the size of the acute angle ABC SAS Use Area = ½ a b sin C need to transpose letters !!! 1 38 = 63sinB 38 = × 9 ×14 × sinB 2 sinB = 38 63 Paper 1 Questions www.mathsrevision.com Credit Level Find points where curve cuts the axes and co-ordinates of minimum turning point. x2 +2x -8 = 0 y =0 x -2 x + 4 = 0 x -2 = 0 x = 2 x + 4 = 0 x = -4 y = (-1)2 +2(-1) -8 when x = 0 y = 02 +2(0) -8 2 (-1, -9) Axis of symmetry is between the roots when x = -1 -1 -4 y = x2 +2x -8 x = -1 y = -9 y = -8 min t.p. = (-1, -9) y-intercept = (0, -8) Paper 1 Questions Credit Level www.mathsrevision.com The diagram shows part of the graph of a quadratic function, with equation of the form y =k(x - a)(x -b) 1 The graph cuts the y-axis at (0, -6) and the x-axis at (-1, 0) and (3, 0) a) Write down the values of a and b. b) Calculate the value of k. c) Find the coordinates of the minimum turning point of the function a = -1 and b = 3 1, 8 y =k x +1 x -3 Choose a point on the curve (0, -6) -6 =k 0 +1 0 -3 y =2 x +1 x -3 y =2 1+11-3 y = -8 -6 = -3k 1, -8 k =2 Paper 1 Questions www.mathsrevision.com Credit Level Two perfume bottles are mathematically similar in shape. The smaller one is 6 centimetres high and holds 30 millilitres of perfume. The larger one is 9 centimetres high. What volume of perfume will the larger one hold. Find the linear scale factor 9 3 6 2 Since we are finding volume – scale factor is cubed 3 3 3 30 ×27 30 × × × = = 101.25 2 2 2 8 Volume = 101.25 mls Paper 1 Questions Credit Level www.mathsrevision.com A sheep shelter is part of a cylinder as shown figure 1. It is 6 metres wide and 2 metres high. The cross-section of the shelter is a segment of a circle with centre O, as shown in Figure 2. OB is the radius of the circle. Calculate the length of OB. Pythagoras M r- 2 O r2 = 32 + r -2 2 3 B r r2 = 32 + r2 - 4r + 4 r r 4r =13 r = 3.25 metres Paper 1 Questions Credit Level www.mathsrevision.com a) A driver travels from A to B, a distance of x miles at a constant speed of 75 kilometres per hour. Find the time taken for the journey in terms of x. x b) The time for the journey from B to A is 50 hours. Calculate the driver’s average speed for the whole journey. D S D S= T T D T= S x T= 75 hours x 5x x x 3x 2x = = = + Distance = 2 x Total time = + 50 75 150 150 30 150 x 30 2 x ÷ = 60 mph = 2x Speed = Distance Time Speed 30 x = Paper 1 Questions www.mathsrevision.com Credit Level Fiona checks out the price of a litre of milk in several shops. The prices in pence are: 49 44 41 52 47 43 x (x-x) a) Find the mean price of a litre of milk. b) Find the standard deviation of the prices. c) Fiona also checks out the price of a kilogram of sugar in the same shops and finds that the standard deviation of the prices is 2.6. Make one valid comparison between the two sets of prices. 276 x - x 2 s= n -1 Mean = 6 84 = 4.1 5 = 46 x - x 2 49 3 9 44 -2 4 41 -5 25 52 6 36 47 1 1 43 -3 9 276 84 Price of milk varies more than price of sugar Paper 1 Questions Credit Level www.mathsrevision.com A microwave oven is sold for £150. This price includes VAT at 17.5% Calculate the price of the microwave oven without VAT. Price without VAT 1.175 = £ 150 150 Price without VAT = 1.175 = £ 127.66 Paper 1 Questions Credit Level www.mathsrevision.com Solve the equation 2 2x -3x -7 = 0 Give your answers correct to 1 decimal place. Use the quadratic formula a = 2, b = -3, c = -7 x= 3 ± 65 4 x= -b ± b2 - 4ac x= 2a -(-3) ± (-3)2 - 4(2)(-7) x= 2(2) 3 + 65 3- 65 or x = 4 4 x = 2.8 or x = -1.3