AQA Higher Practice paper (calculator 2) Higher Tier The maimum mark for this paper is 8. The marks for each question are shown in brackets. Time: 1 hour 3 minutes 1 One billion in the UK is one thousand million. Circle one billion written in standard form. 1 1 6 1 1 6 1 1 9 1 1 8 2 Here are 4 graphs. Circle the letter of the graph of = 3. A B C D 3 The diagram shows part of a regular polgon. Circle the number of sides of the regular polgon. 6 8 7 5 18º 4 Circle the volume that is the same as 7.6 m 3. 76 cm 3 76 cm 3 76 cm 3 7 6 cm 3 5 Solve 6 5 > 1 2 1
AQA Higher Practice paper (calculator 2) Page 2 of 12 6 Factorise 4 2 + 15 4 7 The diagram shows a triangle ABC with an obtuse angle. C 18º 25cm A 1cm B Work out the size of angle. Give our answer correct to 1 decimal place. [3 marks] 8 Not drawn to scale h 12cm 1cm The diagram shows a triangular prism with a volume of 96 cm 3. Find the height of the triangle. 2 [3 marks]
AQA Higher Practice paper (calculator 2) Page 3 of 12 9 Two spheres are mathematicall similar. The ratio of their volumes is 27 8 Circle the ratio of their surface areas. 27 4 9 2 27 8 9 4 1 P is inversel proportional to V. The graph below shows the coordinates of two points that lie on the curve. P (1, 1.6) (a, 4) O V Find the value of a. [3 marks] 11 Sketch the graph of = 2 2 5 + 4 Mark the coordinates where the graph cuts the -ais and the coordinates of the turning point. [4 marks] 3
AQA Higher Practice paper (calculator 2) Page 4 of 12 12 AB is part of a sewer pipe. Part of a house is shown shaded. A pipe is to be fitted from P to the edge of the house. The length of the pipe from B to the house needs to be as short as possible. Using onl ruler and compasses, show where the pipe will join the edge of the house. Show its position with X on the diagram. A P B 13 Here are sketches of four triangles. A B 2 2 3 13 5 1 1 12 C D 2 1 5 3 1 4 Circle the letter of the triangle that ou would use to work out the eact value of Sin 6º. 4
AQA Higher Practice paper (calculator 2) Page 5 of 12 14 Cars A and B are travelling along a straight road. Car A travels with a constant velocit of 2 m/s. At time t =, it overtakes car B. At time t =, car B is travelling with a velocit of 15 m/s. It immediatel accelerates uniforml and both cars travel a distance of 6 m, where car B overtakes car A. a Draw a velocit time graph showing the motion of the cars from t = until car B overtakes car A. P b Show that car B overtakes car A at t = 3 s. Velocit (ms 1 ) O t (s) c Find the acceleration of car B. 15 The line = 3 + 6 intersects the curve = 2 2 + 1 at two points. Find the -coordinates for each of these two points. Give our answers correct to 2 decimal places. [4 marks] 5
AQA Higher Practice paper (calculator 2) Page 6 of 12 16 The first three terms of a term-to-term sequence are a b c The term-to-term rule is multipl b 3 and subtract 2. Show that c = 9a 8 17 Georgina works in a high street fashion shop. On the first da of a sale all the prices are reduced b 2%. On the final da of the sale, the sale prices are all reduced b a further 25%. Georgina sas the shop should on the last da of the sale reduce all the original prices b 2% + 25% = 45%. a Eplain wh she is wrong. [3 marks] b What is the correct overall percentage reduction? 6
AQA Higher Practice paper (calculator 2) Page 7 of 12 18 The graph shows the curve = f() = f() 3 2 The turning point of the curve is at (3, 2) Write down the coordinates of the turning points for the curves with equations a = f( + 2) b = f() + 2 c = f() 19 Disprove the following statement b giving a counter-eample. For all real numbers a and b, if b 2 > a 2, then b > a [3 marks] 7
AQA Higher Practice paper (calculator 2) Page 8 of 12 2 One of these graphs is a sketch of the curve with equation = 2. Which one? Circle the correct letter. A B 1 C D 21 a Make v the subject of the following formula. 1 v + 1 u = 1 f b Solve the equation 2 2 7 + 4 = giving our answer to 2 decimal places. 8
AQA Higher Practice paper (calculator 2) Page 9 of 12 22 Giovanni deposited 2 in a savings account on 1 Januar 217. The account pas 5% interest per ear. At the end of each ear, Giovanni withdraws 2. How much will he have in the account in Januar 221? 23 a Prove that the cubic equation 3 4 + 2 = has a root between and 1. [4 marks] b Show that the equation 3 4 + 2 = can be rearranged to give = 4 + 1 2 3 ( c Starting with =.5, use the iterative formula n + 1 = n ) 3 4 + 1 to find an estimate 2 for one of the roots of the equation b working out 4 Give our answer correct to 3 decimal places. 4 = [3 marks] 9
AQA Higher Practice paper (calculator 2) Page 1 of 12 24 A bag contains onl red and blue counters. The ratio of red to blue counters is 4 : 5 a The total number of counters in the bag is 36. Circle the number of red counters in the bag. 2 16 4 36 b Two counters are removed from the bag at random. Find the probabilit that i both counters are red ii the counters are different colours. 25 The functions f and g are such that f() = 5 2 + 4 and g() = + 1 a Find f( 2) f( 2) = 1
AQA Higher Practice paper (calculator 2) Page 11 of 12 b Find f 1 () f 1 () = c Find fg() fg() = 26 OAB is a sector of a circle with radius 8 cm. A B 8cm 8cm 35º O a Work out the length of arc AB. Give our answer correct to 2 decimal places. cm b Work out the area of sector OAB. Give our answer correct to 2 decimal places. cm 11
AQA Higher Practice paper (calculator 2) Page 12 of 12 27 Three grandchildren visit their grandparents ever 12 das, 16 das and 18 das respectivel. On one da, the all visit their grandparents. a What is the minimum amount of time after which two grandchildren will call on the same da? das b What is the minimum amount of time after which all three will again call on the same da? 28 Show that 1 3 2 + 5 2 1 simplifies to a + b, where a, b, c and d are 9 2 1 c + d integers. Give the values of a, b, c and d. das a = b = c = d = [4 marks] 12