Pre Public Exam Paper 3 June 2016 Higher Tier AQA Style

Transcription

1 Name Class Question Mark Maximum mark 1 1 Pre Public Exam Paper 3 June 2016 Higher Tier AQA Style Calculator Paper Time 1 hour 30 minutes Marks Available 80 Commissioned by The PiXL Club Ltd Total 80

2 1 Work out the cube root of 27 thousand. Circle your answer [ 1 mark] a= 4 3 and b 5 2 Circle the vector a-b [1 mark] Circle the decimal closest in value to!! [1 mark]

3 4 y = x Which graph shows this? Circle the correct letter. [1 mark] A B C D

4 5 In 1999, the average house price in Chesterton was In 2016 it was Work out the percentage increase in the average house price. [3 marks] Answer % 6 A bag of sweets that has toffees, mints, chews and lollies. Toffee Mint Chew Lolly Frequency 12 X+7 X-5 3x+1 A sweet is chosen at random. The probability it is toffee is!"!"" Work out the probability it is a lolly. [4 marks] Answer..

5 7 Use ruler and compasses to answer this question. The region R is Closer to N than O Less than 7cm from M P O N M Shade the region R on the diagram. [3 marks]

6 8(a) Use your calculator to work out (!".!"!!.!! )!!.!"#$ [1 mark] Answer. 8(b) Use approximations to check that your answer to part (a) is sensible. You must show your working. [2 marks] Answer..

7 9 ABC is a triangle with AE=DE AB is parallel to CDE Show that the angle marked x is [3 marks]

8 10 The price of a new Porche 911 is Every year you own it, the value decreases by 6% For example, after 3 years, the Porche will be worth 6% less than after 2 years. What is its value after 4 years. Give your answer to 2 significant figures. [4 marks] Answer.. 11 Circle the correct answer: A regular hexagon has exterior angles that are each [1 mark]

9 12 Tick whether each statement is true or false. 12(a) When x! 25 = 0 the only value that x can be is 5 [1 mark] True False Reason. 12(b) When m is a positive integer, the value of 2m+1 is always an odd number. [1 mark] True False Reason. 12(c) h! is always a positive number. [1 mark] True False Reason.

10 13 Here is some information about the number of hours spent exercising each week by a group of people in One if the frequencies is missing. Time in hours Frequency Midpoint Midpoints are used to work out an estimate for the mean number of hours spent exercising. The answer is 4.5 hours. Work out the missing frequency. [5 marks] Answer..

11 14 (a) The nth term of a sequence is 3! + 3!!! Work out the 5 th term of the sequence. [1 mark] 14(b) The nth term of a different sequence is 9(3! + 3!!! ) Answer.. Circle the expression that is equivalent to 9(3! + 3!!! ) [1 mark] 27! + 27!!! 3!!! + 3! 3!!! + 3!!! 3!!! + 3!!!

12 15 Here are the scores that 80 students gained in their maths PPE. Score (%) Frequency 0 S< S< S< S< S<100 6 Dominic drew this cumulative frequency graph to show the data. Score Make two criticisms of Dominic s graph. [2 marks] Criticism 1 Criticism 2

13 16 A diagram shows a design for a flag pole. There is a wire used to secure the pole. The flag at the top of the pole is 1metre tall. 1m 7m 8m 2m Is the pole tall enough that the flag will not overlap the wire used to secure the pole? You must show how you reach your decision. [4 marks]

14 17 Factorise 3x! + 11x + 10 [2 marks] Answer.. 18 Annie, Ben and Carl play a game where they win and lose coins, there are 72 coins in the game. At the start of the game Annie, Ben and Carl have coins in the ratio 3:4:5 At the end of the game they have won and lost coins so that they now have coins in the ratio 7:8:9 The winner of the game is the person who has increased their number of coins the most. Who is the winner of the game. You must show your working out. [3 marks] Answer..

15 19 Here are 2 function machines, A and B. Input Output A Subtract 3 Square B Input Square Add 2 Output Both machines have the same input. Work out the range of input values for which the output for A is greater than the output of B. [4 marks] Answer..

16 20 A large carton of orange juice contains 4 litres of juice, to the nearest 10ml. A factory uses the large cartons to fill individual cartons that are 5cm by 6cm by 3cm, all to the nearest mm. 1cm 3 =1mm Show that the maximum number of cartons that could be filled by the large carton is 46. [4 marks] Answer..

17 21 In the triangle, angle x is obtuse. x 12cm cm Work out the angle x. [3 marks] Answer..

18 22 Bag A contains 8 chocolates and 16 chews. Bag B contains 11 chocolates and 22 chews. Dave takes an item out of bag A at random. He puts it in to bag B. Mike now takes an item from bag B at random. Show that: P(Dave picks a chocolate) = P(Mike picks a chocolate) [4 marks]

19 23 A tank is filled with water in 15 seconds. The graph shows the depth of water, d cm, at t seconds. Time(seconds)

20 23(a) The water flows in to the container at a constant rate. Which of the diagrams represents the container? Circle the container. [1 mark] 23(b) Use the graph to estimate the rate at which the depth is increasing at 2 seconds. Show your workings. [2 marks] Answer.cm/s

21 24 Iffah and Jenny have a running race. Here is Iffah s speed-time graph from the start of the race. Time (Seconds) The distance of the race was 510 metres. Jenny ran the 510 metres in 90 seconds. Who won the race? You must show your working out. [4 marks] Answer

22 25 In triangle ABC M is the midpoint of AC N is the point on BC where BN:NC = 3:5 AC = 2a AB = 5b C M N A B 25(a) Work out MN giving your answer in terms of a and b. Give your answer in its simplest form. [3 marks] Answer..

23 25(b) Use your answer from part (a) to explain why AB and MN are not parallel [1 mark]

24 26 An approximate solution to an equation is found using this iterative process. x!!! = (!!)!!!! and x! = (a) Work out the values of x! and x! [2 marks] x! =. x! =. 26(b) Work out the solution to 6 decimal places. [1 mark] x=.

25 27 The curve with equation y = x! + 2x 5 is reflected in the y axis. Circle the correct equation [1 mark] y = x! + 2x + 5 y = x! 2x 5 y = x! 2x + 5 y = x! + 2x 5

26 28 The diagram shows a line joining O to Q. y Q x The gradient of the line is 3. The length of the line is 810. Work out the co-ordinates of Q. [4 marks] Answer.. END OF QUESTIONS