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Logic questions apply iterative percentage height reduction, grid-based diagonal path optimisation, symmetric area partition counting on a 4x4 grid, and spot-count combination solving with multiple scenarios, plus tennis selection constraints from nested conditional 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day, $(a+2d) for the third day, and so on.  \nA picker who works for all 30 days will earn $40.75 on the final day.  \n(a) Write an equation in a and d using this information (2 marks)  \n(b) A worker who works for all 30 days will earn a total of $1005.  \nShow that 15(a + 40 .75) = 1005 (2 marks)  \n(c) Hence find the value of a and d (2 marks) Write your answer using money notation  \na =   d =    \nTotal 6 marks  \nQuestion 2  \nA sequence is given by:  \nx 1 = 1  \nxn+1 = xn (p + xn)  \nwhere p is a constant (p≠0) .  \n(a) Work out x2 in terms of p and use this to show that x3 = 1 + 3p + 2p2  \n(2 marks)  \nGiven that x3 = 1,  \n(a) Find the value of p (2 marks)  \n(b) Write down the value of x2008 (2 mark) Give reasons foryour answer  \nTotal 6 marks  \nQuestion 3  \n(a) Factorise completely  \np(x) = x3 – 13x – 12 (2 marks)  \n(b) f(x) = (x + 1)(x2-4x +5)  \nFind the remainder when f(x) is divided by (x-2)  \nExpress f(x) in the form x3 + mx + nx + 5, stating the value of each of the integers m and n (2 marks)  \n(c) Show that the equation x2-4x +5 = 0 has no real roots (2 marks)  \nTotal 6 marks  \nQuestion 4  \nThe first three terms of a geometric series are 4p,(3p+15) and (5p+20) respectively, where p is a positive constant.  \n(a) Show that 11p2-10p-225 = 0 (2 marks)  \n(b) Use your answer from (a) to show that p = 5 (1 mark)  \n(c) Find the common ratio of this series (1 mark)  \n(d) Find the sum of the first ten terms of the series, leave your answer in the form S10 = ab (2 marks)  \nTotal 6 marks  \nQuestion 5  \n(a) Find an equation of the line joining A(7, 4) and B(2, 0), giving your answer in the form ax + by + c = 0 , where a , b , and c are integers. (2 marks)  \n(b) Find the length of AB , leaving your answer in surd form. (1 mark)  \n(a) The point C has coordinates (2, t), where t > 0, and AC = AB.  \nFind the value of t. (3 marks)  \nTotal 6 marks  \nSection B-Logic  \nQuestion 6  \nA ball is dropped and bounces up to a height that is 75% of the height from which it was dropped.  \nIt then bounces again to a height that is 75% of the previous height and so on.  \nHow many bounces does it make before it bounces up to less than 25% of the original height from which it was dropped?  \nExplain your answer.  \nAnswer    \nTotal 6 marks  \nQuestion 7  \nUsing diagonal joins and five numbers from the grid below find the following:  \n1. The Highest total  \n2. The Lowest total  \nThe arrows show diagonal joins and you can start from any square You must show the numbers you have used to find the totals  \n\n| 8 | | 15\u003Cbr>| 6 | 9 |\n| --- | --- | --- | --- | --- |\n| 14 | | | 18\u003Cbr>| 20 |\n| 18 |  | \u003Cbr>17 | \u003Cbr>2 | 5 |\n| 3 |  | 15 | 19 | 6 |\n\n1. The Highest total …………………….  \n2. The Lowest total    \nTotal 6 marks  \nQuestion 8  \nDivide the 4x4 grid below so that it has two identical areas and identical shape.  \nFind the greatest number of ways of dividing the grid into two identical parts by drawing along the lines of the grid.  \nShow the different divisions below  \n\n|  |  |  |  |\n| --- | --- | --- | --- |\n|  |  |  |  |\n|  |  |  |  |\n|  |  |  |  |\n|  |  |  |  |\n|  |  |  |  |\n|  |  |  |  |\n|  |  |  |  |\n|  |  |  |  |\n|  |  |  |  |\n|  |  |  |  |\n|  |  |  |  |\n|  |  |  |  |\n|  |  |  |  |\n|  |  |  |  |\n|  |  |  |  |\n|  |  |  |  |\n|  |  |  |  |\n|  |  |  |  |\n\nQuestion 9  \nBits have 4 spots.  \nBots have 9 spots.  \nAltogether some Bits and Bots have 48 spots.  \nHow many Bits are there?  \nHow many Bots?  \nWhat if Bits have 5 spots, Bots have 7 spots, and there are 140 spots altogether. How many ways can you get 140 spots altogether?  \nFind as many solutions as you can.  \nBits    \nBots    \nCombinations of Bits and Bots:  \n\n| . .\u003Cbr>. |\n| --- |\n| . |\n|  |\n\nTotal 6 marks  \nQuestion 10  \nTwo boys and two girls can play tennis  \nAlisher said: ‘I will only play if Yulduz plays.’  \nYulduz said: ‘I won’t play if ","cbCaiqczrqi3mAW4","https://ap.wps.com/l/cbCaiqczrqi3mAW4","pdf",454678,"English","# Section A - Mathematics\n## Question 1\n## Question 2\n## Question 3\n## Question 4\n## Question 5\n# Section B - Logic\n## Question 6\n## Question 7\n## Question 8\n## Question 9\n## Question 10","[{\"question\":\"What topics are included in Section A Mathematics?\",\"answer\":\"It includes sequences and recursions, factorisation and polynomial division/remainders, checking quadratic equations for real roots, geometric series with parameter solving, and coordinate geometry for lines and distances.\"},{\"question\":\"How does the logic Question 6 determine the number of bounces?\",\"answer\":\"Each bounce reaches 75% of the previous height, and the question asks how many bounces occur before the height drops below 25% of the original.\"},{\"question\":\"What is the main task in Logic Question 8?\",\"answer\":\"Divide a 4x4 grid into two identical areas and identical shapes, then count the greatest number of distinct valid divisions along grid lines.\"}]","WIUT Scholarship Mock - 2018 - Mathematics and Logic Practice Questions | PDF",25]