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Answers with no evidence of calculations will not score any marks.  \nUse the blank pages of the exam paper to do your rough work.  \nNothing should be removed from the exam room.  \nTHIS SAMPLE IS FREE OF CHARGE AND MAY ONLY BE USED FOR ACADEMIC PURPOSES  \nMay 2013  \nQuestion 1 Find x when  \n5  \n2  \nx + 2 −  \nx −1  \nx −13  \nx + 3  \n= 4  \nAnswer: x=  \nQuestion 2  \na) Calculate ⎜ ~~ ~~A~~ ~~−2~~ ~~B~~ ~~ ⎟1000 when A = ~~ ~~log~~ ~~xlog~~ ~~x32~~ ~~−log~~ ~~xlog~~ ~~x and B = log10 75 + log10 28 − log10 12010 1 2  \nb) If x −  2 y 3 z −2 = 3 and if x=y=3 and z>0, express z as a power of 3  \nAnswer: A= , B= , z= .  \nQuestion 3  \nI am one year older than my sister. We also have a younger brother. In ten years, when we will all be ten years older, the sum of our ages will be 80. Ten years ago, two times my age and two times my brother’s age added up to three times my sister’s age. How old is my sister now?  \nAnswer: My sister is years old.  \nQuestion 4 Two circles with centres A and B touch at C. The radius of the larger circle is 12.8 cm and of the smaller 5 cm. PQ is a common tangent. Find the size of PQ  \nAnswer: PQ= m  \nQuestion 5 The two straight lines y=3x+1 and y=-2x+16 and the curve y=x2+x-a, where a is a constant, all meet at the same point. Find the value of a and then, for that value of a, plot the curve y=x2+x-a. The turning point and the points where the curve meets the axes should be clearly marked.  \nX=1, y = 5  \nAnswer: a =  \nQuestion 6  \nLet SN be the sum ofN terms of the progression 401, 403, 405, .... and  \nLet TN be the sum ofN terms of the arithmetic progression 1, 3, 5, ... .  \nFind N if 10SN=41NTN  \nAnswer: N=","cbCaiqACorxvPiIc","https://ap.wps.com/l/cbCaiqACorxvPiIc","pdf",169573,"English","# Question 1\n# Question 2\n# Question 3\n# Question 4\n# Question 5\n# Question 6","[{\"question\":\"Are calculators allowed in this entrance test?\",\"answer\":\"No calculators are allowed. Only writing materials such as pens, pencils, erasers, and rulers can be used.\"},{\"question\":\"Why must rough calculations be presented?\",\"answer\":\"All rough calculations must be shown. Answers without evidence of calculations will not receive marks.\"},{\"question\":\"What is the time allowed and what should students do if a question takes too long?\",\"answer\":\"The time allowed is one hour ten minutes. Students are advised to work quickly and leave behind questions that take too long to answer.\"}]","Mathematics Entrance Test - May 2013 | PDF"]