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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.  \nThe sum S of n terms of an arithmetic progression a, a+d, a+2d, a+[3d...](3d... is)[ is](3d... is)  \nS = n2~~ ~~ [2a + (n − 1)d ]  \nTHIS SAMPLE IS FREE OF CHARGE AND MAY ONLY BE USED FOR ACADEMIC PURPOSES  \nA set of entrance exams for self‐financed students Mathematics 2010  \nJanuary 2010  \nQuestion 1  \nFind x if x = x~~ ~~~~ ~~2  \nAnswer: x = and  \nQuestion 2  \nEvaluate  \n⎛ 1  \nA = ⎜ ~~ ~~ +  \n⎝ 6  \n4  \n2 × 25  ⎞⎟ +   35  \n5 16 ⎠  2   \n15  \n+  \n 59   \n168  \nAnswer: A =  \nQuestion 3 v  \nAnna is n years old. Boris, her brother, is 9 years older than Anna. Their mother is 3 times as old as Anna. Their father is 2 times as old as Boris. If the sum of the ages of the family members is 135½, find a) how old is the father and b) how old was the mother when Boris was born?  \nAnswer: a) , b)  \nTHIS SAMPLE IS FREE OF CHARGE AND MAY ONLY BE USED FOR ACADEMIC PURPOSES 2  \nA set of entrance exams for self‐financed students Mathematics 2010  \nQuestion 4  \nDraw the graphs of 5y = 3(x+3) and 3x+y = 15, clearly showing the point where they meet and hence calculate the area of the triangle formed by these two lines and the x-axis  \nQuestion 5  \nIshmael decided to put in a box one Uzbek soum the first day, two soum the second day, three soum the third day and so on, increasing by one soum the amount he set aside every day. After how many days will he have collected 10,000 soum?  \nAnswer: He will pass 10,000 soum in day __  \nQuestion 6  \nA circle passes through A, B, C and D. Angles ∠ BAD = 110 o, ∠ ACD = 37o and ∠ DBC = 51o. Find  \n∠ ADB, ∠ CFB, ∠ BAC and ∠ AED.  \nA B  \nAnswer: ∠ ADB = , ∠ CFB =  \n∠ BAC = and ∠ AED =  \nTHIS SAMPLE IS FREE OF CHARGE AND MAY ONLY BE USED FOR ACADEMIC PURPOSES 3  \nA set of entrance exams for self‐financed students Mathematics 2010  \nMathematics  \nFebruary 2010  \nQuestion 1  \nFind x if (2x-10)2 – 8(2x-10) = 84  \nAnswer: x = and  \nQuestion 2  \n8 + 2x 7x − 130 Find x when ~~ ~~x~~ ~~−~~  ~~3~~ ~~3~~  ~~ − 3 = 3x2 + ~~ ~~2x~~ ~~+~~  ~~2~~ ~~3~~  ~~  \nAnswer: x =  \nQuestion 3  \nA box contains yellow and white tennis balls. Half the number of white balls equals a third of the number of yellow balls. Also, twice the whole number of balls exceeds three times the number of yellow balls by four. How many balls does the box contain?  \nexceeds = more than  \nAnswer: The box has balls  \nTHIS SAMPLE IS FREE OF CHARGE AND MAY ONLY BE USED FOR ACADEMIC PURPOSES 4  \nA set of entrance exams for self‐financed students Mathematics 2010  \nQuestion 4  \nDraw the lines 3x = 2y and 2x-y = 4 using the same axes and hence find the area of the triangle formed by these two lines and the x-axis.  \nAnswer: Area is  \nQuestion 5  \nA trader bought eggs, oranges and apples to sell in the market. He paid 50,000 (fifty thousand) soum for the eggs and 100,000 sum for the oranges. He sold the eggs at a 19% profit and the oranges at a 10% profit, but made a 5% loss on the apples. When he did his final calculations he found that he had made an overall gain of 4% . How much did he sell the apples for?  \nAnswer: He sold the apples for soum  \nQuestion 6  \nFind the value of the angles marked α, β, θ and φ in the diagram below, where ABCD, ECF and GBH are all straight lines  \nAnswer: α = , β = ,θ = , and φ =  \nTHIS SAMPLE IS FREE OF CHARGE AND MAY ONLY BE USED FOR ACADEMIC PURPOSES 5  \nA set of entrance exams for self‐financed students Mathematics 2010  \nMathematics  \nMarch 2010  \nQuestion 1  \nFind x if","cbCaidMelwqRsqxr","https://ap.wps.com/l/cbCaidMelwqRsqxr","pdf",686196,"English","# Entrance test Mathematics (January-September 2010)\n## Exam instructions\n## Mathematics questions by month (Jan-Apr shown)","[{\"question\":\"是否允许使用计算器？\",\"answer\":\"不允许使用计算器。\"},{\"question\":\"答题时对草稿计算有什么要求？\",\"answer\":\"所有粗略计算必须展示，且给出计算证据的答案才会得分。\"},{\"question\":\"考试主要包含哪些类型的数学题？\",\"answer\":\"包含代数与方程、等差数列求和、作图与求三角形面积、以及几何图形中的角度与圆相关计算。\"}]","Westminster maths - Entrance test Mathematics January-September 2010 | PDF",48]