超干货分享 赖默中学Latymer Upper School year12数学入学考试笔试题!

　　赖默中学作为英国顶尖的私立混校，它拥有着自己独特的学习氛围，该校不仅为学生配套设施以及丰富的课外活动，而且学术成绩也十分优异，每年有20%的学生被牛津、剑桥等名校录取，因此，越来越多的学生去该校留学，可是，入读私校要经过笔试，下面，小编就为大家带来了赖默中学Latymer Upper School year12数学入学考试笔试题，希望对大家有所帮助：

　　16+数学

　　注意

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　　•允许使用计算器，但所有问题都必须完整显示。

　　•提醒你在回答时需要清晰的表达。

　　•允许时间:50分钟

　　1 Find the value(s) of x that make each equation true:

　　.................................................

　　(ii) 2(2x − 1)3 − 24 = 226

　　.................................................

　　(iii) 2(2x + 7) − 5(3 − x) = −5

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　　2 (i) Bob has completed 4 maths tests this year, and his mean score is 20. What must he score on his fifth test to increase his mean score to 24?

　　.................................................

　　(ii) Jane has completed 4 laps of a track at an average speed of 20 km/h. At what average speed must she complete her fifth lap to increase her average speed to 24 km/h?

　　.................................................

　　3 Ed has a card shop.

　　(i) He buys a particular card for £1.20 and sells it for £1.68. Calculate his percentage profit on this card

　　.................................................

　　(ii) Ed’s profit on “Good Luck” cards in 2018 was £360.

　　This was a decrease of 20% on his profit in 2017.

　　Work out Ed’s profit on “Good Luck” cards in 2017.

　　.................................................

　　4 (i) Multiply out and simplify each expression below:

　　(a) (2x + 3y − 1)(x + 2y + 3)

　　.................................................

　　(b) (3p − 2)(2q + 1)

　　.................................................

　　(ii) Factorise each of the expressions below:

　　(a) 14p²q − 21p⁴q³

　　.................................................

　　(b) 6mn − 4n + 21m − 14

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　　5

　　[Diagram NOT to scale]

　　In the diagram, ABC is an isosceles triangle with AB = AC = 7cm and BC = 10cm. M is the midpoint of BC.

　　Find

　　(i) The length AM.

　　.................................................

　　(ii) The area of triangle ABC.

　　.................................................

　　6 (i) In a regular polygon, each interior angle is 8 times as big as each exterior angle. How many sides does the polygon have?

　　.................................................

　　(ii) In an isosceles triangle, one of the angles is four times as big as the other. What could the angles in the triangle be?

　　................................................. or .................................................

　　.................................................

　　(ii) On what fraction of days that Jaideep is late for school has he taken the bus?

　　8 Solve the simultaneous equations

　　2x = 5y − 7

　　3y − 4x + 14 = 0

　　.................................................

　　9 (i) Simplify 3(2p²q³)³

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　　10

　　[Diagram NOT to scale]

　　In the diagram above, F G is parallel to QR.

　　(i) Find the length QR.

　　.................................................

　　The area of triangle P F G is 16cm²

　　(ii) Find the area of the trapezium FGRQ

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