虽说英国私校的学生总数占总人数的7%，但私校的教育可谓是非常出色，英国国会上下议员中有30%的人员都曾接受过私校教育，由此可见，私校教育是英国低龄教育的典范，可是，选校一直困扰着留学家庭，在这里小编为大家推荐一所私立女校，它坐落于剑桥大学城，拥有着全英最顶尖的教学资源，这所私校就是剑桥圣玛丽中学，下面，小编就为大家带来了剑桥圣玛丽中学St Mary’s School, Cambridge Year 12数学入学考试笔试题，希望对大家有所帮助：
Year 12数学
允许时间:60分钟
说明
1. 你不能使用计算器。
2. 尽可能多地做题。
3.方法完整的解决方案将获得满分。
4. 如果你不懂一个问题，跳过它，继续下一个问题。
5. 当你做完所有你能做的事情后，再回到你错过的问题上。
1.
The nth term of a sequence is 2n2
(i) Find the 4th term of the sequence.
...............................................................
(ii) Is the number 400 a term of the sequence?
..............................................................
Give reasons for your answer.
2 (a) Simplify
(i) a5÷a2
...............................................................
(ii) 2x2× 3x2y2
...............................................................
(b) Expand and simplify (x + 3)(x + 7)
...............................................................
(c) Factorise fully 3pq – 12p2
...............................................................
(d) (i) Factorise 3y2- 10y+3
...............................................................
Hence, or otherwise
(ii) Factorise 3(x +2)2- 10(x+2) +3
...............................................................
3. Solve the simultaneous equations
4x – 3y = 11
10x + 2y = −1
x = ………………
y = ………………
4. Work out the value of
..............................................
6. The point A has coordinates (–5, 1).
The point B has coordinates (7, y).
The point (x, 6) is the midpoint of the line segment AB.
Find the value of x and the value of y.
x = ..........................
y = ..........................
8. Prove that the difference between the squares of consecutive odd numbers is a multiple of 8
10.
The diagram shows a trapezium.
The lengths of three of the sides of the trapezium are x – 5, x + 2 and x + 6.
All measurements are given in centimetres.
The area of the trapezium is 36 cm2。
(a) Show that x2– x – 56 = 0
(b) (i) Solve the equation x2– x – 56 = 0
…………………………
(ii) Hence find the length of the shortest side of the trapezium.
…………………… cm
12 (a) On the grid draw the graph of y =x(x -3)
13.
The graph of y = a – b cos (kt), for values of t between 0° and 120°, is drawn on the grid.
Use the graph to find an estimate for the value of
(i) a,
.....................................
(ii) b,
....................................
(iii) k.
....................................
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