汤布里奇公学14+入学考试数学笔试真题分享!

汤布里奇公学14+数学笔试真题分享！汤布里奇公学作为英国三大贵族男校之一的学府，是继伊顿公学、哈罗公学之后的顶尖男校之一，每年有将近四分之一的学生入读牛津大学。汤布里奇公学优秀的学术成绩每年都吸引着众多学生申请。下面小编带大家来了解一下汤布里奇公学14+数学笔试真题，希望大家可以针对这些数学题型做好考试应对准备。

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汤布里奇公学14+入学考试数学笔试真题：

1. Expand and fully simplify the following:

a) 3(6 − 2?)

Answer: …………………………….

b) (4? − 1) (2? + 5)

Answer: ……………………………..

c) (? + ?) (3? − 4?)

Answer: ……………………………..

2. Solve the following equations:

a) 8(? − 3) = 20

Answer: ……………………………..

b) 2? − 8(? – 3) = 1

Answer: ……………………………..

Answer: ……………………………..

Answer: ……………………………..

Answer: ……………………………..

Answer: ……………………………..

3. Triangle ??? has an angle equal to 90° at ?, length of side ?? equal to 6cm and an angle at A equal to 30°

a) Draw a diagram, with appropriate labels and showing all the above information. The diagram does not need to be drawn with accurate lengths.

b) Calculate the length of side ??, giving answer to 3 significant figures.

Answer: ……………………………..

c) Use Pythagoras’ Theorem to calculate the length of side ??, giving your answer to 3 significant figures.

Answer: ……………………………..

4. A line, L, passes through the points (6,0) and (−2, −4).

a) By first drawing a set of axes, illustrate the line, L, on a graph.

b) Calculate the gradient of L.

Answer: ……………………………..

c) Determine the equation of L.

Answer: ……………………………..

5. The following graph is to be drawn:

? = 2?² − 3? + 1

a) Complete the table:

b) By first drawing a set of axes, then plotting appropriate points based on the information in the above table, draw the graph for the values −2 ≤ ? ≤ 3.

c) Using your graph, estimate the solutions of the equation:

2?² − 3? + 1 = 2

Answers: …………… and ……………….

6. Fully simply the following:

a) 3?³x 3?³

Answer: ……………………….

Answer: ……………………….

c) (8?²?⁶)²

Answer: ……………………….

Calculate the value of T when ? = 1200.

Answer: ……………………………..

7. (a) A man is 32 years older than his son. Ten years ago he was three times as old as his son was then. By forming an appropriate equation, or equations, find and list the age of each.

Answer: ………………………….……………..

(b) A bus is travelling with 52 passengers. When it arrives at a stop, x get off and 4 get on. At the next stop one third of the passengers get off and then 3 get on. There are now 25 passengers. Find x.

Answer: …………………………….

8. (a) By first adding the three equations together, or otherwise, solve the equations:

Answer: ……………………………..

(b) Solve the equations:

Answer: ……………………………..

9. Two sides of a regular pentagon, a square and a regular n sided polygon meet at the point P.

Find the value of n, showing your working clearly.

Answer: ……………………………..

10. A car completes a journey in 10 minutes. For the first half of the distance the speed was 60km/h and for the second half the speed was 40km/h. How far is the journey?

Answer: ……………………………..

11. Wallace and Gromit are waiting in a queue. There are x people behind Wallace, who is y places in front of Gromit. If there are n people in front of Gromit, how long, in terms of n, x and y, is the queue?

Answer: ……………………………..

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