汤布里奇公学13+入学考试数学笔试真题分享!

汤布里奇公学13+数学笔试真题分享！汤布里奇公学是获得皇家特许授权的英国顶尖的私立男校，其学术成绩一直声名远扬，每年有大约20名左右的学生被牛津、剑桥大学所录取。汤布里奇公学为录取到适合课程进展的学生，不至于入学后因无法适应课程而失学的申请者，特别推出了入学考试环节，而数学就是其中重要的考核部分之一。下面小编带大家来了解一下汤布里奇公学13+数学笔试真题。

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汤布里奇公学13+入学考试数学笔试真题：

1. (a) Write 45% as a fraction in lowest terms.

Answer: ……………………………….

Answer: ……………………………….

(c) Calculate 30% of $12.50.

Answer: $…….…….………………….

Answer: ……………………………….

2. (a) By first writing each number correct to 1 significant figure, estimate the answer to

Answer: ……………………………….

Answer: ……………………………….

(c) Write 300 as a product of prime factors, using indices.

Answer: ……………………………….

(d) What is the smallest integer by which 300 has to be multiplied by to produce a perfect square ?

Answer: ……………………………….

3. (a) It takes 2 hour 27 minutes to travel from York to London by train. Christopher catches the 11.35 a.m. train from York.

At what time should Christopher arrive in London ?

Answer: ………………………p.m.

(b) A race horse averages 2 miles every 5 minutes. How long will it take the horse to run 26 miles at this rate ?

Answer: …..…... h …..…….… min

(c) How far does a car travel in 35 minutes at 30km/h ?

Answer: ………………………… km

(d) Write 40km/h as a speed in metres per second.

Answer: ………………………. m/s

4. Calculate

(a) the sum of 73.5 and 9.74

Answer: ……………………….

(b) the difference between 84 and 7.7

Answer: ……………………….

(c) the product of 4.3 and 7

Answer: ……………………….

(d) 24 ÷ 0.4

Answer: ……………………….

5. (a) Fully simplify the following:

(i) 2? + 3?

Answer: ……………………….

(ii) 3?³ x 3?³

Answer: ……………………….

Answer: ……………………….

(b) Multiply out the brackets and fully simplify

2(3? + 4?) − 6(? − 2?)

Answer: ……………………….

(c) Factorise completely

9?² + 27?

Answer: ……………………….

6. (a) Solve the following:

(i) 5? − 3 = 21 − ?

Answer: a = …………………….

Answer: b = …………………….

(iii) 5?² = 45

Answer: c = …………………….

Answer: d = …………………….

Answer: e = …………………….

(b) Solve these inequalities:

(i) ? + 2? > 9

Answer: …...………………….

(ii) 2(? − 3) ≤ 6

Answer: ……………………….

7 (a) 60 sweets are to be divided between two people in the ratio of 5:7. How many sweets do each of the two people receive ?

Answers: …………… and ………….

(b) When £143 is divided in the ratio 2:4:5, what is the difference between the largest share and the smallest share ?

Answer: ……………………….

8. Below is a picture of a regular octagon.

Calculate the size of the angles ?, ? and ?

Answers: ? = ………….

? = …… …….

? = …… …….

(a) ? + ?

Answer: ……………………….

Answer: ……………………….

Answer: ……………………….

(d) ???

Answer: ……………………….

An army patrol drinks 18 litres in a day

How many soldiers are there in the patrol ?

Answer: ……………………….

11. A fair, six-sided dice has faces numbered 1, 2, 3, 4, 5 and 6. When the dice is thrown, the number facing up is the score.

The dice is thrown once.

(a) What is the probability that the score is 1 or 2

Answer: ……………………….

(b) If the dice was thrown 300 times, how many times would a score of 5 be expected?

Answer: ……………………….

12. By first drawing a set of axes, draw the line defined by the equation

? = 2? + 5

showing the coordinates where the line intercepts the axes.

13. The following graph is to be drawn

? = 2?² − 3?

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

14. The wage bill for five builders and six carpenters is £1,340, while the bill for eight builders and three carpenters is £1,220. What wage is paid to each builder?

Answer: ………..………………….

15. A sequence begins:

5      8      11      14 …… …….

(a) Write down a formula for the ?th term

Answer: ………..………………….

(b) Calculate the 25th term

Answer: ………..………………….

(c) Find the value of ? when the ?th term equals 146

Answer: ………..………………….

(d) Determine the value of the first term which is greater than 1000

Answer: ………..………………….

(a) Write 1 as the sum of three different unit fractions

Answer: ………..………………….

Answer: ………..………………….

(c) Use your answers to (a) and (b) to write 1 as the sum of five different unit fractions

Answer: ………..………………….

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