英国私校14+数学入学考试笔试真题型 赶紧赶紧收藏吧!

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　　哈里伯瑞学院Haileybury College

　　Mathematics Entrance exam for: 14+ (Sample)

　　Section A

　　Each of the following questions are worth 1 mark

　　Write your answers down the right-hand side

　　1 Calculate 573 + 48

　　………………………………

　　2 Calculate 20 − 2 × 5 − 7

　　………………………………

　　………………………………

　　………………………………

　　5 Calculate 435 × 7

　　………………………………

　　6 Find the value of 2⁵

　　………………………………

　　7 Find the value of 4⁻²

　　………………………………

　　8 Solve 2𝑥 + 7 = 11

　　………………………………

　　9 Solve 3(𝑥 − 4) = 12

　　………………………………

　　10 At the bakers, iced buns cost 80p and cinnamon rolls cost £1.10. How much do 2 iced buns and 1 cinnamon roll cost?

　　………………………………

　　11 Factorise 𝑥² + 2𝑥 – 15

　　………………………………

　　12 Solve 5(3𝑥 − 4) = 10𝑥 + 5

　　………………………………

　　13 Expand and simplify 5(4𝑦 + 5) + 3(5𝑦 − 1)

　　………………………………

　　………………………………

　　15 In a certain year, the value of a painting increased by 20%. If at the start of the year it was worth £2400, how much is it worth now?

　　………………………………

　　Section B

　　Each of these multiple choice questions is worth 2 marks.

　　If you give an incorrect answer you will be deducted 1 mark.

　　Write your answer by putting the relevant letter on the right hand side.

　　1.Which statement is true?

　　A: 24 × 70 = 74 × 20

　　C: 24 × 70 = 12 × 35

　　B: 24 × 70 = 48 × 35

　　D: 24 × 70 = 48 × 140

　　2.What is the value of the missing digit?

　　4714 × 28 = 1319 ? 2

　　A: 4       B: 6         C: 2          D: 9

　　3.A line parallel to 𝑦 = 3𝑥 − 5 passes through the point (2, 9). What is its equation?

　　A: 𝑦 = 9𝑥 + 3           B: 𝑦 = 3𝑥 + 3           C: 𝑦 = 3𝑥 + 9            D: 𝑦 = 3𝑥 + 7

　　4.Write

　　𝑥² + 4𝑥 + 3

　　In the form

　　(𝑥 + 𝑝)² + q

　　A: (𝑥 + 2)² − 4

　　B: (𝑥 + 2)² − 3

　　C: (𝑥 + 2)² − 1

　　D: (𝑥 + 2)² − 7

　　汤布里奇公学Tonbridge school

　　14+数学入学考试：B卷

　　1. Expand and fully simplify the following:

　　a) 4(5 − 3𝑥)

　　Answer: ……………………………..

　　b) (2𝑥 − 1) (𝑥 + 5)

　　Answer: ……………………………..

　　c) (𝑥 + 𝑦) (2𝑥 − 3𝑦)

　　Answer: …………………………….

　　2. Solve the following equations:

　　a) 4(𝑥 − 3) = 20

　　Answer: ……………………………..

　　b) 2𝑥 − 4(𝑥 – 3) = 1

　　Answer: ……………………………..

　　Answer: ……………………………..

　　Answer: ……………………………..

　　Answer: ……………………………..

　　Answer: ……………………………..

　　Answer: ……………………………..

　　h) 2𝑥² = 512

　　Answer: ……………………………..

　　3. Triangle 𝐴𝐵𝐶 has an angle equal to 90° at 𝐶, length of side 𝐴𝐶 equal to 5cm and length of side 𝐴𝐵 equal to 9cm.

　　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 𝐵𝐶, giving your answer to 3 significant figures

　　Answer: ……………………………..

　　c) Calculate the size of angle 𝐴𝐵𝐶, giving your answer to 3 significant figures

　　Answer: ……………………………..

　　4. A line, L, passes through the points (4,0) and (−1, −2).

　　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. a) Solve the simultaneous equations

　　𝑢 = …………… 𝑣 = ……………

　　6. The following graph is to be drawn

　　𝑦 = 2𝑥² − 3𝑥

　　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 ≤ 𝑥 ≤ 3

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

　　2𝑥² − 3𝑥 = 1

　　Answers: …………… and ………………..

　　剑桥圣玛丽中学St Mary’s School, Cambridge

　　Year 10 (14+)数学

　　1.For each expression, multiply out the brackets and simplify:

　　(a)5c+2(3c – 1) =

　　………………(2)

　　(b)7p – 5(4 – p) 

　　………………(2)

　　2. Solve these equations. Show your method clearly.

　　(a) 3(x + 6) = 5x + 12 (b) 5p – 8 = 7p – 9

　　x = ……… p = ………

　　3. Solve this number puzzle. Show all your working clearly.

　　Jack and Harry think of the same number.

　　Jack adds 2 to his number, and then multiplies by 5.

　　Harry multiplies his number by 7 and then subtracts 6.

　　They both get the same answer.

　　What number did they both think of?

　　……………………………………….

　　4.Maya earns £6.50 per hour.

　　Her pay is increased by 4%. Calculate her new hourly rate of pay.

　　……..…… (3)

　　5. Work these out.

　　6. Change each of these to a decimal. State whether your answer is a terminating or recurring decimal.

　　7. A regular polygon has 20 sides. Calculate

　　(a) the size of each exterior angle

　　……………° (2)

　　(b) the size of each interior angle

　　……….……° (2)

　　The sizes of the angles, in degrees, of the quadrilateral are

　　x + 10

　　2x

　　x + 90

　　x + 20

　　(a) Use this information to write down an equation in terms of x.

　　.......................................................... (2)

　　(b) Use your answer to part (a) to work out the size of the smallest angle of the quadrilateral.

　　................................... ˚ (3)

　　8. On the diagram below, draw the following journey

　　A to Q: 55 km on a bearing of 070°

　　Q to R: 30 km on a bearing of 325°

　　9. Calculate the average speed of a car which travels 165 miles in 3 hours

　　……… m.p.h.

　　10. The cheetah is the fastest mammal in the world. It can run at a maximum speed of 29 metres per second.

　　If it maintained this speed, how far would it travel in one minute?

　　……………m

　　11. Calculate the time taken by a cyclist who goes 70 km at a speed of 20 km/h

　　……… hours

　　莱斯特女子中学Leicester High School for Girls

　　1.a. Calculate 15% of £64

　　£ ______________ (2)

　　______________kg (2)

　　c. Calculate 0.65 x 0.3

　　______________ (1)

　　d. Express a test mark of 17 out of 20 as a percentage

　　______________ % (2)

　　e. Sam eats 12 sweets from a bag of 33 sweets. What fraction of the sweets remains? Give your fraction in its lowest terms

　　______________ (2)

　　f. 80p is shared between Ben and Calum in the ratio 3:2. How much more does Ben receive than Calum?

　　______________ (3)

　　g. Diane covers 9 metres when she walks 12 paces. What distance will she cover when she walks 16 paces?

　　_____________m (3)

　　h. Emma won the first prize of £120 in a Prize Draw. This was ¾ of the total prize money paid out. What was the total prize money?

　　£______________ (3)

　　2. a. Show how you would work out a rough estimate of the product 375 x 23， and give your estimated answer.

　　______________ (3)

　　Her teacher looked at her answer and said it could not be correct.

　　Explain how the teacher knew the answer was wrong.

　　3.

　　a. The bar a chart shows the results of a survey on the amount of pocket money given to 24 children.

　　(i) What is the mode?

　　______________________ (1)

　　(ii) How many children have at least £3 per week pocket money?

　　______________ (2)

　　(iii) Find out the total amount of money given to the children.

　　______________ (2)

　　b. A pie chart is drawn to show the same information. Calculate the angle of the sector which represents the children who have £1 per week pocket money.

　　______________ (2)

　　4. The temperatures at noon in Montreal on the seven days of one week were as follows:

　　Sunday -5℃

　　Monday -4℃

　　Tuesday -7℃

　　Wednesday 1℃

　　Thursday 5℃

　　Friday 0℃

　　Saturday -4℃

　　a. Calculate the mean (average) of these temperatures.

　　______________ (3)

　　b. How many degrees did the temperature fall from noon on Thursday to noon on Saturday?

　　______________ (2)

　　c. If a day is chosen at random during that week what is the probability that the temperature at noon was above zero?

　　______________ (2)

　　The boxes are packed into cartons which are cuboids measuring 60 cm by 30 cm by 12 cm.

　　b. Find the number of minipack boxes of lego which may be packed into a carton.

　　______________ (3)

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