英国私校13+数学入学考试笔试真题题型大赏析 赶紧来做题吧!

　　近些年，英国私校以其超高的升学率，不仅吸引了英国本地的贵族和上流人士，而且吸引了来自世界各地的高中产家庭，可进入英国私校并非有钱就能读，英国私校有非常严格的考核标准，笔试是最先经历的一项考试，13+是英国私校最常见的入学时间，下面，小编就为大家带来了英国私校13+数学入学考试笔试真题题型大赏析，希望对大家有所帮助：

　　七橡树中学Sevenoaks school

　　13+数学入学考试

　　______________________

　　2. Simplify 8𝑥 − 4𝑥² − 5𝑥 − 4𝑥²

　　______________________

　　3. Simplify:

　　a. 𝑎⁶ ÷ 𝑎³

　　_____________________

　　b. 2𝑥⁴𝑦² × 5𝑦³

　　______________________

　　4. Expand and simplify:

　　a. 9𝑚𝑛− 𝑛(3 − 7𝑚)

　　______________________

　　______________________

　　b. Is your answer in part (a) larger or smaller than the actual answer, you must justify your decision.

　　__________________________________________________________________________________

　　__________________________________________________________________________________

　　6. Complete the missing numbers in each of the function diagrams below.

　　7. Given that 𝑝 = −2 and 𝑞= 25. Find the value of

　　𝑝²𝑞 − (5𝑝)²

　　______________________

　　8. The cost of petrol is £1.20 per litre. Alice buys £48 worth of petrol.

　　a. How many litres of petrol doe she buy?

　　______________________

　　b. Alice can drive 8.5km for every litre of petrol. How many km can she drive using the petrol she bought?

　　______________________

　　9. A jar contains 60 jelly beans. If 35% of the jelly beans are removed, how many remain in the jar?

　　______________________

　　10. In a mathematics competition, the winner won £100 more than twice the amount won by the runner-up. The total winnings were £2350. Let the amount won by the runner-up be 𝑟.

　　Form an equation in 𝑟 for this information and solve it to find out how much the winner received.

　　______________________

　　11. The grid below contains numbers where all rows, columns and diagonals have the same product.

　　Complete the grid.

　　12. A sports club has 65 men and 35 women as members. A new activity has just begun and 50 new members have joined. Given that the number of men is now 60% of the total members, how many of the 50 new members were women?

　　______________________

　　特鲁罗学校Truro School

　　13+数学

　　时间允许1小时。

　　1. (a) A rugby club is planning a trip.

　　The club hires 17 coaches. Each coach holds 42 passengers.

　　How many passengers is that altogether?

　　Show your working.

　　………………… passengers

　　(b) The club wants to put one first aid kit into each of the 17 coaches.

　　These first aid kits are sold in boxes of 5

　　How many boxes does the club need?

　　………………… boxes

　　2.

　　(a) 137 people paid the entrance fee on Monday.

　　How much money is that altogether?

　　Show your working.

　　£…………………

　　(b) The museum took £660 in entrance fees on Friday.

　　How many people paid to visit the museum on Friday?

　　Show your working.

　　…………… people

　　3. (a) Look at these fractions.

　　Mark each fraction on the number line.

　　The first one is done for you.

　　(b) Fill in the missing numbers in the boxes.

　　4. The number 6 is halfway between 4.5 and 7.5

　　Fill in the missing numbers below.

　　The number 6 is halfway between 3.5 and .....................

　　The number 6 is halfway between –2 and ......................

　　(b) Work out the number that is halfway between 39 × 13 and 41 × 13 Show your working.

　　....................

　　5. The table shows some percentages of amounts of money

　　You can use the table to help you work out the missing numbers.

　　6. On a farm 80 sheep gave birth.

　　30% of the sheep gave birth to two lambs.

　　The rest of the sheep gave birth to just one lamb.

　　In total, how many lambs were born?

　　Show your working.

　　………………… lambs

　　7. Here is a list of numbers:

　　You can choose some of the numbers from the list and add them to find their total.

　　For example,

　　(a) Choose two of the numbers from the list which have a total of 1

　　(b) Choose two of the numbers from the list which have a total of –3

　　Choose two other numbers from the list which have a total of –3

　　(c) What is the total of all eight of the numbers on the list?

　　(d) Choose the three numbers from the list which have the lowest possible total.

　　Write the three numbers and their total.

　　You must not use the same number more than once.

　　8. Kay is drawing shapes on her computer.

　　(a) She wants to draw this triangle. She needs to know angles a, b and c。

　　Calculate angles a, b and c.

　　a = .............................. º

　　b = .............................. º

　　c = .............................. º

　　(b) Kay draws a rhombus:

　　Calculate angles d and e.

　　d = .............................. º

　　e = .............................. º

　　9. Write each expression in its simplest form.

　　4 + 3t + 5t

　　…………………

　　3b + 6 + 2b + 7

　　…………………

　　(3d - 5) + 3(d + 2)

　　…………………

　　(m + 1)(m + 3)

　　…………………

　　10. (a) When x = 3, work out the values of the expressions below.

　　3x + 2 = ........................

　　5x – 14 = ..........................

　　7 – 4x = ........................

　　(b) When 3y + 1 = 19, work out the value of y Show your working.

　　y = .................

　　(c) Solve the equation 7y + 5 = 3y + 13 Show your working.

　　y = .................

　　帕克林顿学校Pocklington School

　　13+ Mathematics Sample

　　1. Calculate the following, showing a clear method where appropriate:

　　a. 25 ÷ (22 + 6 - 5)

　　____________

　　b. 34.5 + 1.89 + 300

　　____________

　　c. 2.3 × 1.9

　　____________

　　d. 44.5 ÷ 0.5

　　____________

　　e. 4³ − 17

　　____________

　　f. 3836 ÷ 7

　　____________

　　2. Solve the following equations:

　　a. 5𝑦 = 90

　　𝑦 = __________

　　𝑞 = __________

　　c. 4𝑡 − 9 = 63

　　𝑡 = __________

　　d. 𝑝² = 25

　　𝑝 = __________ p= __________

　　e. 68 = 4(2𝑥 + 3)

　　𝑥 = __________

　　3. Calculate the following. You must show all your working out. Give your answers as mixed numbers in their simplest form.

　　____________________

　　____________________

　　4. Expand these brackets and simplify where possible:

　　a. 3(2𝑥 − 1)

　　___________________

　　b. 3(2𝑥 + 1) + 4(𝑥 + 2)

　　___________________

　　5. Put these numbers in order from smallest to largest:

　　6. Write down the next 3 terms in each of these sequences:

　　a. 2, 9, 16, 23, 30, _____, _____, _____

　　b. -1, -5, -9, -13, -17, _____, _____, _____

　　c. 1, 4, 8, 16, 32, _____, _____, _____

　　d. 8.2, 8.6, 9.0, 9.4, 9.8, _____, _____, _____

　　7. A car is travelling for 3 hours and it travels 180 miles. What is the car’s average speed?

　　____________________ miles per hour

　　8. There are 120 pupils in year 8 in Daventry High School.

　　95% of these pupils go out of school on a Geography field trip.

　　How many pupils are left at school?

　　____________________ pupils

　　9. Find the missing angles from the diagrams below:

　　Angle d = _________ (1 mark)

　　Angle e = _________ (1 mark)

　　Angle f = _________ (1 mark)

　　Angle g = _________ (1 mark)

　　10. In a class of 30 children the boys and girls are in the ratio 3:2.

　　Calculate how many boys and girls there are.

　　There are ______ boys

　　There are ______ girls

　　哈博戴斯阿斯科男校The Haberdashers' Aske's Boys' School

　　13+ Entrance Examination MATHEMATICS

　　1. Work out the value of the following

　　(a) 4+6÷2_______________

　　(b) −3 −7 −12_______________

　　(c)120+60÷(20−5) _______________

　　(d)−16÷4×−2_______________

　　2. Simplify the following expressions fully

　　(a)3x+2y+6y−5x_______________

　　(b)(3a)²×2a_______________

　　(c)xy+2y²+3yx+4y²+5x²_______________

　　3. Solve the following equations showing your method clearly.

　　(a)3(2x+9)-7x=4( x+3)

　　x =_______________

　　x =_______________

　　4. An Old Haberdasher Tamal is baking some cakes for a bake off. His recipe gives the following information about ingredients for a cake for 6 servings.

　　(a) The sugar needs to be split in the ratio 5:1 for the sponge and the icing respectively. Find how much sugar is needed for the sponge.

　　_______________________________

　　(b) Find how much flour would be needed to make this cake for 11 servings.

　　__________________________________

　　(c) Tamal has a box of 20 eggs and plenty of sugar, butter and flour to make as much cake as possible. Find the maximum number of servings he can make.

　　__________________________________

　　5. The graph below shows a line and an arrow shape.

　　(a) Find the gradient of the line.

　　___________________

　　(b) Reflect the arrow in the line.

　　(c) Draw the line with gradient 2 and y-intercept 8 on the graph.

　　6. Work out the value of the formulae below when x is -4 and y is 0.2.

　　(a)25-3x_______________

　　(b)y²_______________

　　_______________

　　(d)2x2_______________

　　7. Find the labelled missing angles in the following diagrams. The diagrams are not to scale.

　　(a) ABCE is a rectangle and CG and DF are parallel lines.

　　a =_____________

　　b =_____________

　　c =_____________

　　(b) BCDEF is an irregular pentagon and AF and AB are the same length. ABC is a straight line.

　　x =_____________

　　y =_____________

　　8. All the items in an antique shop have been reduced by 40% in a sale.

　　(a) David buys an antique for £120. Find the price of the antique before the sale.

　　__________________________________________________

　　(b) David then sells the antique for £150. Find what percentage of the £150 which is profit.

　　__________________________________________________

　　9. The graph 3x-2y= 6 is to be drawn.

　　(a) Complete the table of values for the graph.

　　(b) Draw the graph on the set of axes below.

　　10. In a test there are 5 marks for correct answers and 2 marks are lost for incorrect answers. Bob got n correct answers.

　　(a) In terms of n find the number of marks he gained for his correct answers.

　　__________________________________________________

　　(b) He answered 20 questions in total. Find a formula for the number of questions he got wrong.

　　__________________________________________________

　　(c) Find a formula for the number of marks he lost for the wrong answers.

　　__________________________________________________

　　(d) In total he got 65 marks. Using your previous answers write down an equation in n for the number of marks he got.

　　__________________________________________________

　　(e) By solving the equation find how many questions he got right.

　　__________________________________________________

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