作为一所历史悠久、充满活力的私立寄宿混校，格瑞萨姆中学成立于1555年，距今已有400多年的历史，该校非常注重学生的全面培养，不仅为学生提供了各种各样的课外活动，而且还拥有非常严谨的学习氛围，因此，越来越多的学生去该校留学，可是，入读私校要经过笔试，下面，小编就为大家带来了格瑞萨姆中学Gresham's School Year9数学入学考试笔试题，希望对大家有所帮助：
Year 9 数学
允许时间:60分钟
考生须知
试着问尽可能多的问题
允许使用计算器
总是让你的方法清晰，并展示你的工作
Q1.
(a) Write the following numbers in order of size.
Start with the smallest number.
(b) Write the following numbers in order of size.
Start with the smallest number.
Q2.
(a) Work out +8 − 6
.........................
(b) Work out −5 − 4
.........................
(c) Work out −12 ÷ +4
.........................
Q3.
(a) What fraction of this shape is shaded?
Give your answer in its simplest form.
...........................................................
(b) Write down the order of rotational symmetry of the shape.
...........................................................
(c) On the shape below, shade as few squares as possible so that the dotted line is a line of symmetry.
Q4.
(a) Write the number 6458 correct to the nearest hundred.
...........................................................
(b) Write down the number marked by the arrow.
...........................................................
(c) Find the number 7.2 on the number line above.
Mark the number with an arrow (↑).
Q5.
(a) Write 0.7 as a fraction.
..............................................................................................................................................
(b) Write 0.3 as a percentage.
..............................................................................................................................................
(c) Write 8⁄12 in its simplest form.
..............................................................................................................................................
Q6.
Without using a calculator work out, (you must show your working) 342 × 24
..............................................................................................................................................
Q8.
(i)
(a) Write down the coordinates of the point A.
(..................................... , .....................................)
(b) Write down the coordinates of the point B.
(..................................... , .....................................)
(c) On the grid, mark with a cross (×) the point (−3, −1).
Label this point C.
(d) On the grid, draw the line x = 3
(ii)
Q10.
(a) Solve 4x = 20
x = . . . . . . . . . . . . . . . . . . . . . .
(b) Solve y + 5 = 12
y = . . . . . . . . . . . . . . . . . . . . . .
Q11.
(a) Simplify 5x + 4y + x – 7y
..............................................................................................................................................
(b) Solve 7(x + 2) = 7
..............................................................................................................................................
(c) Expand and simplify 11 – 3(x + 2)
..............................................................................................................................................
(d) Simplify a5 × a4
..............................................................................................................................................
Q12.
Lydia is buying a ring.
The ring costs £60
She pays a deposit of 40%.
Work out how much she pays as the deposit.
£. . . . . . . . . . . . . . . . . . . . . .
Q13.
The table shows information about the numbers of Year 10 students absent from Ellen's school last week.
(a) Work out the mean number of Year 10 students absent each day.
...........................................................
Ellen's school has a total of 240 Year 10 students.
(b) What percentage of Year 10 students were absent on Monday?
........................................................... %
Q14.
Here is a list of numbers.
5 15 30 50 60 90 100 125
From the numbers in the list, write down
(i) two different numbers that add up to an even number
..............................................................................................................................................
(ii) a multiple of 20
..............................................................................................................................................
(iii) a factor of 45
..............................................................................................................................................
(iv) a cube number
..............................................................................................................................................
Q15.
Stephanie thinks of a positive number.
She squares the number and adds 7
The result is 43
What number did Stephanie think of?
...........................................................
Q16.
(a) Factorise completelyt2 + 6t
..............................................................................................................................................
(b) Factorise completely 12 x3y – 18 xy2
..............................................................................................................................................
(c) Simplify 5x4y3 × 2x3y2
..............................................................................................................................................
Q17.
All the measurements in the diagram are in centimetres.
(a) Given x = 2, mark on the diagram the lengths of all the sides.
(b) Calculate the area of the shape.
...........................................................
Q18.
Q19.
ABC is parallel to DEF.
EBP is a straight line.
AB = EB.
Angle PBC = 40°.
Angle AED = x°.
Work out the value of x.
Give a reason for each stage of your working
Q20.
The diagram shows the floor plan of Mary's conservatory.
Mary is going to cover the floor with tiles.
The tiles are sold in packs.
One pack of tiles will cover 2m2
A pack of tiles normally costs £24.80
Mary gets a discount of 25% off the cost of the tiles.
Mary has £100
Does Mary have enough money to buy all the tiles she needs?
You must show all your working.
Q21.
The diagram shows a rectangular framework.
The framework is made from 5 metal rods.
The metal rods have a weight of 0.9 kg per metre.
Work out the total weight of the framework.
Give your answer, in kg, correct to 3 significant figures.
........................................................... kg
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