Download 2 hours - The English School

THE ENGLISH SCHOOL, NICOSIA
FOR ENTRY INTO YEAR 2
SAMPLE PAPER 1
MATHEMATICS
Time allowed: 2 hours
Instructions to candidates
In the boxes below write your name, surname and form.
Answer the questions in the spaces provided.
Without sufficient working, correct answers may be awarded no marks.
Information to candidates
This paper has 32 questions.
There are 16 pages in this question paper.
Full marks may be obtained for answers to all questions.
The total marks for this paper is 150.
The marks for each question is shown in round brackets, e.g. (2)
CALCULATORS ARE NOT ALLOWED.
Advice for candidates
Write your answers neatly and in good English.
Work steadily through the paper.
Do not spend too long on one question.
Show all stages in any calculations.
Materials required for the paper
Calculator, ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB
pencil, eraser. Tracing paper may be used.
Surname:
Name:
.........................................................
...............................................................................
....
Total Marks:
1) A regular decagon has 10 sides. Calculate the size of each:
a) exterior angle,
………………………………….
(2)
b) interior angle.
………………………………….
(2)
(Total marks 4)
2) For the numbers 12 and 64 find:
a) the lowest common multiple (LCM),
………………………………….
(1)
b) The highest common factor (HCF).
………………………………….
(1)
(Total marks 2)
3) Construct the bisector of the angle ABC. You must show all construction lines.
A
B
C
(Total marks 2)
2
4) Use algebra to solve the following equations:
A  C  14
B  C  13
A  B  15
A=………………….
B=………………….
C=………………….
(Total marks 4)
5) The following data is the result of 10 spins of a five-sided fair spinner with sides numbered
from 1 to 5. The median of the values was 2.5.
1, 5, 2, 1, 4, 5, x , 2, 1, 4
Find:
a) the value of x ,
………………………………….
(1)
b) the mode,
………………………………….
(1)
c) the mean.
………………………………….
(2)
The spinner was spun 200 times.
d) how many times would an odd number be expected.
………………………………….
(2)
(Total marks 6)
3
6) The cross-section of the cube which is shaded is a square.
12 cm
1m
Find:
a) the volume, giving your answer αs a fraction in m3 ,
………………………………….
(3)
b) the surface area, giving your answer as a fraction in m2
………………………………….
(3)
(Total marks 6)
7) The sum of two consecutive odd numbers is 344. Let the larger number be x .
a) Write down an expression for the smaller number in terms of x .
………………………………….
b) Write down and simplify an equation from the above information.
(1)
………………………………….
c) Solve your equation to find the two numbers.
(2)
………………………………….
(3)
(Total marks 6)
4
8)
a) Give the next two terms in the following sequences:
i)
13
7
, 5, , 2
2
2
............, ............
ii) 124, 32, 8, 2
............, ............
iii) 2, 5, 11, 23
............, ............
(3)
th
b) Find the n term of the sequence:
5, 7, 9, 11, 13,.....
………………………………….
(2)
c) For a sequence the nth term is 2n  5 , find:
i) The second and third terms,
………………………………….
(2)
ii) the 1000th term,
………………………………….
(1)
iii) which term has α value of 15.
………………………………….
(1)
(Total marks 9)
9) If 3  20  5  2 , find the value of
2
a)

if:
  4,
………………………………….
b)
(2)
  4 ,
………………………………….
(2)
(Total marks 4)
5
10) E
F
A
The point A is the centre of a square of side 10 cm,
ABCD is a trapezium where AB = 2 cm.
B
D
C
not drawn to scale
Find:
a) the area of the triangle ADE,
………………………………….
(2)
b) the area of the trapezium ABCD,
………………………………….
(3)
c) the area of the pentagon ABCFE.
………………………………….
(2)
(Total marks 7)
11)
Expand and simplify:
5  3  2 p  2   4  3 p  1
………………………………….
(2)
(Total marks 2)
6
12)
Convert 6000 seconds to:
a) hours,
………………………………….
(1)
b) days, giving your answer as a fraction.
………………………………….
(1)
(Total marks 2)
13)
A
D
3
5
B
C
Calculate the following:
a)
Area of triangle ABC : Area of triangle ACD
………………………………….
b) the height of the trapezium, given that the area is 10 square units.
(1)
………………………………….
(3)
(Total marks 4)
7
14)
A reduction of 17
Find:
1
% is made on a new car costing €10,000.
2
a) the price reduction,
………………………………….
(2)
b) the price for which the car can be bought,
………………………………….
(1)
Another car increases in price, from €5,500 to €6,000.
c) Find the percentage increase, giving your answer as a mixed number.
………………………………….
(3)
(Total marks 6)
15)
The area of a circle is
9 cm2. Find:
a) the diameter,
………………………………….
b) the circumference in terms of
(3)
.
………………………………….
(2)
(Total marks 5)
8
16)
The diagram below shows a shape split into three rectangles.
10
5
2
x
x 1
Find:
a) The perimeter,
………………………………….
(4)
b) The area in terms of
x.
………………………………….
(3)
(Total marks 7)
17)
Write down the full solutions to each of the equations:
a) x  121 ,
2
………………………………….
(1)
b) 3x  48 ,
2
………………………………….
(2)
c) 2 x  17  115 ,
2
………………………………….
(3)
(Total marks 6)
9
18)
B
AD and BC are parallel AE=ED.
EAB  140o . D lies on EC.
A
Diagram not drawn to scale.
72o
E
C
D
Find the size of:
a) ADC
………………………………….
(1)
b) ADE
………………………………….
(1)
c) AED
………………………………….
(1)
d) BAD
………………………………….
(1)
e) ABC
………………………………….
(1)
(Total marks 5)
19)
Round the numbers given below to the specified accuracy.
Number
4.7519
1 decimal place
2 decimal places
3 decimal places
2.9958
(total 3 marks)
10
20)
Simplify the following:
10
a) 10 x
 5 x5
………………………………….
(2)
b)
8y  6y
3
………………………………….
(2)
(Total marks 4)
21)
Calculate the following:
a)
9.23  0.1
……………….
(1)
b)
0.01 10
2
……………….
(1)
c)
9.23  0.1
2
……………….
(1)
(total 3 marks)
22)
Given that:
2
3
1
bc 
5
ab 
Find:
i)
a c
……………….
(2)
ii)
 a  2b  c 
2
……………….
(2)
(total 4 marks)
11
23)
Find the following:
3  2
2
 3  12001   43  2  6 
2
……………….
(total marks 3)
24)
Estimate the answer to the following:
3.92  39
2.1 24
……………….
(total marks 1)
25)
Complete the following tables, simplifying all fractions where necessary.
Decimal number
1.6
Fraction
Percentage
9
4
1
%
2
(total 6 marks)
26)
Find the missing values and expression in the following function.
Find also the value of a.
3
7
4
9
5
11
6
23
x
a
a
a=…………….
(total 4 marks)
27)
Factorise the folowing:
12
a) y  7 y
2
………………………………….
(1)
b) 3x  9 x
2
………………………………….
(1)
c) ax  ay  a
2
………………………………….
(1)
(Total marks 4)
28)
Find the values of x, y and z.
y
z
2x
3x+20o
x=…………………………….
(3)
y=…………………………….
(1)
z=…………………………….
(1)
(total 5 marks)
13
29)
Sketch the graphs of:
a) y  3 ,
(1)
b) x  2 ,
(1)
c) y  2 x  1.
(2)
(total 4 marks)
30)
Solve the following equation
a)
x  2  3x  5   4
………………………………….
b)
(2)
x7
5
2x  4
………………………………….
(3)
(Total marks 5)
14
31)
A fair dice and a fair five-sided spinner show the following:
Dice:
0, 1, 2, 3, 4, 5
Spinner: 2, 3, 4, 5, 6
a) Draw a sample space to show all the possible outcomes for the DIFFERENCE of the two
scores when thrown and spun together.
(3)
b) Find the probability of obtaining the same score on the die and the spinner.
………………………………….
c) Find the probability of obtaining a difference which is a factor of 6.
(2)
………………………………….
(2)
d) Which DIFFERENCE is the most likely?
………………………………….
(1)
(total 8 marks)
15
32)
a) Reflect the triangle in the line y 
1
.
2
b) Rotate the triangle A 90ο anti-clockwise about (5,1).
c) Enlarge the triangle A by a scale factor of 2, about (-1,1).
A
(total 7 marks)
END
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