Download GCSE in Mathematics B

GCSE in Mathematics B
Modular 2381
Unit 2 stage 2
Practice Paper B
Higher
(Calculator)
EDEXCEL
GCSE Mathematics 2540/2544
Formulae sheet — Higher tier
Volume of prism = area of cross-section  length
Volume of sphere =
4 3
r
3
Surface area of sphere = 4 r2
Volume of cone =
4 2
r h
3
Curved surface area of cone =  rl
C
In any triangle ABC
b
A
a
c
B
a
b
c
=
=
sin A
sin B
sin C
Sine Rule:
Cosine Rule: a2 = b2 + c2 –2bc cos A
Area of a triangle =
1
ab sin C
2
The Quadratic Equation
 b  (b 2  4ac)
The solutions of ax + bx + c = 0, where a  0, are given by x =
2a
2
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1.
Work out
40.8
1 .2
…………
(2)
(Total 2 marks)
2.
(a) Factorise 3x + 6
………………
(1)
(b) Factorise completely
6a3 − 9a2
………………
(2)
(Total 2 marks)
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3.
Write an expression, in terms of m and c, for the total number of seats on m
minibuses and c coaches
….………….…….
(2)
(Total 2 marks)
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Diagram NOT accurately
drawn
4.
A
O
T
B
A and B are points on the circumference of a circle, centre 0.
TA and TB are tangents to the circle.
Calculate the size of the angle ATO when angle AOT = 56°
Give a reason for each stage in your working.
………………….°
(Total 3 marks)
5.
x°
101°
(a)
Diagram NOT
accurately drawn.
79°
Find the size of the angle marked x°
………………..°
(2)
(b)
Give a reason for your answer.
………………………………………………………………………………………………….
(1)
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(Total 3 marks)
Mr Smith owns minibuses and coaches.
Each minibus has 12 seats.
(a) Write an expression, in terms of m, for the number of seats in m minibuses.
….………….…….
(1)
Each coach has 48 seats.
(b) Write an expression, in terms of m and c, for the total number of seats on m
minibuses and c coaches
….………….…….
(2)
(Total 3 marks)
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6
6.
Evaluate
3−2
………………
(Total 1 mark)
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7.
Here is a right-angled triangle.
5x + 10
3x + 6
4x + 8
The lengths of the three sides of the triangle are 3x + 6, 4x + 8 and 5x + 10
(b) Find an expression, in terms of x, for the perimeter of the triangle.
Give your answer in its simplest form.
………………
(2)
(Total 2 marks)
8.
Factorise
9x2 − 6x + 1
….………..…….
(Total 2 marks)
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9.
35°
Diagram NOT
accurately drawn
50°
x°
(i)
Work out the value of y°.
(ii)
Explain how you worked out your answer.
y°
y = ……….……
……………………………………………………………………….……….…
……………………………………………………………………….….………
(2)
(Total 2 marks)
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10.
(a)
Use your calculator to work out the value of
6.27  4.52
4.81  9.63
Write down all the figures on your calculator display
........................
(2)
(b)
Write your answer to part (a) to an appropriate degree of accuracy.
........................
(1)
(Total 3 marks)
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11.
B
A
C
35°
Diagram NOT
accurately drawn
94°
D
y
E
Find the size of the angle marked y.
Give your reason for your answer.
y = …….…….°
…………………………………………………………………………………………………..
…………………………………………………………………………………………………..
(Total 2 marks)
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1.
40.8 408

= 408  12 = 34
1 .2
12
2.
(a)
3x + 6 = 3(x + 2)
(b)
3a² (2a – 3)
3.
4.
12m + 48c
Angle between tangent and radius = 90°
Angle T = 180 − 90 − 56 = 34°
(angle in a triangle add up to 180°)
Angle ATO = 34°
5.
(i)
x = 79°
ii)
alternate angles
(a)
12m
6.
(i)
7.
3x + 6 + 4x + 8 + 5x + 10 = 12x + 24
3−2 =
1
1

2
9
3
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8.
9x2 − 6x + 1 = (3x − 1)(3x − 1)
9.
(a) (i) 180 − 50 = 130
130  2 = 65°
The angles in a triangle add up to 180°, and the angles opposite the equal sides of an
isosceles triangle are equal.
(b) (i) 30°
10.
11.
(ii)
the exterior angle (x = 65°) of a triangle = the sum of the 2 interior opposites angles
(a)
28.3404
= 1.962631579
14.44
(b)
1.96 or 2.0
35°
(as all numbers in original sum have 2dp or 3sf)
alternate angles
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