General Certificate of Secondary Education Higher Tier June 2013
Mark
2–3 4–5 6–7
Mathematics (Linear)
43651H
10–11
Paper 1 Tuesday 11 June 2013
H
9.00 am to 10.30 am
12–13 14–15 16–17
For this paper you must have: l
8–9
mathematical instruments.
18–19 20–21
You must not use a calculator.
22
Time allowed l 1 hour 30 minutes
TOTAL
Instructions l Use black ink or black ball-point pen. Draw diagrams in pencil. l Fill in the boxes at the top of this page. l Answer all questions. l You must answer the questions in the spaces provided. Do not write outside the box around each page or on blank pages. l Do all rough work in this book. Information l The marks for questions are shown in brackets. l The maximum mark for this paper is 70. l The quality of your written communication is specifically assessed in Questions 14 and 16. These questions are indicated with an asterisk (*). l You may ask for more answer paper, tracing paper and graph paper. These must be tagged securely to this answer book. Advice l In all calculations, show clearly how you work out your answer.
(JUN1343651H01)
WMP/Jun13/43651H
43651H
2
Formulae Sheet: Higher Tier
a 1 Area of trapezium = – (a + b)h
h
2
b
Volume of prism = area of cross-section × length
crosssection h lengt
r
4 Volume of sphere = – πr3 3
Surface area of sphere = 4 π r 2
1 Volume of cone = – πr2 h 3
l
h
Curved surface area of cone = π rl
r
In any triangle ABC
C
1
Area of triangle = 2 ab sin C Sine rule
a sin A
=
b sin B
=
b
a
c sin C
A
c
B
Cosine rule a 2 = b 2 + c 2 – 2bc cos A
The Quadratic Equation The solutions of ax 2 + bx + c = 0, where a ≠ 0, are given by
x=
(02)
– b ± √ (b2 – 4ac) 2a
WMP/Jun13/43651H
Do not write outside the box
3
Answer all questions in the spaces provided.
1
This shape is made from five cubes. C
A
B
Draw what the shape looks like when seen from A, B and C. From A
x = .............................................................................
(1 mark)
Turn over for the next question
4 Turn over
(07)
䊳
WMP/Jun13/43651H
Do not write outside the box
8 6
6 (a)
The times taken by 100 students to travel to school are shown. Time, t (minutes)
Frequency
10 ⬍ t ⭐ 10
36
10 ⬍ t ⭐ 20
34
20 ⬍ t ⭐ 30
18
30 ⬍ t ⭐ 40
12
Draw a frequency diagram for the data.
40
30
Frequency 20
10
0 0
10
20 30 Time, t (minutes)
40 (2 marks)
6 (b)
The school has 600 students. Estimate how many students take more than 20 minutes to travel to school. ............................................................................................................................................
A triangle, square and pentagon have a total area of 48 cm2. The areas of the shapes are in the ratio of their number of sides. Work out the area of the pentagon.
The times that 100 customers spent queuing in a post office were recorded. The cumulative frequency diagram shows the results.
100 90 80 70 Cumulative Frequency
60 50 40 30 20 10 0 0
5
10
15
20
25
Time (minutes)
13 (a)
How many customers queued for more than 15 minutes? ............................................................................................................................................
Work out the median queuing time. ............................................................................................................................................
ABC is a triangle. AD is perpendicular to BC. AB = 3√3 cm, BD = 3√2 cm, DC = √2 cm A Not drawn accurately 3√3 cm
B 3√2 cm
D
C
√2 cm
Work out the area of triangle ABC. Give your answer in the form a√2 where a is an integer. ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................ ............................................................................................................................................