SHREWSBURY SCHOOL
SIXTH FORM ENTRANCE
EXAMINATION 2009
MATHEMATICS
(1 Hour 15 Minutes)
Instructions to candidates:
Answer all questions, writing your answers on lined or squared paper.
Do not write your answers directly on this question paper.
Section A contains questions of a GCSE nature. Attempt this ction first, but do not spend too long on any particular question.
Section B does not require any further knowledge, but the questions are intended to be more difficult.
You are expected to u a calculator in this examination.
Relevant working must be shown in order to gain high marks.
Formulae
Quadratic formula If 02
=++c bx ax then a
ac
英国留学中介费用b b x 242−±−=
Sine Rule B
常和b
A a sin sin =publicenemy
Cosine Rule
A bc c b a cos 2222−+= bc
a c
b A 2cos 2
常用日语单词
22−+=
Section A (60 marks)
Answer all questions in this ction. 1)
Expand the following, simplifying where appropriate: a) )2(5)73(4q p q p −−+ b) 2)43(−x
c)
()()24325−+
(leave square roots in your answer)血染拜占庭
[2, 3, 3 marks]
2)
Factori the following fully: a) 204−a b) 15722−+x x c)
229d c −
[1, 2, 2 marks]
gearbox3)
You must not u a calculator in this question. Full working is required to obtain any marks. a)
adfs
Calculate the following, giving your answers as mixed numbers in their simplest form: i) 65
11456+ ii)
65
11456÷
b)
Explain carefully which of the fractions is bigger:
179 and 19
10. Show relevant working and remember not to u a calculator.
[2, 3, 2 marks]
Plea turn over.
4) a) Adam scores 68 out of 80 in a maths test. What is this as a percentage?
b) A computer game is on sale for £13.93, having already been reduced by 30%. What was the original cost of the game? c)
affection
An investor owns shares in Asda, Sainsbury’s and Tesco with values in the ratio 1 : 2 : 3. If the Asda and Sainsbury’s shares go up in value by 7% and 10% respectively, by what percentage would the Tesco shares need to decrea in value in order for the investor to make zero profit?
[1, 2, 4 marks]
5)
a) Calculate the value of x in the triangle above.
b) Calculate the angle marked θ, giving your answer in degrees to 4 significant figures.
number_formatc)
Given that the lengths of 280 and 450 cm are correct to 2
significant figures, and that the triangle is perfectly right-angled, calculate the upper bound and the lower bound for the area of the triangle.
[2, 2, 3 marks]
6)
A bag contains 5 bananas and 4 oranges. Two pieces of fruit are removed, one at a time, without replacement. a) What is the probability that the first piece of fruit is a banana? b) What is the probability that both pieces of fruit are oranges? c)
If this experiment was carried out 2400 times, on how many occasions would you expect to take two oranges?
[1, 3, 2 marks]
450 cm
280 cm
7) Rearrange the following formulae to make x the subject: a) c x y +=
3
2 b) ()3
12−=x t c)
a
x a
x u −+=
[3, 3, 3 marks]
8)
Solve the following equations: a) 433)14(2+=−x x b) 31
54=−x x
c) 0141762=−+x x d)
78
41
42121=−+−+−x x x [2, 3, 3, 3 marks]
Section B (20 marks)
Only attempt this ction if you have done and checked as much of ction A as you can. Answer all the questions in this ction if you have time. 9)
Simplify the expressions, giving your answers as exact fractions or surds if appropriate. You must show full working ; no marks will be awarded for using your calculator. a)
3
28328328
+
+initiative
b)
...
328328328
328
++
+
+
[3, 4 marks]
Plea turn over.
