Question 2:
2
Section A (36 marks)
1 Find, in the form y (cid:4) ax(cid:2)b, the equation of the line through (3, 10) which is parallel to
y (cid:4) 2x(cid:2)7. [3]
2 Sketch the graph of y (cid:4) 9 (cid:1) x2. [3]
3 Make a the subject of the equation
2a(cid:2)5c (cid:4) af(cid:2)7c. [3]
4 When x3(cid:2)kx(cid:2)5 is divided by x (cid:1) 2, the remainder is 3. Use the remainder theorem to find the
value of k. [3]
5 Calculate the coefficient of x4 in the expansion of (x(cid:2)5)6. [3]
6 Find the value of each of the following, giving each answer as an integer or fraction as appropriate.
3
(i) 252 [2]
-2
Ê7ˆ
(ii) [2]
Ë3¯
3 9- 17 9+ 17
7 You are given that a (cid:4) , b= and c= . Show that a(cid:2)b(cid:2)c (cid:4) abc. [4]
2 4 4
8 Find the set of values of k for which the equation 2x2(cid:2)kx(cid:2)2 (cid:4) 0has no real roots. [4]
9 (i) Simplify 3a3b (cid:3) 4(ab)2. [2]
(ii) Factorise x2 (cid:1) 4 and x2 (cid:1) 5x(cid:2)6.
x2 (cid:1) 4
Hence express as a fraction in its simplest form. [3]
x2 (cid:1) 5x(cid:2)6
2
11 (i)
y
8
7
1
y= x+
6 x
5
4
3
2
1
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 x
–1
–2
–3
–4
–5
–6
–7
–8
–9
––1100
8
7
y | = | x | + | 1
x
6
5
4
3
2
1
– | 6 | – | 5 | – | 4 | – | 3 | – | 2 | – | 1 | 0 | 1 | 2 | 3 | 4 | 5 | 6
– | 1
– | 2
– | 3
– | 4
– | 5
– | 6
– | 7
– | 8
– | 9
––1100
PMT
4751/01
ADVANCED SUBSIDIARY GCE UNIT
MATHEMATICS (MEI)
Introduction to Advanced Mathematics (C1)
THURSDAY 7JUNE 2007 Morning
Time: 1 hour 30 minutes
Additional materials:
Answer booklet (8 pages)
MEI Examination Formulae and Tables (MF2)
INSTRUCTIONS TO CANDIDATES
• Write your name, centre number and candidate number in the spaces provided on the answer booklet.
• Answer all the questions.
• You are not permitted to use a calculator in this paper.
• Final answers should be given to a degree of accuracy appropriate to the context.
INFORMATION FOR CANDIDATES
• The number of marks is given in brackets [ ] at the end of each question or part question.
• The total number of marks for this paper is 72.
ADVICE TO CANDIDATES
• Read each question carefully and make sure you know what you have to do before starting your
answer.
• You are advised that an answer may receive no marks unless you show sufficient detail of the
working to indicate that a correct method is being used.
WARNING
You are not allowed to use
a calculator in this paper
This document consists of 4 printed pages.
HN/4 © OCR 2007 [L/102/2657] OCR is an exempt Charity [Turn over
2
Section A (36 marks)
1 Solve the inequality 1 (cid:2) 2x (cid:4) 4(cid:3)3x. [3]
2 Make t the subject of the formula s (cid:1) 1 at2. [3]
2
3 The converse of the statement ‘P fi Q’ is ‘Q fi P’.
Write down the converse of the following statement.
‘n is an odd integer fi 2n is an even integer.’
Show that this converse is false. [2]
4 You are given that f(x) (cid:1) x3(cid:3)kx(cid:3)c. The value of f(0) is 6, and x (cid:2) 2 is a factor of f(x).
Find the values of k and c. [3]
5 (i) Find a, given that a3 (cid:1) 64x12y3. [2]
-5
Ê1ˆ
(ii) Find the value of . [2]
Ë2¯
6 Find the coefficient of x3in the expansion of (3 (cid:2) 2x)5. [4]
4x(cid:3)5
7 Solve the equation (cid:1)(cid:2)3. [3]
2x
8 (i) Simplify 98- 50. [2]
6 5
(ii) Express in the form a+b 5, where a and b are integers. [3]
2+ 5
9 (i) A curve has equation y (cid:1) x2 (cid:2) 4. Find the x-coordinates of the points on the curve where
y (cid:1) 21. [2]
Ê2ˆ
(ii) The curve y (cid:1) x2 (cid:2) 4 is translated by .
Ë0¯
Write down an equation for the translated curve. You need not simplify your answer. [2]
6 5
2+ 5