AS GCE MATHEMATICS (MEI) :4751/01 Introduction to Advanced Mathematics (C1)
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Module
OCR GCE MATHEMATICS
Institution
OCR GCE MATHEMATICS
1 Simplify 5a2c 3 #2a4c 5 ^ h - . [2]
2 Find the equation of the line joining the points (-1, 9) and (2, -3), giving your answer in the form
y = mx + c. State the coordinates of the points where this line intersects the axes. [5]
3 Find the value of
(i) 2 2
4 1
- a k , [2]
(ii) 8000 3
2
^ ...
Wednesday 16 May 2018 – Morning
AS GCE MATHEMATICS (MEI)
4751/01 Introduction to Advanced Mathematics (C1)
QUESTION PAPER
Candidates answer on the Printed Answer Book.
* 7 3 0 9 4 0 4 4 8 3 *
OCR supplied materials: Duration: 1 hour 30 minutes
• Printed Answer Book 4751/01
• MEI Examination Formulae and Tables (MF2)
Other materials required:
None
INSTRUCTIONS TO CANDIDATES
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• Answer all the questions.
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INFORMATION FOR CANDIDATES
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paper
2 Find the equation of the line joining the points (-1, 9) and (2, -3), giving your answer in the form
y = mx + c. State the coordinates of the points where this line intersects the axes. [5]
3 Find the value of
(i) a2 14k ,
-2
[2]
(ii) ^8000h3 .
2
[2]
4 For the following equation, express x in terms of y.
x 2x + 1
= [4]
3y y+2
5 Find the coordinates of the point of intersection of the lines y = 4x + 3 and 3x + 2y = 9. [4]
Find the term that is independent of x in the binomial expansion of a - 3xk .
1 6
6 [3]
x
7 (i) Express 28 + 3 175 in the form a b, where a and b are integers and b is as small as possible. [2]
6 3 2 a+b 2
(ii) Simplify - , giving your answer in the form , where a, b and c are integers. [3]
5- 2 5+ 2 c
8 For each of the following pairs of sentences A and B, give a reason why the statement A + B is false and
write either ‘A & B ’ or ‘A % B ’ to show the correct relationship.
(i) A: n is positive.
B: n2 + 6 is positive. [2]
(ii) A: The diagonals of a quadrilateral bisect each other but not at right angles.
B: The quadrilateral is a rectangle but not a square. [2]
9 You are given that f(x) = ax3 + cx and that f(-1) = 3. You are also given that when f(x) is divided by (x - 4),
the remainder is 108. Find the values of a and c. [5]
10 (i) Express 3x2 - 9x + 5 in the form a(x + b)2 + c. Hence state the equation of the line of symmetry and
the y-coordinate of the minimum point of the curve with equation y = 3x2 - 9x + 5. [6]
(ii) Find the coordinates of the points where the graph of y = 3x2 - 9x + 5 intersects the axes. Give your
answers in an exact form. Hence state the solution of the inequality 3x2 - 9x + 5 < 0. [4]
11 You are given that f(x) = (2x + 5)(x2 - 5x + 4).
(i) Sketch the graph of y = f(x). [4]
(ii) You are given that g(x) = 2x3 - 5x2 - 17x + 48. Show that x = -3 is a root of g(x) = 0 and that it is the
only real root. [6]
(iii) Show that y = g(x) is a translation of y = f(x) by c m , finding the value of k.
0
[3]
k
12
y
A (7, 4)
x
O
Fig. 12
Fig. 12 shows a sketch of the circle with equation (x - 2)2 + (y + 1)2 = 50. You are given that the point
A (7, 4) lies on the circle.
(i) Write down the radius of this circle and the coordinates of its centre. [2]
(ii) The line L has equation y = 2x - 10 and passes through the point A (7, 4). Use algebra to find the
coordinates of the point B where the line L meets the circle again. Hence show that the perpendicular
distance from the centre of the circle to the line L is 5. [6]
(iii) Show that, when the line y = 2x + k is a tangent to the circle, k satisfies the equation
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