2007 IJC Prelims Paper 1 Question

# 2007 IJC Prelims Paper 1 Question - 2 1 The curve with...

This preview shows pages 1–2. Sign up to view the full content.

9740/1/2007 [Turn over 2 1 The curve with equation y = ax 2 + bx + c passes through the points (1, 7), ( - 3, 11) and (5, 99). Find the equation of the curve. [4] 2 Given that 0.4 (10 ) dy yy dx =- and 5 y = when 1 x , find an expression for y in terms of x . [6] 3 Let 1 3 3 ( 9e) x y . (i) Show that 23 d 90 d y x - += . [2] (ii) By further differentiation of this result, or otherwise, find Maclaurin’s series for y up to and including the term in 2 x . [4] (iii) Deduce the equation of the tangent to the curve 1 3 3 ( x y at the point 0 x = . [1] 4 Sketch, on an Argand diagram, the locus of P representing the complex number z where 22 i2 z - += . [2] The point Q representing complex number w is the point on the locus of P such that 4i z + is maximum. Find (i) the exact value of 4i w + , [2] (ii) the value of w in the form x + i y , giving the exact values of x and y . [3] 5 The position vectors of the points A , B , and C are given by i + j + k , 4 i + 3 j + 2 k and –7 i – 2 j k respectively. (i) Prove that the points A , B and C are not collinear. [2] (ii) Find a vector which is perpendicular to the plane ABC . [2] (iii)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 08/29/2009 for the course MA 9740 taught by Professor Moe during the Summer '07 term at Singapore Management.

### Page1 / 4

2007 IJC Prelims Paper 1 Question - 2 1 The curve with...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online