Edexcel Core Mathematics C1 January 2013

Questions and Worked Solutions for C1 Edexcel Core Mathematics January 2013.

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Core 1 Mathematics Edexcel January 2013 Question 7
Arithmetic Series
7. Lewis played a game of space invaders. He scored points for each spaceship that he captured. Lewis scored 140 points for capturing his first spaceship. He scored 160 points for capturing his second spaceship, 180 points for capturing his third spaceship, and so on. The number of points scored for capturing each successive spaceship formed an arithmetic sequence.

(a) Find the number of points that Lewis scored for capturing his 20th spaceship.

(b) Find the total number of points Lewis scored for capturing his first 20 spaceships.

Sian played an adventure game. She scored points for each dragon that she captured. The number of points that Sian scored for capturing each successive dragon formed an arithmetic sequence.
Sian captured n dragons and the total number of points that she scored for capturing all n dragons was 8500.

Given that Sian scored 300 points for capturing her first dragon and then 700 points for capturing her nth dragon,

(c) find the value of n.

Core 1 Mathematics Edexcel January 2013 Question 8
Differential Equations
dy/dx = -x³ + (4x -5)/2x³, x ≠ 0
Given that y = 7 at x = 1, find y in terms of x, giving each term in its simplest form. Core 1 Mathematics Edexcel January 2013 Question 9
Roots of a Quadratic
The equation (k + 3)x² + 6x + k = 5, where k is a constant, has two distinct real solutions for x.
(a) Show that k satisfies k² -2k + 24 < 0

(b) Hence find the set of possible values of k.

Core 1 Mathematics Edexcel January 2013 Question 10

Completing the Square
4x² + 8x + 3 ≡ a(x + b)² + c

(a) Find the values of the constants a, b and c.

(b) On the axes, sketch the curve with equation y = 4x² + 8x + 3, showing clearly the coordinates of any points where the curve crosses the coordinate axes.

Core 1 Mathematics Edexcel January 2013 Question 11
Tangents
11. The curve C has equation

y = 2x -8√x + 5, x ≥ 0

(a) Find dy/dx , giving each term in its simplest form.

The point P on C has x-coordinate equal to 1/4

(b) Find the equation of the tangent to C at the point P, giving your answer in the form y = ax + b, where a and b are constants.

The tangent to C at the point Q is parallel to the line with equation 2x - 3y + 18 = 0
(c) Find the coordinates of Q.