Questions and Worked Solutions for C1 Edexcel Core Mathematics June 2010.

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Core 1 Mathematics Edexcel June 2010 Question 6

1. Figure 1 shows a sketch of the curve with equation y = f (x). The curve has a maximum

point A at (–2, 3) and a minimum point B at (3, – 5).

On separate diagrams sketch the curve with equation

(a) y = f (x + 3)

(b) y = 2 f(x)

On each diagram show clearly the coordinates of the maximum and minimum points.

The graph of y = f (x) + a has a minimum at (3, 0), where a is a constant.

(c) Write down the value of a.

Core 1 Mathematics Edexcel June 2010 Question 7

7. Given that y = 8x^{3} - 4√x + (3x^{2} + 2)/x, x > 0

find
dy/dx

Core 1 Mathematics Edexcel June 2010 Question 8

8. (a) Find an equation of the line joining A (7, 4) and B (2, 0), giving your answer in the

form ax+by+c=0, where a, b and c are integers.

(b) Find the length of AB, leaving your answer in surd form.

The point C has coordinates (2, t), where t > 0, and AC = AB.

(c) Find the value of t.

(d) Find the area of triangle ABC

Core 1 Mathematics Edexcel June 2010 Question 9

9. A farmer has a pay scheme to keep fruit pickers working throughout the 30 day season.

He pays £a for their first day, £(a + d ) for their second day, £(a + 2d ) for their third day,

and so on, thus increasing the daily payment by £d for each extra day they work.

A picker who works for all 30 days will earn £40.75 on the final day.

(a) Use this information to form an equation in a and d.

A picker who works for all 30 days will earn a total of £1005

(b) Show that 15(a + 40.75) = 1005

(c) Hence find the value of a and the value of d

Core 1 Mathematics Edexcel June 2010 Question 10

10. (a) On the axes below sketch the graphs of

(i) y = x (4 – x)

(ii) y = x

showing clearly the coordinates of the points where the curves cross the coordinate

axes.

(b) Show that the x-coordinates of the points of intersection of

y = x (4 – x) and y = x

are given by the solutions to the equation x(x

The point A lies on both of the curves and the x and y coordinates of A are both positive.

(c) Find the exact coordinates of A, leaving your answer in the form (p + q√3, r + s√3)

where p, q, r and s are integers.

Core 1 Mathematics Edexcel June 2010 Question 11

11. The curve C has equation y = f(x), x > 0, where

dy/dx = 3x - 5/√x - 2

Given that the point P (4, 5) lies on C, find

(a) f(x),

(b) an equation of the tangent to C at the point P, giving your answer in the form

ax + by + c = 0, where a, b and c are integers.

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