Edexcel Core Mathematics C1 June 2010

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 = 8x3 - 4√x + (3x2 + 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 = x2(7 – 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 = x2(7 – x)
are given by the solutions to the equation x(x 2 – 8x+ 4) = 0

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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