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

Question Paper (pdf)

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.

7. Given that y = 8x

find dy/dx.

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.

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.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.