Edexcel A Level Maths C1 · Core Mathematics 1 June 2010 question paper 6663

Write

in the form k √x, where k and x are integers.

Find

giving each term in its simplest form.

Find the set of values of x for which

3(x – 2) < 8 – 2 x

(2 x – 7)(1 + x) < 0

both 3(x – 2) < 8 – 2 x and (2 x – 7)(1 + x) < 0

Show that x² +6x + 11 can be written as

where p and q are integers to be found.

In the space at the top of page 7, sketch the curve with equation y x² 6x 11, showing clearly any intersections with the coordinate axes.

Find the value of the discriminant of x² +6x + 11

A sequence of positive numbers is defined by

Find a₂ and a₃, leaving your answers in surd form.

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

y = f (x + 3)

y = 2f (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.

Write down the value of a.

Given that

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.

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

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

Find the value of t.

Find the area of triangle ABC.

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 + 2 d) 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.

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

Show that 15(a + 40.75) = 1005

Hence find the value of a and the value of d.

On the axes below sketch the graphs of

y = x (4 – x)

y = x² (7 – x) showing clearly the coordinates of the points where the curves cross the coordinate axes.

Show that the x-coordinates of the points of intersection of

are given by the solutions to the equation x(x² – 8x + 4) = 0

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

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.

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

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

f(x),

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.