Edexcel A Level Maths C1 · Core Mathematics 1 January 2008 question paper 6663

Find (3² 4⁵ 7) d.

Write down the value of 16

Simplify

giving your answer in the form a + b√3, where a and b are integers.

The point A (–6, 4) and the point B (8, –3) lie on the line L.

Find an equation for L in the form ax + by + c = 0, where a, b and c are integers.

Find the distance AB, giving your answer in the form k√5, where k is an integer.

find , simplifying the coefficient of each term.

Figure 1

Figure 1 shows a sketch of the curve with equation y = f(x). The curve crosses the x-axis at the points (1, 0) and (4, 0). The maximum point on the curve is (2, 5). In separate diagrams sketch the curves with the following equations. On each diagram show clearly the coordinates of the maximum point and of each point at which the curve crosses the x-axis.

y = 2f(x),

y = f(– x).

The maximum point on the curve with equation y = f(x + a) is on the y-axis.

Write down the value of the constant a.

A sequence is given by:

find the value of p,

write down the value of x₂₀₀₈.

The equation

has no real solutions for x.

Hence find the set of possible values of k.

Given that the point P (4, 1) lies on C,

find f(x) and simplify your answer.

Find an equation of the normal to C at the point P (4, 1).

The curve C has equation

Sketch C showing clearly the coordinates of the points where the curve meets the coordinate axes.

Show that the equation of C can be written in the form

where k is a positive integer, and state the value of k.

There are two points on C where the gradient of the tangent to C is equal to 3.

Find the x-coordinates of these two points.

The first term of an arithmetic sequence is 30 and the common difference is –1.5

Find the value of the 25th term.

The r th term of the sequence is 0.

Find the value of r.

The sum of the first n terms of the sequence is S_n .

Find the largest positive value of S_n .