Edexcel A Level Maths C1 · Core Mathematics 1 June 2009 question paper 6663

Simplify

8 5 2 5

Given that 32 √ 2 = 2^a, find the value of a.

Find the set of values of x for which

4 x – 3 > 7 – x

both 4x – 3 > 7 – x and 2x² – 5x – 12 < 0

A 40-year building programme for new houses began in Oldtown in the year 1951 (Year 1) and finished in 1990 (Year 40). The numbers of houses built each year form an arithmetic sequence with first term a and common difference d. Given that 2400 new houses were built in 1960 and 600 new houses were built in 1990, find

the value of d,

the value of a,

the total number of houses built in Oldtown over the 40-year period.

The equation x² + 3px + p = 0, where p is a non-zero constant, has equal roots. Find the value of p.

A sequence a₁, a₂, a₃,... is defined by

where k is a constant.

Write down an expression for a₂ in terms of k.

find the value of k.

The points A and B have coordinates (6, 7) and (8, 2) respectively. The line l passes through the point A and is perpendicular to the line AB, as shown in Figure 1.

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

Given that l intersects the y-axis at the point C, find

the coordinates of C,

the area of OCB, where O is the origin.

₂

Show that f (x) = 9x Ax B, where A and B are constants to be found.

Find f ' (x).

Evaluate f ' (9).

Factorise completely x³ – 6x² + 9x

Sketch the curve with equation

showing the coordinates of the points at which the curve meets the x-axis.

Using your answer to part (b), or otherwise,

sketch, on a separate diagram, the curve with equation

showing the coordinates of the points at which the curve meets the x-axis.

The curve C has equation

The point P has coordinates (2, 7).

Show that P lies on C.

Find the equation of the tangent to C at P, giving your answer in the form y = mx + c, where m and c are constants.

The point Q also lies on C. Given that the tangent to C at Q is perpendicular to the tangent to C at P,

show that the x-coordinate of Q is 2 6.