Edexcel A Level Maths C1 · Core Mathematics 1 June 2015 question paper 6663

Simplify

Solve the simultaneous equations y – 2 x – 4 = 0

Given that y = 4x³ – , x  0, find in their simplest form

A sequence U₁, U₂, U₃,... is defined by

Find the value of

Another sequence V₁, V₂, V₃,... is defined by

Find V₃ and V₄ in terms of k.

find the value of k.

The equation (p – 1)x² + 4x + (p – 5) = 0, where p is a constant has no real roots.

Show that p satisfies p² – 6p + 1 0

Hence find the set of possible values of p.

The curve C has equation

Find in its simplest form.

Find an equation of the tangent to C at the point where x = –1 Give your answer in the form ax + by + c = 0, where a, b and c are integers.

Given that y = 2^x,

express 4^x in terms of y.

Hence, or otherwise, solve

Factorise completely 9x – 4x³

Sketch the curve C with equation

Show on your sketch the coordinates at which the curve meets the x-axis.

The points A and B lie on C and have x coordinates of –2 and 1 respectively.

Show that the length of AB is k 10 where k is a constant to be found.

Jess started work 20 years ago. In year 1 her annual salary was £17000. Her annual salary increased by £1500 each year, so that her annual salary in year 2 was £18500, in year 3 it was £20000 and so on, forming an arithmetic sequence. This continued until she reached her maximum annual salary of £32000 in year k. Her annual salary then remained at £32000.

Find the value of the constant k.

Calculate the total amount that Jess has earned in the 20 years.

A curve with equation y = f(x) passes through the point (4, 9). Given that

find f(x), giving each term in its simplest form.

Point P lies on the curve . The normal to the curve at P is parallel to the line 2 y + x = 0

Find the x coordinate of P.