Edexcel A Level Maths C1 · Core Mathematics 1 June 2012 question paper 6663

Find

giving each term in its simplest form.

Evaluate 32(32 , giving your answer as an integer.

Find giving each term in its simplest form.

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

where c is a constant.

Write down an expression, in terms of c, for a₂

find the range of values of c.

A boy saves some money over a period of 60 weeks. He saves 10p in week 1, 15p in week 2, 20p in week 3 and so on until week 60. His weekly savings form an arithmetic sequence.

Find how much he saves in week 15

Calculate the total amount he saves over the 60 week period.

The boy’s sister also saves some money each week over a period of m weeks. She saves 10p in week 1, 20p in week 2, 30p in week 3 and so on so that her weekly savings form an arithmetic sequence. She saves a total of £63 in the m weeks.

Show that m (m + 1) = 35 × 36

Hence write down the value of m.

The point P (4, –1) lies on the curve C with equation y = f(x), x > 0, and

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

Find f(x).

4x – 5 – x² = q – (x + p)² where p and q are integers.

Find the value of p and the value of q.

Calculate the discriminant of 4x – 5 – x²

On the axes on page 17, sketch the curve with equation y = 4x – 5 – x² showing clearly the coordinates of any points where the curve crosses the coordinate axes.

The line L₁ has equation 4y + 3 = 2x The point A (p, 4) lies on L₁

Find the value of the constant p.

The line L₂ passes through the point C (2, 4) and is perpendicular to L₁

Find an equation for L₂ giving your answer in the form ax + by + c = 0, where a, b and c are integers.

The line L₁ and the line L₂ intersect at the point D.

Find the coordinates of the point D.

Show that the length of CD is 5 A point B lies on L₁ and the length of AB = The point E lies on L₂ such that the length of the line CDE = 3 times the length of CD.

Find the area of the quadrilateral ACBE.

Figure 1 shows a sketch of the curve C with equation y = f(x) where

There is a minimum at the origin, a maximum at the point (3, 27) and C cuts the x-axis at the point A.

Write down the coordinates of the point A.

On separate diagrams sketch the curve with equation

y = f(x + 3)

y = f(3 x) On each sketch you should indicate clearly the coordinates of the maximum point and any points where the curves cross or meet the coordinate axes.

The curve with equation y = f (x) + k, where k is a constant, has a maximum point at (3, 10).

Write down the value of k.