Edexcel A Level Maths C1 · Core Mathematics 1 June 2013 question paper 6663R

Express 27 in the form kV3, wherek is an integer. (4)

Find

giving each term in its simplest form. (4)

Find the gradient of L,. (2) The line L, is perpendicular to L, and passes through the point (2, 5).

Solve

A-sequence x,, x,,x,... is defined by

Find an expression for x, in terms of k. (1)

Hence find the value of ¥ x,

Each year, Abbie pays into a savings scheme. In the first year she pays in £500. Her payments then increase by £200 each year so that she pays £700 in the second year, £900 in the third year and so on.

Find out how much Abbie pays into the savings scheme in the tenth year. (2) Abbie pays into the scheme for n years until she has paid in a total of £67200.

Hence find the number of years that Abbie pays into the savings scheme. (2)

Arectangular room has a width ofx m.

The length of the room is 4 m longer than its width. Given that the perimeter of the room is greater than 19.2 m,

Given also that the area of the room is less than 21 m2,

write down an inequality, in terms ofx, for the area of the room.

Solve this inequality. (4)

Hence find the range of possible values for x. (1)

The curve C passes through the point (—1, 0) and touches the x-axis at the point (2, 0). The curve C has a maximum at the point (0, 4).

The equation of the curve C can be written in the form

where a, b andc are integers. Calculate the values of a, b and c. (5)

Show clearly the coordinates of all the points where the curve crosses or meets the coordinate axes. (3)

Given that

equal to 10 (4)

Figure 2.

Find the coordinates ofA and the coordinates of B. (6)

Find the distance AB in the form r \2 wherer is a rational number. (3)