as level pure math

The sum of the first nine terms of an arithmetic progression is 117. The sum of the next four terms

is 91.

Find the first term and the common difference of the progression.

find +constant k

Each year the selling price of a diamond necklace increases by 5% of the price the year before. The

selling price of the necklace in the year 2000 was $36 000.

(a) Write down an expression for the selling price of the necklace n years later and hence find the

selling price in 2008.

The company that makes the necklace only sells one each year. Find the total amount of money

obtained in the ten-year period starting in the year 2000.

• -1<fx<2

• _1>f(x)<2

• -2<f(x)>4

The equation of a line is y = mx + c, where m and c are constants, and the equation of a curve is

xy = 16.

(a) Given that the line is a tangent to the curve, express m in terms of c.

(b) Given instead that m = −4, find the set of values of c for which the line intersects the curve at

two distinct points.

The coordinates of the points A and B are 􀀀−1, −2 and 􀀀7, 4 respectively.

(a) Find the equation of the circle, C, for which AB is a diameter