Pure 1 Mathematics

Find f(x):

Find the required set of values:

• c > 0 , c < 3

• c = 3, c = 0

• c < 0 , c > 3

• c = 3

• 486

• 4680

• 3040

• 4860

• 54

• 540

• 5400

• 640

The first term of a geometric progression and the first term of an arithmetic progression are both equal to a. The third term of the geometric progression is equal to the second term of the arithmetic progression. The fifth term of the geometric progression is equal to the sixth term of the arithmetic progression. Given that the terms are all positive and not all equal, find the sum of the first twenty terms of the arithmetic progression in terms of a.

• 590a + 20

• 59a

• 590a

• 520a

Write the answer in the given blank spaces:

Describe fully a sequence of transformations that maps the graph of
y = f(x) onto the graph of y = g(x), making clear the order in which the transformations are applied.

Answer order should be: Translation, Stretching.

• Translation {2; 3} and Stretching by the factor 2 in the y direction

• Translation {3; 0} and Stretching by the factor 2/3 in the x direction

• Translation {2; 3} and Stretching by the factor 1/2 in the y direction

• Translation {3; 7} and Stretching by the factor 2 in the x direction

Find, by calculation, the coordinates of A and B:

Answer should be in the form of → A(x,y); B(x,y)

Given that A(8,4) and B(5,-5).

Find an equation of the circle which has its centre at C and for which the line with equation y = 3x − 20 is a tangent to the circle

• (x-1)² + (y-2)² = 52.6

• (x+1)² + (y-2)² = 62.5

• (x+1)² + (y+2)² = 64.5

• (x-1)² + (y-2)² = 65.2