9709/May June/33/2016/Q2

The variables x and y satisfy the relation 3^y = 4^(2−x).

(i) By taking logarithms, show that the graph of y against x is a straight line. State the exact value of the gradient of this line. [3]

(ii) Calculate the exact x-coordinate of the point of intersection of this line with the line with equation y = 2x, simplifying your answer. [2]

Solutions:

Reference: PYQ - May/Jun 2016 Paper 33 Q2

9709/MayJune/2009/3/Q1

Solve the equation ln (2 + e^-x) = 2, giving your answer correct to 2 decimal places.

Solution:

Reference: PYQ - May/June 2009 Paper 3 Q1

9709/OctNov/2008/2/Q3

The variables x and y satisfy the equation y = A(b^−x), where A and b are constants. The graph of ln y against x is a straight line passing through the points (0, 1.3) and (1.6, 0.9), as shown in the diagram. Find the values of A and b, correct to 2 decimal places.

Solution:

Reference: PYQ - Oct/Nov 2008 Paper 2 Q3

Logarithms and Exponentials tricky question

Find how many terms there are in these geometric sequences.

(i) –1, 2, –4, 8, …, –16 777 216

Solution: