CIE A level -Pure Mathematics 2 : Topic : 2.3 Trigonometry- properties and graphs of all six trigonometric functions : Exam Style Questions Paper 2


(a) Find

(i)\(\int \frac{e^{2x}+6}{e^{2x}}\),

(ii) \(\int 3\cos ^{2}xdx\),

(b) Use the trapezium rule with 2 intervals to estimate the value of,

\(\int _{1}^{2}\frac{6}{\ln (x+2)}dx\),

giving your answer correct to 2 decimal places.


(a) (i) Attempt to divide by \(e^{2x}\) and attempt to integrate 2 terms 

Integrate a term of form \(ke^{-2x}\) correctly.

Fully correct integral \(x-3e^{-2x}\).

(ii) State correct expression \(\frac{1}{2}\cos 2x+\frac{1}{2}\) or equivalent 
Integrate an expression of the form a + b cos 2x, where ab ≠ 0, correctly 
State correct integral \(\frac{3\sin 2x}{4}+\frac{3x}{2}\).

(b) State or imply correct ordinates 5.46143…, 4.78941…, 4.32808… 
Use correct formula, or equivalent, correctly with h = 0.5 and three ordinates 
Obtain answer 4.84 with no errors seen