GCE Maths Core 2 -Jan 11(OCR)

Revise with this OCR core 2 maths online test(1) with answers. (detail at end)
72 marks, A=80%, B=70% etc

1. Binomial expansion  Menu

i)Find and simplify the first four terms of the binomial expansion of (1 + 3x)6

ii) Hence find the coefficient of x2 in the expansion of (1 + 3x)6 (2 – 7x)


2. Sequences  Menu

A sequence P has terms u1, u2 and u3 defined by un = 5n + 1

i) What are the values of terms u1, u2 and u3
ii) What type of sequence is P?
iii) Find sum


3. Trapezium rule  Menu

The diagram shows the curve: equation

i) Use the Trapezium rule, to approximate the area bounded by the curve, the line x = 8 and the x-axis.
Use 6 strips each of width 0.5 and give your answer correct to 3 sf.
ii) Explain why this approximation is an overestimate or underestimate.


4. Logarithms  Menu

a) Solve the equation 6x–2 = 240 using logarithms.
Give your answer to 3 sf.

b) Solve the equation log42x + 2log45 = log4(5x + 5)


5. Geometric Progression  Menu

In a geometric progression the sum to infinity is five times the first term

i) Show that the common ration is 4/5
ii) Given that the third term is 16 find the first term.
iii) Find the sum of the first ten terms


6. Integration  Menu

a) integration

b) Find in terms of z , the value of

c) Deduce the value of


7. Trig Identities  Menu

Solve the following equations for 0° ≤ θ ≤ 180°

i) 5tan3θ = 4

ii) 3cos2θ + 13sinθ = 0


8. Sector area and perimeter  Menu

A sector XOY of a circle with centre 0 and radius 6cm is shown below.
The angle XOY is in radians and the area of the triangle XOY is 12 cm2
A shaded segment is bounded by the cord XY and the arc XY.

a) Find the obtuse angle θ.
b) Find the perimeter of the shaded segment to 3 sf.
c) Find the area of the shaded segment to 3 sf.

9. Factor, remainder theorem  Menu

The curve f(x)is shown below.

i) Show that the curve crosses the x-axis at (5, 0) and hence state a factor of f(x)
ii) Express f(x) as a product of a quadratic and linear factor.
iii) Hence find the other two points of intersection of the curve with the x-axis
iv) Use integration to find the total area shaded in the diagram.