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)

ANS

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


ANS

3. Trapezium rule  Menu

The diagram shows the curve: equation

graph
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.

ANS

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)


ANS



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


ANS

6. Integration  Menu

a) integration

b) Find in terms of z , the value of

c) Deduce the value of


ANS

7. Trig Identities  Menu

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

i) 5tan3θ = 4

ii) 3cos2θ + 13sinθ = 0


ANS

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.

  sectors
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.


ANS
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.

ANS

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