Solve the equation 4 sin² Ө+4 cos Ө =5

For 0^o ≤ Ө ≥ 360^o  give the answer in degrees

• a) Calculate the volume of the :

• • i) Cylindrical part

  • ii) Hexagonal part

• b) An identical pillar is to be built but with a hollow centre cross – section area of 0.25m². The density of the material to be used to make the pillar is 2.4g/cm³.Calculate the mass of the new pillar.

The displacement x metres a particle after seconds given by:

• b) On the grid provided draw, on the same axis, the graph of y = 3cos 2x and y = sin(2x +30⁰) for 0^o ≤ x ≥ 180^0. Take the scale: 1cm for 150 on the axis and 2cm for 1 unit on the y-axis.
• c) Use your graph to estimate the range of value of x for which 3 cos 2x ≤ 2sin (2x+30^o).

An electric pylon is 30m high. A point S on top of the pylon is vertically   above another point on the ground . Points A and B are on the same horizontal ground as R. Point A is due south of the pylon and the angle of elevation of S from A is 26⁰. Point B is due west of the pylon and the angle of elevation of S from B is 32⁰.

S_n = n² +4n
Hence or otherwise find the first largest integral value of n such that.
S_n < 725

The marks obtained by 10 pupils in an English test were 15,14,13,12,P,16,11,13,12 and 17.The sum of the squares of the marks, ∑x = 21,794

A helicopter is stationed at an airport H on a bearing 060^o and 800km from another airport P.A third airport is J is on bearing of 140⁰ and 1,200km from H. 

Determine:

• i) Value of P
• ii)The bearing of P from J

The diagram below shows the graph of:

 Y ≥ ³/_10x  –  ³/₂, 5x + 6y = 30 and x = 2

By shading the unwanted region, determine and label the region R that satisfies the three inequalities.

Y ≥ ³/₁₀x – ³/_{2  ,} + 6y ≥ 30 and x ≥ 2

Given that tan 75⁰ = 2 + √3, find without using tables tan 15⁰ in the form p + q√m, where p,q and m are integers.

Expand (2 + x)⁵ in ascending powers of x up to the term in x³. Hence, approximate the value of (2.03)⁵ to 4 s.f.