a) A chord PQ of a circle of radius 5 cm subtends an angle of 70° at the centre, O. Find correct to 3 significant figures,

i.    the length of the chord PQ;
ii.    the length of the arc PQ;
iii.    the area of the sector POQ;
iv.    the area of the minor segment cut off by PQ.

b) A right circular cone has base radius 5 cm and height 12 cm. Calculate
i.    its volume;
ii.    its total surface area


a) Draw a table of multiplication ⊗ in modulo 8 on the set (2,3,5,7)

b) Use your table to find the solution set of
i.    3 ⊗ n = 5
ii.    n ⊗ n = 1

c) The set P =(-2, -1, 0, 1, 2)  maps onto Q by the function f(x) = x2 – 2, where x ∈ P.
i.    Find the elements of Q
ii.    Draw a diagram showing the mapping between P and Q.

(a)    Using a scale of 2 cm to 2 units on both axes, draw on a graph sheet two perpendicular axes OX and OY for the intervals  -10 ≤ x ≤ 10 and -10 ≤ y ≤ 10

(b)     Draw,, labeling all vertices and indicating the coordinates clearly,

i)     ΔPQR with coordinates P(2, 0), Q(8, -4) and R (8, 0);

ii)     the image ΔP1Q1R1 of ΔPQR under a reflection in the line y = 2 where P→P1,  Q→Q1 and R→R1

iii)     the image ΔP2Q2R2  of  ΔPQR under a rotation through 90o about the origin, where P→P2,  Q→Q2 and R→R2

iv)      the image ΔP3Q3R3  of  ΔPQR under a rotation through 180o about the origin, where P→P3,  Q→Q3 and R→R3

(c)    What single transformation maps ΔP3Q3R3 on  ΔP2Q2R2  ?
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A boy 1.5 m tall is standing 12 m away from a church building which has a tower on top of its roof. The top of the cross on the tower is 14.6 m away from the boy’s head(eyes). If the boy has to raise his eyes through an angle of 31° in order to see the top of the roof, calculate,

a)    correct to the nearest degree, the angle through which the boy must raise his eyes to see the top of the cross on the tower.

b)    correct to one decimal place, the height of the top of the cross from ground:

c)    correct to one decimal place the height of the church building.


(a)    Kofi bought six books and ten pencils from a store. Ama bought three books and twenty-two pencils of the same kind from that store. If each of them paid Ȼ17,000.00 for the items, find the cost of
i.      each pencil
ii.     each book
iii.    two books and four pencils

(b)  Find the truth set of  3x + 8/x = 10, x  0

Three candidates K, L and M were voted into office as school prefects. K secured 45% of the votes, L had 33% of the votes and M had the rest of the votes. If M secure d 1,430 votes, Calculate,

a)    The total number of votes cast;
b)     How many more votes  K received than