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Core Maths 👇👇

1. If 3m x 3n = 243 and 3m ÷ 32n = 9, write down two Hence equations connecting m and n. find the values of m and n.

2. a) The cost of a packet of sugar is x cedis and the cost of a tin of milk is y cedis. If 3 packets of sugar and 4 tins of milk cost ¢635.00 and 4 packets of sugar and 3 tins of milk cost é695.00, write two equations connecting x andd y. Hence find x andy.
b) The cost of production of a wireless set was ₵40,000.00. The manufacturer sold it to a wholesaler at a profit of 20 per cent. The wholesaler also sold it to a retailer at a profit of 25 per cent. The retailer marked the set to be sold at a price 50 per cent above what he paid for it.
i) Find the marked price
ii) To a customer who paid cash, the retailer reduced the price to ₵75,000.00. Find the percentage discount.

3. a) Without using tables or calculator, evaluate 3√7(7-2√7), if √7 = 2.646
b) The cost of producing a motor car in a certain factory is partly constant and partly varies inversely as a number of cars produced per day. If the cost of producing each car is 1,600 dollars when 4 cars are produced per day and 1,420 dollars when 5 cars are produced per day, find the rate of production necessary to bring the cost down to 1,150 dollars per car. dollars

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*FURTHER (E-MATHS) MATHEMATICS 2022 WASSCE TRIALS PREPARED BY BLOGGER 1 Your Examination Messiah 🔥 0550914474

(1)If f(y) = log2 (y + 1) – log2 (y + 3),

1. find the domain of f(y);

solve f(y) = 1

(2)A binary operation * is defined on the set R, of real numbers by

X * Y = x²/x=y¹ where x, y ∈ R.

(a) Evaluate (2 * 3) * 5.

(b) If (x + 1) * (x + 2) = 1/3 find the value of x.

(3) If f(x) = 6×3 + 13×2 + 2x – 5 and f(-1) = 0, find the factors of f(x).

(4) Find the truth set of sin θ + cos 2θ = 0, 0o ≤ θ ≤ 360o

(5)(a) The position vectors of the points X and Yare x = (-2 j + 5 j) and y = (i -7 j)

respectively.

(i) (3 x + 2y);

(ii) I (y – 2x) I;

(iii) the angle between x and y;

(iv) the unit vector in the direction of (x + y).

(b) A bullet of mass 0.084 kg is fired horizontally into a 20 kg block of wood at rest on a smooth floor. If they both move at a velocity of 0.24 ms” after impact, calculate, correct to two decimal places, the initial velocity of the bullet.



(6)(a) Two ships M and N, moving with constant velocities, have position vectors (3 i + 7 j) and (4

i + 5 J] respectively. If the velocities ofM and N are (5 i + 6)] and ( i+ 3 J] and the distance covered by the ships after t seconds are in meters, find

i) MlJ.

(ii) lNfNI, when t = 3 seconds.

(b) A particle is acted upon by forces F 1 = 5 i +

pj, F2 = q r + j, F3 = -2p i + 3 j and F4 = -4 i + qj, where p and q are constants. If the particle remains in equilibrium under the action of these forces, find the values ofp and q.

(b) A particle is acted upon by forces F 1 = 5 i +

pj, F2 = q r + j, F3 = -2p i + 3 j and F4 = -4 i + qj, where p and q are constants. If the particle remains in equilibrium under the action of these forces, find the values of p and q.

(7)(a) A manufacturer produces light bulbs which are tested in the following way: A batch is accepted in either of the following cases:

(i) The first sample of 5 bulbs contains no faulty bulbs;

(ii) The first sample of 5 bulbs contains at least one faulty bulb but a second sample of 5 bulbs contains no faulty bulb. If 10% of the bulbs are faulty, what is the probability that the batch is accepted?

(b) A bag contains 15 identical marbles of which 3 are back. Keshi picks a marble at random from the bag and replaces it. If this is repeated 10 times, what is the probability that he

(i) did not pick a black ball?

(ii) picked a black ball at most three times?

(8)(a) Eight coins are tossed once. Find, correct to three decimal places, the probability of obtaining

(i) exactly 8 heads;

(ii) at least 5 heads;

(iii) at most 1 head.

(b) In how many ways can four letters from the word SHE E P be arranged.

(i) without any restriction

(ii) with only one E
(9)The images of (3,2) and (-1,4) under a linear transformation T and (-1,4) and (7, 11) respectively. P is another transformation where

P: (x, y) – (x + y, x + 2y).

(a) Find the matrices T and P of the linear transformation T and P.

(b) Calculate TP.

(c) Find the image of the point X (4, 3) under TP.

(10)(a) Ify = (2x + 3)7 + x-l ,find the value of dy when x

2x-l dx

Using the substitution, u = x + 2, evaluate f12

X-14 dx.

(x+2).

(11)A uniform plank PQ of length 8 m and mass 10kg is supported horizontally at the end P and at point R, 3 meters from Q. A boy of mass 20 kg walks along the plank starting from P. If the plank is in equilibrium, calculate the

(a) reaction at P and R when he has walked 1.5 meters;

(b) distance he had walked when the two reactions are equal;

(c) distance he walked before the plank tips over. (Take g = 10 ms”)
(12)The position vector of a particle of mass 3 kg moving along a space curve is given by r = (4t3 – () i – (2t2 – t) j at any time t seconds. Find the force acting on it at t = 2 seconds.
(13)Five students are to be selected from a large population.

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