WASSCE 2025 *FURTHER (E-MATHS) MATHEMATICS TEST* BY DR. TABI'S EXAMS LINK 👇👇👇👇👇👇👇 (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? 0542743763_Dr. (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? 0542743763 (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. https://whatsapp.com/channel/0029VaEW2JPEawdvPSdOBG1m (10)(a) If y = (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.