Please, fill out the information below to continue. NAME E,MAIL PHONE NUMBER 1. PQRS is a quadrilateral in which, PS is parallel to QR. PQ = 16cm, SR = 15 cm and angle QPS = 60° and angle PSQ = 44°.Calculate <QRS 64° 57° 67° 24°2. From the diagram shown below, if the forces are in equilibrium, what is the value of tension T? 50.00N 70.71N 241.42N 100.00N3. Solve the equation 4 sin x = -1 for 0° ≤x≤ 360° 194.5 73.4 244.2 234. The 5th and 10th terms of an AP are 0 and 10 respectively, the 20th term is 30 36 40 205. Use the binomial theorem to expand (1 + 2x)^{5} in ascending powers of x. Hence find the value of (1.02)^{5} correct to 4 decimal places. 1 + 10x + 40x² + 80x3 + 80x4 + 32x5, 1.1041 1 + 80x3 + 80x4 + 32x5, 1.1041 1 + 10x + 40x² + 80x3 + 90x4 + 32x5, 1.10 1 + 10x + 40x² + 80x4 + 32x5, 1.16. The 8th term of the A.P. -4, -2, 0... is -10 10 8 127. If a = x^{1/n}, log_{a}x^{n} is n-² n-¹ n n²8. Two fair dice are thrown together. The probability that the sum of the outcomes is at least 10 is 1/2 1/36 1/6 1/39. If sin 49° = 3/4, find the value of sin 581°. √7 √3 √7/4 √210. If 2 log_{4}P + log_{4}Q² = 0 , then P = ? Q 2/Q PQ Q/2 1/Q11. A box contains yellow, blue and white counters.The probability of picking a yellow counter is 3/8 and the probability of picking a blue counter is 35%. If there are 40 counters in the box, find the number that is blue 12 14 13 1112. If sin-¹(0.966) = 75°, then sin-¹(-0.966) equals 255 or 285 degrees 105 or 255 degrees 195 or 285 degrees 75 or 105 degrees13. Given that find the value of Q 1/3 1 1/2 214. If cosθ = x/y, then 1 + tan²θ equals y²/x² (y² - x²)/ y² (x² - y²)/ y² x²/y²15. Find the range and interquartile range, respectively, of the following data5, 7, 2, 8, 9, 5, 7, 7, 10, 3, 6, 6 8, 3 5, 2 5, 3 8, 516. Evaluate the determinant -14 14 10 1217. If x³ + y³+ 6xy = 0, find dy/dx by implicit differentiation - (2y + x²)/ y - (2y + x²)/(2x + y²) (2y + x²)/ (2x + y²) x/(2x + y²)18. The radius of a spherical balloon is increasing at the rate of 0.25cm/s, find the rate at which the volume is increasing when its radius is 4cm 4π cm³/s 16π cm³/s 7π cm³/s 12π cm³/s19. If (3/4)^{x}(2/3)^{y }= 32/27, the values of x and y respectively are 2, 2 1, 2 2, -2 -2, 120. Find the derivative of f(x)=6x³ − 9x + 4x x²-9 18x²-9 18-x x²+321. If 3 tan θ = 4, evaluate (3sin θ + 2 cos θ)/(3sin θ - 2cos θ). 4 2 3 122. Solve for y if 5 log (y+3) = log 32 -1 0 2 123. Evaluate the definite integral: -4 12/5 -10/3 -324. The polynomial f(x) = 3 x^{ 4} + 5 x^{ 3} - 17 x^{ 2} - 25 x + 10 has irrational zeros at + √(5) and - √(5). Find the other zeros 2/3, 1/2 -2, 1/3 2, 2/3 1, 425. Decompose into partial fractions : (2x^{2} + 6x - 2) / (x^{3} - 1) 2/ x²+1 4/ 3x+2x² -1 2/(x - 1) + 4/(x²+ x + 1) 2/(x² - 1) + 4/(x2 + 2x + 1)26. Tara received a cash gift from her parents on her 10th birthday. On each succeeding birthday, she received twice the amount received in the previous year. If she had received a total of £31,500 by the time she was 15, the cash gift for her 12th birthday was £5,000 £4,000 £2,000 £3,000 £1,00027. Find the values of x for whichis equal to zero 4 or 1/2 2 or 6 -3 or 5 4 or -3/228. Solve the equation 3x + 10 = x² 5 or -2 -5 or 2 -5 or -2 5 or 229. Find the derivative of h(x) = 3x-2 3-2x-¹ 8x-8x-¹ 4x-¹30. Find the coordinate of the point which will divide the line joining the point (2, 4) and (7,9) internally in the ratio 1:2? (8/3 11/3) (11/3, 17/3) (3/8, 3/11) (5/3, 1/3)31. If 4 sin²θ - 3 = 0, the value of θ for 0° < θ < 90° is 90 degrees 30 degrees 60 degrees 45 degrees32. If f ( x+ 2 ) = x² + 3x + 1, then f ( -2 ) is 11 0 1 -1 533. The points of intersection between a straight line and the curve y = -x² + x + 2 give the roots of the equation x² - 2x - 1 = 0. The equation of the line is y = 1 + x y = x + 3 y = x -1 y = 1 - x34. A binary operation * is defined over the set of real numbers such thata * b = a (b + 2). Find 3 * (4 * 2). 72 80 54 60 1835. The diagram shows a uniform meter rule AB which balances horizontally at the 90cm mark when a mass of 0.2kg is suspended from B. Calculate the mass of the meter rule 0.05kg 0.20kg 1.00kg 0.80kg 1.20kg36. Find dy/dx if : y = cos2xsinx + sin2xcosx -3cos2x cosx + 3sin2x sinx 3sin2x sinx 3cos2x cosx - 3sin2x sinx -3cos2x cosx - 3sin2x sinx37. A straight line y = ax intersects the parabola y = x² -5x + 6 at points P(1,2) and Q(m,n). The values of m and n are (6, 12) (3, 6) (-2, -4) (-1, -2)38. In a coordinate system, P = (2, 7) and Q = (2, –3). Which could be the coordinates of R if PQR is an isosceles triangle? I. (12, –3) II. (–6, –9) III. (–117, 2) I and III only I, II and III II and III only II only39. Evaluate: (3^{0 }- 9^{-1/2})^{-3} 2/3 3/2 27/8 1/940. Find the fourth term in the expansion of (1+x)^{15} 13 1 455x³ 13x³ 41. Two cards are drawn, one after the other, with replacement from a pack of 52 cards containing four aces and four queens. The probability that the cards are either both aces or both queens is 2/169 4/13 2/13 2/22142. The common ratio in the G.P log 2, log 4, log 16, ... is 2 3 log 2 443. Find the binomial expansion of (2.01)^{6} 65.944 12.322 34.573 24.54444. If log_{10}2 = 0.3010, the number whose logarithm is equals 0.08 0.008 0.06 0.00645. A coin is tossed 3 times. What is the probability of getting 2 heads and a tail in any order? 1/4 1/8 3/8 1/246. Without using tables, evaluate sin(- 1320°) 0.866 1/2 -1/2 -0.86647. Solve for x:log (3x - 4) - log 2 = 1 6 5 8 748. Find the value of θ (0° ≤ θ ≤ 90°), when sin^{2} θ - 3 sin θ + 2 = 0 90° 80° 60° 70°49. Given that dy/dx = 6x² + 5x, find the function which passes through the point (2, 30). y = 2x³ + 5/2 x² + 4 y = 6x² + 5x y = 2x³ + 5/2 x² - 4 y = x³ + 2x² + 450. If cos θ = √3/2, evaluate (√3-2)/ 3 √3/2 -1 1/2 (3-2√3)/ 351. Find the value of k if the expression kx³ + x² - 5x - 2 leaves a remainder 2 when divided by 2x + 1 -5 10 -10 452. Find the minimum value of the function 2x³ - 6x² -8 5 8 -553. A die is thrown and a coin is tossed. Find the probability that the die shows an even number and the coin shows a head 1/2 1 1/6 1/4 4/654. If tan θ = 2/3, then sec²θ equals 13/9 13/4 4/13 9/1355. A letter is chosen at random from the alphabet. Find the probability that it is either in the word WHITE or in the word RANDOMLY 10/13 1/2 4/13 1/1356. Without using trigonometric tables, evaluate sin 35° sin 55° - cos 35° cos 55° 0 2 1 -157. Without using tables or any calculating device find the value of √2-2 √2-3 √2-1 √3-158. A body of mass 10kg on a smooth inclined plane is connected over a smooth pulley to a mass of 15kg as shown. The acceleration of the system in terms of g is g g/2 8g/25 3g/4 2g/559. The gradient of a curve that passes through the point (-2, 6) is given by x. Determine the equation of the curve. y = 1/2 x² + 4 y = x² + 4 y = x² - 4 y = -1/2 x² - 460. The graphs of the functions y = x³ - 9x and y = 18 - 2x² intersect at the points which the x-coordinates -3, 1 and 3 0, 2 and 3 -3, 2 and 3 -1, 0 and 361 out of 60Time is Up!