Please, fill out the information below to continue. NAME EMAIL PHONE NUMBER 1. In an experiment, the mean of 25 observations was 6. One of the observations, which has the value of 30, was cancelled. The mean of the remaining observations is 4.8 4.5 3.5 52. Points X and Y are respectively 48m North and 20m East of point Z, The bearing of X and Y is approximately 067° 247° 157° 337°3. Find the maximum and minimum values of thefunction 3x² - x³ max = 4, min = 0 max = 10, min = 4 max =-2, min = -6 max = 1, min = -14. Differentiate the functions wrt x:5(3x-4)² 3x²+4 30(3x-4) 60x+4x² 60x²5. If a graph of the function y = 3x² -5x - 7 is provided, the roots of the equation 3x² - 2x -5 = 0 are given by the points of intersection of the curve y = 3x² -5x - 7 and the line y = -7x - 2 y = 7x - 12 y = -3x - 2 y = 3x - 26. If P = {positive integers less than 20, and divisible by 3} and Q = {odd numbers from 1 to 20 inclusive}, then PnQ is P {3,9,15} ∅ {1,3,9,15}7. Water flows at the rate of 10 metres/minute from a cylindrical pipe 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cms and depth 24 cms? 52 min 48 min 51 min 55 min8. If xy + 1 = y² and z= (1/x) - (1/xy), express z in terms of y 1 + y 1/ y-1 1/ y+1 1/ x-y9. Find the slope of the line 1 1/2 2 2/310. A photograph is to be taken of five people including a married couple. If the married couple insist on sitting next to each other, the number of different arrangements is 60 48 24 1211. Find the variance and the standard deviation, respectively of the data below-3, -5, -7, 2, 5, 0, 4, 6 4.52, 20.2 20.4, 4.52 12.6, 19 12.3, 1712. Simplify : y/3 3/y 1/3y 3y13. A card is drawn from an ordinary pack of 52 playing cards. Find the probability that it is a Queen of Hearts 9/13 1/52 3/52 4/1314. A hunter on the ground observes a bird perching on a tree on a bearing of S15°W. The bearing of the hunter from the bird is N15°E N75°W N75°E N15°W15. The data below shows the distribution of workers in a certain secondary school. Teacher 30 Gardeners 15Typists 9 Cleaners 6Clerks 12 Messengers 3If one of the workers is absent from work on one particular day, the probability that he is a clerk is 1/25 2/25 3/25 4/2516. An aircraft flies from Jordan(30°S, 44°E) to Riyadh(30°S, 28°W) in 26/3 hours. If radius of the earth is 6,370 km, π = 22/7, and the plane flies along the parallel of latitude, its average speed, to the nearest kilometer is 620 km/h 462 km/h 800 km/h 770 km/h17. If there is no stop-over at Dubai, and the average speed of the airplane is 500km/hr, the total time taken for the plane to fly from Lagos to Kuala Lumpur via Dubai is approximately 7 h 10 h 5 h 8 h18. The product of the present ages of a mother and her daughter is 432. Four years ago, the mother was exactly four times as old as the daughter. Their present ages are 48, 9 30, 18 36, 12 28, 1419. In a mock quiz taken by 40 boys and y girls, the mean scores were 5.5 and 6 respectively. If the total score was 412, find the value of y 34 32 30 38 3620. A dealer makes a profit of 20% by selling a crate of soft soft drinks for £600.00. The cost of the crate of soft drinks to the dealer was £500.00 £480.00 £540.00 £520.0021. Differentiate (x² - 1/x)² wrt x 2/x³ +3x +2 4x³ -2/x³ -2 2x²-2 x³-3x²+222. If y is a positive number, for what values of y is 4 + 3y < 10 ? 0 < y < 2 0 > y > 2 y < 2 1 < y < 223. Using the product rule differentiate wrt x(3x + 4)(x - 3) 6x-5 x²+12 9x-12 6x²24. One of the roots of the equation: 6y² = 5 - 7y is -1/2 -1/3 1/2 5/325. The ratio of the price of a tin of milk to that of a packet of sugar is m : p. If the price of milk now goes up by 25% while that of sugar now goes up by 15%. What is the new ratio of the prices? 5m : 3p 5p : 3m 25m : 23p 5m : 23p 23m : 25p26. Given that a+b = 3/2 and a-b = 5/2, the value of 2b + a is 1/2 2/3 -2 127. Three cities London, Seoul and Harare are such that Seoul is located 50 km away from London on a bearing of 065°. Harare is 100 km away from London on a bearing of 305°. The distance between Seoul and Harare is 50√5 km 50√2 km 50√7 km 50√3 km28. The values of tan 225° and tan 315° are respectively -1 and 1 1 and 1 -1 and -1 1 and -129. The data below shows the distribution of workers in a certain secondary school. Teacher 30 Gardeners 15Typists 9 Cleaners 6Clerks 12 Messengers 3If one of the workers is on leave, the probability that he is either a teacher or a gardener is 1/5 2/5 3/25 3/530. Factorize the polynomial x^{ 3} - 1 (x-1)² 2x+1 (x - 1)(x² + x + 1) x-131. There is a vast grassy farm in which there is a rectangular building of the farmhouse whose length and breadth is 50 m and 40 m respectively. A horse is tethered at a corner of the house with a tether of 80 m long. What is the maximum area that the horse can graze? 5425π 5245π 245π 254π32. Find the sum to infinity of the series 1 + 7/10 + (7/10)² + (7/10)³ + ... 5 27/10 10/3 733. Evaluate: 6- 2In5 4/5In 3 10/3 - 5In3 8In 534. If a = x^{1/n}, log_{a}x^{n} is n² n-² n-¹ n35. The table below shows the frequency distribution of marks obtained by 40 students in a testIf a student is selected at random, find the probability that he scored 6 marks 27/40 1/8 1/4 7/836. What fraction of the area of a regular hexagon is the area of regular hexagon obtained by joining the midpoints of the sides of the first hexagon in order? 2/3 1/2 1/4 3/437. Correct each of the numbers 38.7152 and 0.05381 to two significant figures and find their product , correct to two significant figures. 2.1 2.6 0.21 1.9 2.038. A right-angled triangle has sides of lengths (3m-1) cm, (m) cm and (3m+1) cm. The value of m is 18 2 6 1239. A trader sold an article for N 660.00 at a profit of 20%.In order to make a profit of 30%, the article should have been sold for N858 N792 N715 N99040. Evaluate 4512 ÷ 0.05 correct to three significant figures 90200 90240 9020 902 90200041. A reception hall is arranged such that the first row contains 10 seats and each successive row has two more seats than the preceding row. The total number of seats in the first twelve rows is 362 120 222 240 25242. A bag contains only gala and royal apples. The probability of picking a gala at random is 0.3. Find the probability of picking a royal apple 0.9 0.8 0.7 0.643. Three guests X, Y and Z arrive in that order for a dinner party. If guests are served randomly, the probability that the three guests will be served in the sequence of their arrival is 1/3 1/2 1/6 2/344. Solve for a:2log_{8}a – 5log_{8}a = 2 2 1/4 1/2 445. A container has 32 blue pens, 28 black pens and 20 red pens. If a pen is selected at random, what is the probability that it is a blue pen or a red pen? 1/20 1/4 13/20 3/446. The vertices of the inscribed (inside) square bisect the sides of the second (outside) square. Find the ratio of the area of the outside square to the area of the inscribed square. 2:3 1:4 1:3 2:147. Which of the following statements is false? An equilateral triangle is also equiangular An equiangular triangle is also equilateral If two triangles are similar, then they are also congruent If two triangles are congruent, then they are also similar48. The quadrants where abcissa and ordinate have different signs are? 2nd & 3rd quadrant 2nd & 4th quadrant 1st & 2nd quadrant 1st & 3rd quadrant49. In a trapezium PQRS, PQ//SR, |PQ| = 5 cm, |SR| = 7 cm and the trapezium has an area of 24 cm². The area of the triangle PQS is 12 cm² 16 cm² 10 cm² 14 cm²50. Determine the order of the matrix 3x3 1x2 2x4 3x451. Two locations on the parallel of latitude φ°S have a difference in longitude of θ°.If R = 6,370 km and π=22/7, the distance between the two locations in km, is approximately (222θ) cos φ° (111φ) cosθ° (111θ) cos φ° (56φ) cosθ°52. If the shadow of a pole 7 m high is half of its length, what is the angle of elevation of the sun 34° 63° 23° 12°53. Given thattanx = 5/12, what is the value of sinx + cosx? 13/17 17/13 13 1754. Find the maximum value of the function 3x²-x³ 4 -2 -3 1/255. A cone of height 12 cm has a volume of 330 cm³. The volume of a cone wih the same radius but of height 8cm is 270 cm3 146 2/3 cm3 220 cm3 300 cm356. If 101010_{2 }= x_{10 }+ 1111_{2,} the value of x is 19 13 32 2757. A man bought a wrist watch for $750.00 and re-sold it for $600.00. His percentage loss was? 22.5% 20% 25% 15%58. By solving equation c³-125 = 0, value of 'c' will be 5 15 20 1059. Solve the equation: 4^{(w - 1)} × 5^{(2w - 2) }× 10^{w }= 1 5/4 2/3 4/3 1 3/460. Simplify : 3a-² 3a² 3a³ 3a61 out of 60Time is Up!