Please, fill out the information below to continue. NAME E,MAIL PHONE NUMBER 1. Find the value of cos (-45)°0.8712-0.70710.43350.70712. Solve for x log_{x} 0.0001 = 41/51/2-11/103. Using the product rule differentiate wrt x(3x + 4)(x - 3)6x²6x-5x²+129x-124. Solve the equation: 4^{(w - 1)} × 5^{(2w - 2) }× 10^{w }= 12/315/44/33/45. Find the fourth term in the expansion of (1+x)^{15}1313x³ 1455x³ 6. A wooden block of weight 16N is placed on a rough surface. If the co-efficient of friction between both surfaces is 0.25, the least horizontal force required to move the block is6.4N4.0N64.0N0.4N7. Solve for y if 5 log (y+3) = log 321-1028. The gradient of a curve which passes through the point ( 1, 2) is given by x². Determine the equation of the curve.y = 3x³ + 3/5y = 1/3 x³ + 5/3y = x³ + 2xy = 1/3 x³ - 5/39. Given thatFind the values of x for which |A| is zero.-4, 44, -2(twice)2, 3(twice)-2, 310. 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)(5/3, 1/3)(3/8, 3/11)11. If y + 1/y = 4, find y² + 1/y²161214912. The gradient of a curve at any point (x, y) is given by dy/dx = 2(x - 3) and the point(3, -12) lies on the curve. Find the equation of the curve.y = x² - 6x - 3y = x - 18y = x² - 6xy = x² - 6x - 513. Which of the following is a root of the equationy² + 6y = 0 ?312014. A figure is selected randomly from a group of figures consisting of a square, a triangle, a rectangle, a trapezium and a rhombus. The probability that the figure selected is a parallelogram is2/51/53/54/515. The figure below shows four forces 3N, 10N, 3√3N and 6N acting on a particle P. The resultant of the four forces is10√3N5√3N10N5N16. During the same interval, it is observed that a train travels the same distance as does a lorry. The two vehicles therefore have the sameaverage velocityaverage speeduniform accelerationinstantaneous velocityinitial velocity17. Tara pushes a 500kg box along a floor with a force of 2000N. If the velocity of the box is uniform, the coefficient of friction between the box and the floor is. (g = 10m/s²)0.651.00.80.40.518. Given that y and x are two variables such that dy/dx = 2x - 6, and y = -1 when x = 3, express y in terms of x.y = x - 3y = x² - 6x + 8y = x² + 6y = x² + 6x + 819. The gradient of a curve is given byx² - 4x + 3If the curve passes through the point (3, 1). Find the area of the finite region enclosed by the curve, the lines x = 1, x = 3 and y = 010/35/98/76/720. Find angle a°40.3°27°72°50.1°21. The radius r of a circular disc is increasing at the rate of 0.5 cm/s. At what rate is the area of the disc increasing when its radius is 6 cm?6π cm²/s3π cm²/s36π cm²/s18π cm²/s22. Find the value of x for which 3^{2x} + 6(3^{x}) = 27-113-323. The line y =3x + 1 intersects thecurve y = x² -2x + 7 at the points(2, 7) and (3, 10)(-1, -2) and (3, 10)(-2, -5) and (1, 4)(1, 4) and (2, 7)24. Find a positive angle between 0° and 360° that is equivalent to -315°421°45°124°105°25. Write the value of the angle in surd form sin 300°√2√3/2-√2-√3/226. The speed s of a particle after t seconds is given by v = 7 + 25t -4t² . Find the acceleration of the particle after 2 seconds.28 m/s²25 m/s²41 m/s²9 m/s²27. Tireni stands on a spring scale placed in a lift. The lift descends at constant velocity. As a result, the scale reads a weightgreater than the weight of Tirenithe same as the weight of Tireniof zeroless than the weight of Tirenigreater than the weight of Tireni by 1kg28. If (x-3) and (x+5) are factors of the expression x³ + mx² - nx - 45, what is the product of m and n6745355529. Determine the order of the matrix:1x22x32x21x130. cos 65° is equal tosin 115°cos 295°cos 115°cos 245°31. Solve the equation 8 sin x = 3 for 0° ≤x≤ 360°98°17°22°100°32. The velocity of a particle is given by v =3t² + 8t. Find the acceleration when t = 8s56 m/s²23 m/s²8 m/s²18 m/s²33. Find the angles between 0° and 360° whose sine is -0.978123°235°443°258°34. Two forces of magnitude 7N & 3N act at right angles to each other. The angle θ between resultant and the 7N force is given bysinθ = 3/7cosθ = 3/7cotθ = 3/7tanθ = 3/735. The sine, cosine and tangent of 240° are, respectively-0.866, 1/2, -1.732-0.866, -1/2, 1.7320.866, -1/2, 1.7320.866, 1/2, 1.73236. Resolve into partial fractions.2/(x-1) - 3/(x+1) + 2/(x+3)2/(x-1) - 1/(x+1) + 1/(x+3)2/(x-1) + 3/(x+1) + 1/(x+3)2/(x-1) - 3/(x+1) + 1/(x+3)37. Multiply (x + 3y + 5) by (2x² + 5y + 2)x²+31y+18x+2x+92x³+6yx²+5xy+15y²+31y+10x²+2x+102x²+6y²x+4xy+12x²+31y+18x+2x+92x³+6yx²+5xy+15y38. Using the binomial theorem in the expansion of (x + 3/x)^{4}, find the term which is independent of x.5474666439. The gradient of a curve is given by dy/dx = 10x - 3x². If the curve passes through the point (-1, 10), find the equation of the curvey = 5x³ - x² + 8y = x² -4y = 5x² - x³ + 4y = 5x² - x³40. Solve for x2^{2x} - 6(2^{x}) = - 8-121041. If x + 1 is a factor of x^{3} + 3x^{2} + kx + 4, find the value of k463542. The 1st and the 11th terms of an A.P. are -5 and 20 respectively. The common difference is3545/243. A ball is thrown vertically upwards and its height s metres after t seconds is given by s = 16t - 4t². Find the time when the velocity is 8 m/s.2s4s3s1s44. A triangle has sides of lengths y cm, (y-4) cm and (y+4) cm. If the largest angle of the triangle is cos^{-1} (1/5), find the value of y24 cm20 cm28 cm90/7 cm45. Find, from the first principles, the derivative with respect to x of the function y = 2x² - x + 34x - 14x4x - 44x - 246. If y = 2xcos2x - sin2x, find dy/dx when x = π/4ππ/2-ππ/447. Given that dv/dt = -64t and v = 10 when t = 0, find v when t = 2.v = 118v = -118v = -64v = 6448. Given that log_{b}2 = 0.693 and log_{b}5 = 1.609, evaluate: log_{b}62.51.0165.5204.1342.20249. The marks scored by students in a test are recorded in the table belowCalculate the median364550. Differentiate, with the respect to x: cosx - x sinx2sinx -xcosx-2sinx - xcosxxcosx-2sinx + xcosx51. Given thattanx = 5/12, what is the value of sinx + cosx?171313/1717/1352. Find the value of x if log_{4}x = 3.5142561286453. The standard deviation of the set of numbers -3, -2, -1, 0, 1, 2, 3, is0244√22√254. 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, 1/32, 2/32/3, 1/21, 455. Which of the following pairs of graphs cannot be used to find the solution to the cubic equation x³ -3x² + 3x - 9 = 0 ?y = x³ and y = 3x² - 3x + 9y = x³ -3x² and y = 3x - 9y = x³ -3x² + 3x and y = 9y = x² - 3x + 3and y = 9/x56. Line M has a y-intercept of –4, and its slope must be an integer-multiple of 1/7. Given that Line M passes below (4, –1) and above (5, –6), how many possible slopes could Line M have?789657. Evaluate the determinant 141012-1458. Find ∫x tan²x dxIncos x+Cx(tanx- x) +In cosx + Cx(tanx -x) + Cx(tanx- x) +In cosx + x²/2 + C59. Find the value of x if1/2 log_{10}x = 1100√100.011/√1060. If cos θ > 0 and sin θ < 0, then270°< θ < 360°90° < θ < 180°180° < θ < 270°0° < θ < 90°61 out of 60Time is Up! Time's up