Please, fill out the information below to continue. Note: This is a sample test, and you can only take it for a limited period, after which you will be required to subscribe to a plan NAME EMAIL PHONE NUMBER 1. Find the equations of the straight lines joining (0, 3), (2, 0) x-y+6=0 2x+6=0 3x+2y-6 = 0 y-4+2 None 2. If cos θ = 4/5, then for 0° < θ < 90°, tanθ is equal to 4/3 5/3 3/4 5/4 None 3. If ax² + 6x + k is a perfect square, then k equals 9 9/a 3 9a 3/a None 4. A grocer sells an article for $54 at a profit of 8%. What is her percentage profit or loss if she sells the same article for $44? 18.5% profit 12% loss 18.5% loss 12% profit 25% loss None 5. Four books whose authors' surnames start with the letters A, J, P, and W are placed randomly on a shelf. The probability that the books will be arranged in the alphabetical order of the authors' last names is 1/12 1/24 4/18 1/6 1/4 None 6. If y = (2/3)x + 1 andz = (2/3) y + 1, then the value of z when x = 66 is 61 31 21 31/2 None 7. The following marks were obtained by candidates in an examination Calculate the third quartile 82.4 73 65.3 53.8 None 8. Factorise xyz + yzp xz(y + p) xp(y + z) yz(x + p) yp(z + p) xy(z + p) None 9. When the monthly budget for a household is displayed on a pie chart, the sectorial angles for the various items of expenditure are as follows: Food (162°), Education (90°), Transportation (36°), Clothing (x°), and miscellaneous (18°). If £900 is the amount budgeted for clothing, then the education budget is £900 £2,000 £1,800 £1,250 £1,500 None 10. Each of the exterior angles of a regular polygon is 24°. How many sides has the polygon ? 12 8 15 10 None 11. If m > n, then which of the following is NOT correct for all values of m and n? -m < -n 0 < m - n² m² > n² -m² < n² m² < n None 12. In the diagram below , WXYZ is a cyclic quadrilateral in which WZ = 6cm, ZY = 8.5cm and the diagonal WY = 10 cm. If XW = XY, calculate <XYW 43° 18° 53° 78° None 13. A square tile measures 20 cm by 20 cm. How many of such tiles will cover a floor measuring 5m by 4m 500 250 400 320 None 14. The value of x which satisfies the equation is 2 -1/2 -2 1/2 None 15. In the figure (not drawn to scale) given below, if AD = CD = BC and ∠BCE =96^{0} , how much is the value of ∠DBC? 84° 28° 32° 64° None 16. Evaluate: (xy² - yz²) (x²z - xyz) when x = 2, y = -2 and z = -½ -28 -34 0 -30 None 17. The probability of an event X is 2/3 and that of another event Y is 1/4. If the probability of either X or Y is 1/3 11/12 1 3/4 None 18. Factorise 27ab + 36b² ab(27 + 36b) 9b(3a - 4b) 6b²(3a - 4b) 3a(9b + 6b²) 9b(3a + 4b) None 19. Simplify 2/5 3/5 1 2x-y None 20. A square pyramid and a cuboid have the same height and the areas of their bases are equal. Find the ratio of their volumes 1/4 1/6 1/3 1/8 1/2 None 21. Find the gradients and the intercepts on the y- axis for 5x = 6y m = 1, c = -1/2 m = -1, c= -1 m = 1/6, c= -1 m = 5/6, c= 0 None 22. A sum of £50,000 was invested by two partners in a project which yielded £90,000. If the profit was shared in the ratio 3 : 5, the difference between the amounts received by the partners is £25,000 £10,000 £15,000 £40,000 None 23. How long will it take for a sum of money invested at 8% simple interest to double itself? 11.5 years 12.5 years 10.5 years not enough information 10 years None 24. The expressionis equal to 4/9 2/3 9/4 3/2 None 25. If y is a positive number, for what values of y is 4 + 3y < 10 ? 0 < y < 2 1 < y < 2 y < 2 0 > y > 2 None 26. If z ∝ 1/y² and z = 4 when y = 3, find the value of z when y = 2 9 18 1 3 None 27. The equation of the line is y = x+2 y = -2/3x + 2 y = 1/2x -2 -y = x+2 None 28. Two brothers Kameel and Kafeel owned a business in which the ratio of shares, was 3 : 2 respectively. Kafeel later sold 1/2 of his share to Kameel for £12,000. What was the value of the business? £24,000 £84,000 £60,000 £48,000 £42,000 None 29. PQRS is a cyclic quadrilateral and the diagonals PR and QS intersect at T. If <SPR = 47° and <PTQ = 98°,calculate <PRQ 94 degrees 51 degrees 47 degrees 145 degrees None 30. Factorise a^{2}c – 2ac^{2} ac(1 - 2c) ac(a -c) ac(c - 2a) ac(a - 2c) a(c – 2c²) None 31. If X = ( -1, 2 ) and Y = ( 0, 1 ), which of the following points lies on the line XY produced? ( 2, -2 ) ( -3, 4 ) ( 3, 4 ) ( 3, -2 ) ( 1, 3 ) None 32. If the bearing of New York from Kansas city is 125°, the bearing of Kansas city from New York is? 215° 235° 55° 305° None 33. Find the size of angle x in the figure below 36° 24° 84° 56° None 34. Solve the equation:5x² = 3x x = 0 or 3 x = 3 or 5 x = 0 or 5 x = 0 or 3/5 None 35. In the figure, the point on segment JK that is four times as far from K as it is from J is: (-1, 3) (-1/3, 7/3) (2,0) (0, 2) None 36. In the diagram, PQR and RST are two semicircles with diameters 7 cm and 3.5 cm respectively and PT = 3.5 cm respectively and PT = 3.5 cm.What is the area of the region PQRST enclosed by the figure, to the nearest whole number 24 cm² 48 cm² 193 cm² 96 cm² None 37. Points X and Y are respectively 48m North and 20m East of point Z, The bearing of X and Y is approximately 157° 337° 247° 067° None 38. If P = {positive integers less than 20, and divisible by 3} and Q = {odd numbers from 1 to 20 inclusive}, then PnQ is ∅ {3,9,15} P {1,3,9,15} None 39. For the following set of numbers: 8, 3, 7, 5, 4, 2, 6, 5, 1, 3the range and the median are, respectively, 7, 3 10, 5 7, 5 8, 4.5 7, 4.5 None 40. Find the slope from the points 2 -2/3 9 -3 None 41. Factorize 9y^{2}– 1 (9y - 1)² (3y + 1)² (3y - 1)² (3y - 1)(3y + 1) (6y - 1)² None 42. The speed of 144 km/hr, expressed in metres per second is 28 40 36 72 20 None 43. The size of each interior angle of a regular polygon with n sides is 160°. The value of n is 18 16 12 14 None 44. Evaluate 4512 ÷ 0.05 correct to three significant figures 902000 90240 90200 902 9020 None 45. Factorise:10uv + 5u – 2v – 1 (5u + 1)(2v - 1) (5u - 1)(2v - 1) (10uv + 5)(2v - 1) (5u + 1)(2v + 1) (5u - 1)(2v + 1) None 46. The quantity x varies inversely as y, and y varies directly as the square of z. If z is halved, then the value of x is halved quadrupled tripled reduced by a factor of 4 doubled None 47. Consider the triangle ABC shown in the following figure where BC = 12 cm, DB = 9 cm, CD = 6 cm and <span id="MathJax-Element-124-Frame" class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: 400;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px;color: #4c4c4c;font-family: 'Open Sans', sans-serif;background-color: #ffffff" role="presentation" data-mathml="∠BCD=∠BAC">∠BCD=∠BAC∠BCD=∠BAC What is the ratio of the perimeter of <span id="MathJax-Element-125-Frame" class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: normal;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px" role="presentation" data-mathml="ΔADC">ΔADCΔADC to that of the <span id="MathJax-Element-126-Frame" class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: normal;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px" role="presentation" data-mathml="ΔBDC">ΔBDCΔBDC? 6/9 5/9 7/9 8/9 None 48. Find the gradients and the intercepts on the y- axis for y+3= 0 m = -3, c= 0 m = 3, c = 0 m = 0, c = 3 m= 0, c= -3 None 49. The sides /AB/ and /AC/ of a triangle ABC are produced to D and E respectively such that <DBC = 125° and <BCE = 95°. Find the value of <BAC 85 degrees 40 degrees 55 degrees 90 degrees None 50. A number is selected randomly from the set of integers 1 to 20 inclusive. The probability that the number is prime is 7/20 2/5 9/20 1/2 None 1 out of 50 Time's upTime is Up!