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. Solve the equation: 6z² - 7z - 5 = 0 z = -5/3 or 1/2 z = 1/3 or 5/2 z = 1/2 or -5/2 z = 5/3 or -1/2 2. Given that A varies inversely as B, and B varies directly as the square of C, and A = 1 when C = 3, find the value of A when C = 1/3 81 1/9 1/27 27 3. A cylindrical metal rod of radius 10cm and length 35cm is to be melted down and recast into circular cones of base radius 7cm and height 15cm. If π = 22/7, the maximum number of cones which can be cast from the original material is 5 12 18 7 14 4. Five years ago, a father was four times as old as his son. In five years time the father will be twice as old as the son. If x and y are the present ages of the father and the son respectively, the equations relating x and y are: x - 4y = 15; y - 2x = 5 4y - x = 0; x- 2y = 0 4y - x = 25; x - 2y = 5 4y - x = 15; x - 2y = 5 5. The cost(y) of feeding n people for a week is given as y = 250 + 80n, where y is expressed in dollar ($). What is the cost of feeding two persons? $160 $660 $410 $80 6. Based on the figure below, what is the value of x, if y = 10? 11 12 13 10 7. The two perpendicular sides of a right-angled triangle are 9 cm and 12 cm in length. The smallest angle of the triangle is 53.1 degrees 36.9 degrees 30 degrees 36 degrees 8. The length of a rectangle exceeds its width by 2cm. If the area of the rectangle is 80cm², the length of the rectangle is 8 cm 5 cm 16 cm 10 cm 9. Factorise the expression 25x2 – 1 (25x + 1)(x - 1) (5x - 1)(5x - 1) (5x + 1)(5x + 1) (25x - 1)(x + 1) (5x +1)(5x - 1) 10. The area of the trapezium PQRS in the figure is 36√3 cm² 18√3 cm² 72 cm² 36 cm² 11. Which point is the reflection of the point (–7, 5) over the line y = –x? (5, -7) (7, 5) (-5, 7) (7, -5) 12. Factorise 27 – 3p2 completely 3(3 + p)(3 - p) 3(p + 3)(p - 3) (3 + p)(3 - p) 3(p- 3)² (p + 3)(p- 3) 13. The angle of a sector of a circle of radius 4.2 cm is 150°.If π = 22/7, the perimeter of the sector is 15.2 cm 16.8 cm 11 cm 19.4 cm 14. If the lengths of the sides of a right-angled triangle are given as (x-1), x and (x+1), then the hypotenuse is 3 13 7 4 5 15. Each of the exterior angles of a regular polygon is 24°. How many sides has the polygon ? 8 12 15 10 16. Evaluate: 81-1/4 × 361/2 ×100 3 10 2 1 0 17. Solve the simultaneous equations2/x + 1/y = 33/x - 2/y = 8 x = -1, y = 2 x = 1/2, y = 1 x = 1, y = -2 x = 1, y = 2 x = 1/2, y = -1 18. A regular polygon with (2m + 1) sides has each interior angle equal to 144°. The value of m is 10 8 9/2 5 19. Two triangles have the same area if the three angles of one are equal to the three angles of the other they are similar the three sides of one are equal to the three sides of the other they lie between the same parallels 20. If m and n are the lengths of the diagonals of a rhombus of side x, andm² + n² = kx², the value of k is 2 3 4 1 21. 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 < 2 22. If P = {positive integers less than 20, and divisible by 3} and Q = {odd numbers from 1 to 20 inclusive}, then PnQ is {1,3,9,15} P {3,9,15} ∅ 23. The diameter of a rod is measured as 3.70cm to three significant figures. Find the maximum error in the measurement. 5cm 0.5cm 0.005cm 0.05cm 0.045cm 24. 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) 25. In a game involving two dice, Kamsi will win if she throws at least one six, or the sum of the numbers is 10. The probability of Kamsi winning at the next throw is 7/18 4/9 1 1/4 1/3 26. The bearing of a point P from an observer Q is S37°W. The bearing of Q from P is S 37° E N 53° W N 37° E S 53° W 27. The volume of a cone of radius 6 cm and vertical height 7 cm is take (π= 22/7) 21 cm3 264 cm3 26.4 cm3 42 cm3 28. P is directly proportional to M and inversely proportional to N. If P = 9 when M = 24 and N = 8, find the value of P when M = 5 and N = 6 5/4 5/2 11 18/5 29. Arrange the following numbers in ascending order of magnitude 5/6, 11/13, 0.837 5/6, 0.837, 11/13 0.837, 11/13, 5/6 11/13, 5/6, 0.837 0.837, 5/6, 11/13 5/6, 11/13, 0.837 30. Find the area of the shaded region. 270 sq. cm 208 sq. cm 175 sq. cm 73 sq. cm 31. If f ( x+ 2 ) = x² + 3x + 1, then f ( -2 ) is 0 5 1 -1 11 32. Factorise xyz + yzp xp(y + z) xz(y + p) yp(z + p) yz(x + p) xy(z + p) 33. If y = (2/3)x + 1 andz = (2/3) y + 1, then the value of z when x = 66 is 31/2 61 21 31 34. In the adjoining figure, chord ED is parallel to the diameter AC of the circle. If <span id="MathJax-Element-111-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="∠">∠∠ CBE = 650, then what is the value of <span id="MathJax-Element-112-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="∠">∠∠DEC? 55° 25° 45° 35° 35. A bucket in the form of a truncated cone of end radii 14cm and 21cm, and height of 30cm. What is the capacity of the bucket? 15,300 cm³ 41,580 cm³ 53,900 cm³ 29,260 cm³ 12,320 cm³ 36. A parallelogram of area 425 cm² has a height of 17cm. The length of the base is 20 cm 50 cm 12.5 cm 25 cm 37. Correct each of the numbers 38.7152 and 0.05381 to two significant figures and find their product , correct to two significant figures. 2.6 2.0 0.21 2.1 1.9 38. A girl walks 30 m from a point P on a bearing of 040º to a point Q. She then walks 30 m on a bearing of 140º to a point R. How far is R from P 30 km 42.4 km 38.6 km 25.2 km 39. Find the gradients and the intercepts on the y- axis for y+3= 0 m= 0, c= -3 m = 3, c = 0 m = 0, c = 3 m = -3, c= 0 40. 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 quadrupled doubled tripled reduced by a factor of 4 halved 41. What is the lowest common multiple of the prime numbers between 1 and 10? 35 105 90 70 210 42. Factorise 16b2– 1 (4b – 1)(4b + 1) (16b + 1)(b – 1) (2b – 1)(8b – 1) (2b – 1)(8b + 1) (4b – 1)(4b – 1) 43. The following marks were obtained by candidates in an examination Calculate the median 54.6 45.7 12.9 10.8 44. What is the shape of the plane face of a cylinder? Solid Circle Square Rectangle Triangle 45. Simplify 1 3/5 2/5 2x-y 46. Find the gradients and the intercepts on the y- axis for 5x = 6y m = 1, c = -1/2 m = 1/6, c= -1 m = -1, c= -1 m = 5/6, c= 0 47. Which of the following specified sets of data is not necessarily sufficient for the construction of a triangle? Three sides Two sides and a right angle Three angle Two sides and an included angle 48. The marks scored by students in a test are recorded in the table belowCalculate the mean 2.32 4.78 5.67 4.34 49. The sum of the prime numbers between 40 and 50, divided by the sum of the prime numbers between 1 and 6 is 9.0 13.1 8.4 18.0 50. Two years ago, a woman was six times as old as her son. Four years from now, she will be three times as old as the son. Find their present ages 28, 7 32, 8 40, 10 30, 7 26, 6 1 out of 50 Time is Up! Time's up