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. In the figure, PQ and RS are two concentric arcs, center O. If the ratio of the lengths of the arcs is 1:4, the ratio of the areas of sector OPQ to ORS is1:163:161:81:42. Solve the simultaneous equations2/x + 1/y = 33/x - 2/y = 8x = 1/2, y = 1x = -1, y = 2x = 1, y = -2x = 1/2, y = -1x = 1, y = 23. An isosceles triangle of sides 65 mm, 65 mm and 50 mm is inscribed in a circle. The radius of the circle is60 mm40 mm35.21 mm35 mm4. The profit on a business was shared between two sisters Tara and Tise in the ratio 3 : 4. If Tise received $8,000 more than Tara, find the profit shared.$56,000$65,000$32,000$24,000$42,0005. Which of the following statements about a cylinder is false?A cylinder has one curved faceA cylinder has two curved edgesThe net of a cylinder has one rectangle and two circlesA cylinder has two verticesA cylinder has two plane faces6. What is the smallest number by which 180 can be multiplied to make a perfect square?326457. Factorise the expression 25x2 – 1(5x +1)(5x - 1)(25x - 1)(x + 1)(25x + 1)(x - 1)(5x + 1)(5x + 1)(5x - 1)(5x - 1)8. The angle of a sector of a circle of radius 4.2 cm is 150°.If π = 22/7, the perimeter of the sector is15.2 cm11 cm16.8 cm19.4 cm9. Solve the equation: 6z² - 7z - 5 = 0z = 5/3 or -1/2z = 1/2 or -5/2z = -5/3 or 1/2z = 1/3 or 5/210. 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 is1/61/124/181/41/2411. Evaluate: (2-3 × 163/4 × 20)21-1/201/212. In the diagram, O is the center with radius 7 cm and <QPR = 30°. Find the length of arc QR (Take π = 22/7) 22/3 cm21/2 cm11/3 cm12 cm13. From an observation point close to the edge of the sea, a ship is 14 km away on a bearing of 130°.A second ship is 48 km away on a bearing of 220º. The distance separating the ships is34 km50 km62 km55 km14. The table below shows the heights to the nearest cm of a group of peopleCalculate an estimate of the mean151.5 cm25.5 cm59.5 cm10.3 cm15. The interior angles of a polygon add up tp 1980°. How many sides has the polygon?1512131016. 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 is4/52/51/53/517. If X = ( -1, 2 ) and Y = ( 0, 1 ), which of the following points lies on the line XY produced?( 2, -2 )( 1, 3 )( 3, -2 )( -3, 4 )( 3, 4 )18. Solve the equation: 3y-2 = 4/279/22/9814/8181/419. 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 <BAC40 degrees55 degrees90 degrees85 degrees20. A number is selected randomly from the set of integers 1 to 20 inclusive. The probability that the number is prime is2/51/27/209/2021. The difference between 0.003286 correct to three significant figures and 0.003286 correct to four decimal places is0.00010.0000040.000010.00030.0000922. In the diagram given below, ∠ABD = ∠CDB = ∠PQD = 90° . If AB:CD = 3:1, the ratio of CD: PQ is 1: 0.720.5 : 11:0.691 :0.7523. Factorise 27ab + 36b²3a(9b + 6b²)6b²(3a - 4b)9b(3a + 4b)ab(27 + 36b)9b(3a - 4b)24. The speed of 144 km/hr, expressed in metres per second is403620722825. Correct each of the numbers 38.7152 and 0.05381 to two significant figures and find their product , correct to two significant figures.1.92.62.00.212.126. The chord BA is extended to a point T such that CT becomes a tangent to the circle at point If ∠ATC = 30° and ∠ACT = 50°, then the angle ∠BOA is 100°2°150°80°27. The figure shows a rectangle of dimensions 3x by 2x. The shaded portion of uniform width 2 cm, has an area of 64 cm². Find the value of x6 cm8 cm7 cm4 cm28. The ratio of the radii of two cylinders whose heights are equal is 2 : 3. If the volume of the smaller cylinder is 32cm2, find the volume of the bigger one.72cm³108cm³27cm³81cm³216cm³29. Simplify2x-y13/52/530. The number 0.0047049, correct to three significant figures is0.0047050.00470.0050.004700.0047131. If the lengths of the sides of a right-angled triangle are given as (x-1), x and (x+1), then the hypotenuse is13457332. Two sectors of the same circle subtend angles of 75° and 30° at the centre of the circle. Their areas are in the ratio√5:√25:22:53:125:433. Find the equations of the straight lines joining (0, 3), (2, 0)x-y+6=03x+2y-6 = 02x+6=0y-4+234. Given that a² + b² + c² = 50 and a = 5, √b = 2, find c35.74.2235. Solve the equation 3x + 10 = x²5 or 2-5 or -25 or -2-5 or 236. Solve the equation:3x-² = 4/272/99/24/8181/437. If cos θ = 4/5, then for 0° < θ < 90°, tanθ is equal to5/43/44/35/338. Four of the interior angles of a pentagon are specified as (80 - y)°, (80 + y)°, (120 - 2y)° and (120 + 2y)°. The size of the fifth interior angle must be130 degrees120 degrees144 degrees140 degrees39. Reduce each number in the following expressions to two significant figures and then evaluate: ( 0.04371 × 2.44913 ) ÷ 0.047522.214.171.124.42.240. Four of the interior angles of a pentagon are equal and each is twice the fifth angle. What is the value of each of the four equal angles?90°135°60°120°75°41. Evaluate 4512 ÷ 0.05 correct to three significant figures9020009024090290209020042. ABC is a right triangle. AM is perpendicular to BC. The size of angle ABC is equal to 55 degrees. Find the size of angle MAC.55°75°65°106°43. If 3y + 4 - ( y/3) = y + 9What is Y ?654344. Each of the exterior angles of a regular polygon is 24°. How many sides has the polygon ?815121045. Factorise 16b2– 1(2b – 1)(8b + 1)(4b – 1)(4b + 1)(4b – 1)(4b – 1)(2b – 1)(8b – 1)(16b + 1)(b – 1)46. Find the gradients and the intercepts on the y- axis for y+3= 0m= 0, c= -3m = 0, c = 3m = 3, c = 0m = -3, c= 047. An arithmetic sequence has five terms between 2 and 20. Determine the fourth term of the sequence.14111281848. Factorize 9y2– 1(9y - 1)²(6y - 1)²(3y - 1)(3y + 1)(3y + 1)²(3y - 1)²49. If a : b = 3 : 4 and m : n = 2 : 5Find a/m : b/n3 : 1015 : 85 : 98 : 1510 : 350. 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 is3/411/311/1251 out of 50Time is Up!