24/09/2019 Free Test British Junior Checkpoint 0Comments by Gate Academy 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. Factorize: 5x²+2ax-3a²(x+a)(5x-3a)(5x-a)(x+3a)(5x+a)(x-3a)(x-a)(5x+3a)2. Simplify: (3^{2y + 1 }× 9^{y }× 4^{2y}) ÷ (18^{y }× 2^{y} × 6^{2y})2y3y2133. Two men and six boys can cut a field in 3 hours. If the men work at 3/2 times that of the boys, how many men are required to cut the field in 2 hours?9118464. Of the 30 students in a class, 8 surnames begin with A or O and 18 begin with a consonant.No surname begins with any of the letters C,Q,U, V,X,Y and Z.The probability that a surname selected randomly begins with E or I is3/513/152/154/155. Anne spent a quarter of her food budget on provisions, half the balance on staples and one-third of the remainder on beef. If she was left with $350, how much was her food budget?$800$1,050$2,100$700$1,4006. What is the probability that the sum of any two numbers drawn from the set { 1, 2, 3, 4 } is odd?1/22/35/61/317. Choose the word that best completes the sentence:I`m sure he`s got the job. He`s walking around with a/an __________ air.broadexcitingbloodytriumphantconstant8. What is the value of 5410_{6 }- 2535_{6 }4135 base 72431 base 63241 base 63141 base 79. A pump P can fill a water tank in 5hrs. With a second pump Q also operating, the tank can be filled in 2hrs. Pump Q operating alone can fill the tank in7/2hrs10/3hrs2hrs4hrs3hrs10. The probability that a baby born by a certain couple will grow up to be tall is 1/4. The probability that the couple will have a tall daughter is1/21/41/83/811. Find the values p and q in the arithmetic progression -12, p, q, 18, ...1, 11-1, 8-2, 80, 912. Choose the word that best completes the sentence:We need to make sure that there is enough _________ accommodation to house all the delegates.carelessyellowluxurywholehearteddreadful13. The length of a rectangle exceeds its width by 2cm. If the area of the rectangle is 80cm², the length of the rectangle is8 cm16 cm5 cm10 cm14. A string of length 66 cm is shaped into an arc of a circle of radius 28 cm. The angle of the sector is45 degrees90 degrees135 degrees120 degrees15. An open, rectangular wooden box of internal depth 40 cm has a base of internal dimensions 50 cm by 30 cm. If the box is made of wood of thickness 1 cm, the total volume of wood in the box is9,888 cm38,224 cm312,000 cm38,552 cm316. If 19x = 240² - 235², the value of x is125952520517. Two chords AC and BD of a circle intersect inside the circle at E. If <BAC = 35°, <CAD = 42° and <ABD = 70°, find <ACB.70 degrees77 degrees33 degrees42 degrees18. The difference in longitude betweenP(55°N, 12°W) and Q(15°S, 65°W) is53°77°70°40°19. A sum of $50,000 was invested by two partners in a project which yielded $90,000. If the profit was shared in the 3 : 5, what is the difference between the amounts received by the partners?$15,000$40,000$10,000$30,000$25,00020. A die is rolled 100 times with the following outcomes:Number 1 2 3 4 5 6Frequency 15 20 18 14 17 16The experimental probability of obtaining a 2 is0.800.100.200.4021. cos 65° is equal tocos 295°cos 245°cos 115°sin 115°22. The probability that a number selected at random from 1 to 40 is a multiple of 7 is1/103/201/87/2023. If X = ( -1, 2 ) and Y = ( 0, 1 ), which of the following points lies on the line XY produced?( -3, 4 )( 3, 4 )( 3, -2 )( 2, -2 )( 1, 3 )24. Which of the following lines is perpendicular to the line 5x + 2y = 6?5x - 2y = 62y - 5x = 65y -2x = 65y + 2x = -625. The size of each interior angle of a regular polygon with n sides is 160°. The value of n is1416121826. A ______ of books. (Fill in the blanks)coursepackgroupliberty27. Choose the word that best completes the sentence:Everyone ____ expected to come with their passports.wasisarewere28. A bowl contains two white, one blue and two red balls. A ball is drawn randomly from the bowl, replaced and another ball is drawn. What is the probability that exactly one of the balls is white?36/2256/252/5216/22512/2529. The probability of obtaining a number less than 5 in a single toss of a fair die is2/31/31/61/230. Choose the word that best completes the sentence:The poor ______ suffering.areiswaswere31. The standard deviation of the set of numbers -3, -2, -1, 0, 1, 2, 3, is2042√24√232. If two triangles are similar, thenI. the corresponding angles are similarII. the areas of the triangles are in the same ratio as the lengths of the corresponding sides.III. the triangles are congruent.IV. the corresponding sides are proportional.Which of the above statements are CORRECT?III and IV onlyI, III and IV onlyI, II and III onlyI and II onlyall of the above33. Choose the word that best completes the sentence:Collecting match-boxes ______ one of his favorite pastimes.werearewasis34. The line 3y - x = 7 makes an angle of θ with the positive x-axis. Find the value of sin θ.3/71/3√10/103√10/103√1035. A worker employed in 1992 on a salary of $50,000 a year had his salary increased annually in arithmetic progression. If his salary in 1997 was $80,000, what was his salary in 1995?$56,000$70,000$62,000$68,000$65,00036. The expression (x² - 6x + 9)/x(x² - 9) is undefined forx = 0 or 9x = 0 or 3x = 3x = 0 or -3x = 0, 3 or -337. In a certain class, 37 students take at least one of Chemistry, Economics and History. 8 students take Chemistry, 19 take Economics and 25 take History. 12 students take Economics and History but nobody takes Chemistry and Economics . How many students take both Chemistry and History?354638. When the price of eggs was raised by £2 an egg, the number of eggs which can be bought by Tara for £120 is reduced by 5. What is the present price that Tara would buy an egg?£8£7£6£1039. Two men and six boys can cut a field in 3 hours. If the men work at 3/2 times that of the boys, how many men are required to cut the field in 2hrs?864940. 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 y343230363841. A sum of money invested at 6% per annum simple interest increased to $14,750 after 3 years. Determine the amount invested.$13,500$12,000$12,800$13,000$12,50042. In a Year 12 class of 45 students, every student has to offer either Chemistry or Economics or both. If 25 students offer Chemistry while 34 offer Economics,how many students offer both subjects?1511201443. The diameter of a rod is measured as 3.70cm to three significant figures. Find the maximum error in the measurement.5cm0.045cm0.05cm0.5cm0.005cm44. A ball has diameter 20cm. What is the volume of the ball, correct to two significant figures?5,000 cm³6,000 cm³4,000 cm³3,500 cm³4,200 cm³45. X, Y, and Z are subsets of U = {1, 2, 3, 4, 5}. If X∪Z = U, X∩Z = Ø, X∪Y = {2, 3} and Y∩Z = Ø, then Z isU{1}Ø{1, 5}{1, 4, 5}46 out of 45Time is Up!