The Manchester Grammar School Entrance Examination 2011 Arithmetic Paper 2 Online Quiz view all papers Welcome to your THE MANCHESTER GRAMMAR SCHOOL 11 PLUS ARITHMETIC PAPER 2011 - 21 HourDo not open this booklet until told to do soCalculators may not be usedWrite your names, school and candidate number in the spaces provided at the top of the page.Show all your working in full, as this will be marked, and then writeAnswer all the questions, attempting them in order. If you find thatcannot answer a question straight away leave it blank and retur1. To bake 2 cakes, Jo usesWrite down the amounts she needs for 5 cakes 750g flour,20 eggs, 17.5tablespoons of milk, 95g coconut, 3.5ml vanila assence 450g flour,15 eggs, 12.5tablespoons of milk, 65g coconut, 4.5ml vanila assence 650g flour,19 eggs, 16.5tablespoons of milk, 75g coconut, 5.5ml vanila assence 850g flour,12 eggs, 15.5tablespoons of milk, 85g coconut, 3 ml vanila assence 550g flour,14 eggs, 14.5tablespoons of milk, 45g coconut, 5ml vanila assence None 2. Write numbers in the boxes to make this division correct 8 & 2 8 & 4 6 & 4 2 & 8 None of the Above None 2.(b) Write numbers in the boxes to make this subtraction correct 7, 3, 7 5, 2, 7 8, 4, 8 5, 3, 5 6, 3, 7 None 3. A clock shows 2 o’clock, with the minute hand on 12 and the hour hand on 2.(a) How many times does the minute hand go past thehour hand between 2.00pm and 7.00pm? 5times 7times 3times 8times 4times None 3.(b) What time will the clock show when the hour hand hasturned through an angle of 60°? 4:00pm 2:00pm 3:00pm 5:00pm None of the Above None 3.(c) What time will the clock show when the minute handhas turned through an angle of 900°? 4:30pm 2:30pm 3:30pm 5:30pm 6:30pm None 3.(d) Through what angle will the minute hand have turnedfrom 2 o’clock, when the clock shows 10 o’clock? 2880 3000 2780 2500 None of the Above None 3.(e) Through what angle will the hour hand have turnedfrom 2 o’clock, when the clock shows 6:30? \[135^{o}\] \[125^{o}\] \[115^{o}\] \[145^{o}\] \[105^{o}\] None 4. The formula to work out the sum of the angles inside any shape isSum of angles = 180° × number of sides – 360°For example,a + b + c + d + e = 180° × 5 – 360°= 900° – 360°= 540°(a) Find a \[110^{o}\] \[120^{o}\] \[100^{o}\] \[90^{o}\] None of the Above None 4.(b) Find b \[130^{o}\] \[120^{o}\] \[110^{o}\] \[140^{o}\] \[100^{o}\] None 4.(c) Find c \[45^{o}\] \[55^{o}\] \[35^{o}\] \[65^{o}\] None of the Above None 5. In this pyramid of bricks, after the bottom row, the number on each brick is the product of the two bricks underneath it.For example, if we start withwe end up with(a) Fill in the remaining numbers on the bricks 6, 12 & 72 8,12, & 96 7, 6 & 42 6, 6 & 30 12, 9 & 108 None 5.(b) Fill in the numbers on the bottom row 2, 7, 3, 9 3, 6, 5, 8 3, 6, 2, 7 2, 5, 4, 6 3, 8, 2, 7 None 5.(c) a and b are whole numbers, neither of which is 1.Find the values of a and b. 15, 33 & 5, 3 15, 11 & 6, 5 11, 45 & 5, 4 12, 35 & 5, 6 None of the Above None 6. (a) Write down a number which has exactly three factors,including 1 and itself. 4, 9, 25 8, 4, 6 4, 10, 9 3, 6, 8 None of the Above None (b) Write down the smallest multiple of 17 which isgreater than 200. 204 221 238 255 None of the Above None (c) Write down a prime number between 90 and 100. 97 93 95 91 Both a & d None (d) Write down a fraction which is between ¹/3 and ½ \[\frac{5}{12}\] \[\frac{3}{4}\] \[\frac{1}{4}\] \[\frac{7}{12}\] \[\frac{3}{12}\] None (e) Write down a number whose square is between400 and 450. 21 20 22 19 None of the Above None 7.The graph shows the number of pets owned by the children in aprimary school class.(a) How many girls own 2 pets? 4 3 2 1 None of the Above None (b) How many more girls than boys are there in the class? 1 16 2 15 3 None (c) What fraction of the children in the class have no pets? \[\frac{9}{31}\] \[\frac{5}{16}\] \[\frac{4}{15}\] \[\frac{1}{1}\] None of the Above None (d) How many pets in total are owned by the boys? 19 15 16 20 18 None 8. When a gas meter was read in October 2010, the meter reading showed 3165 units.When it was read again, in January 2011, the meter reading was 3945.(a) Work out how many units of gas were used in the3 months from October to January. 780units 700units 820units 720units 800units None (b) The cost of the gas is 7p for each unit. Also there isa fixed charge of £12.50 to be paid. Work out the totalcost of the gas and the fixed charge. £67.10 £54.60 £42.10 £65.20 £62.50 None (c) Finally, 10% of this total is then added on for tax purposes.Work out the final cost. £73.81 £60.06 £46.31 £71.72 £68.85 None 9. Using the fact that 52 × 316 = 16 432, find the answers to(a) 5.2 × 316 1643.2 1542.2 1642.2 1543.2 1613.2 None (b) 16 432 ÷ 52 316 136 336 326 216 None (c) 5 200 × 0.316 1643.2 1542.2 1642.2 1543.2 1613.2 None (d) 16 432 ÷ 3160 5.2 4.2 2.5 6.2 5.6 None (e) 26 × 158 4108 3768 2768 4168 3968 None 10. The table shows part of the railway timetable for trains from Andforth to Ermston.Some trains stop at stations between, and others are express trains.All stopping trains take the same time between stations as each other.(a) How many minutes does it take to travel from Andforthto Cheeble? 35minutes 45minutes 25minutes 55minutes 38minutes None (b) Complete the times in the table for the stopping trainwhich leaves Andforth at 15:34. (c) David lives in Bowlton and he wants to travel to Delf.He misses the 14:06 train by 10 minutes. How long willhe have to wait for the next train? 48minutes 40minutes 38minutes 28minutes 50minutes None (d) The stopping trains travel at an average speed of36 miles per hour for the whole journey. Work out thedistance from Andforth to Ermston? 33miles 23miles 43miles 13miles None of the Above None (e) Work out the average speed of the express trains in milesper hour. 45mph 35mph 25mph 55mph None of the Above None 11. In Madd arithmetic there are only four digits, 1, 2, 3, and 4.Here are the addition and multiplication tables for Madd arithmetic:So, for example, 2 + 3 = 1 and 3 × 4 = 2.Use the tables to find the answers to:(a) 3 + 3 2 3 4 1 6 None (b) 4 × 2 3 1 2 4 6 None (c) (3 × 4) × 2 4 2 3 6 1 None (d) (4 × 3) + (3 × 1) 1 2 3 4 5 None (e) m + m = 2. What two possible numbers could m stand for? 1, 3 2, 4 1, 4 3, 4 None of the Above None (f) u + v = u × v where u and v are different numbers.What numbers do u and v stand for? 2, 3 1, 3 1, 4 2, 4 3.2 None (g) t + y = y where y can stand for any number.What number does t stand for? 4 2 3 1 None of the Above None (h) (w × w) + w = w. What are the two possible numbersthat w could stand for? 2, 3 1, 3 1, 4 2, 4 3, 4 None 12. This is a question which needs you to be organised, and to work in a logical manner. Set your answers out clearly.Write down(a) all the 3-digit numbers which can be made by using eachof the digits 1, 2, and 3 once only. 123 213, 231 312, 321 132 All of the Above None (b) all the 4-digit numbers which can be made by using eachof the digits 1, 1, 2, and 2 once only. 1122, 2121 1212, 2121 1221 2211 All of the Above None (c) all the 5-digit numbers which can be made by using eachof the digits 1, 1, 1, 2 and 3 once only. 11123, 11132, 21311 11213, 11312, 21131 11231, 11321, 21113 12113, 13112, 31211 All of the Above None Time's up
