To change from tonnes to kilograms, multiply by This means: tonnes = 225 kg [ = 225]

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1 Q1. [1 tonne = 1000 kg] To change from tonnes to kilograms, multiply by This means: tonnes = 225 kg [ = 225] Difference between tonnes and 128 kg means the same as: Difference between 225 kg and 128 kg = 97 kg [difference means 'subtract'] [Difference between tonnes and 128 kg = 97 kg] Q2. [a = 2] [b = 3] 4a 2b =? [substitute in the values for 'a' and 'b'] [Be aware that in Maths: 4a = 4 a; 2b = 2 b] (4 a) (2 b) (4 2) (2 3) 8 6 = 2 [4a 2b = 2] Q3. The easiest way to complete this question is to find out how many times 38 can fit into To do this, round 38 up to 40 (nearest 10). Then find out how many times 40 will fit into [ = 25] This gives a rough idea that a book with 38 lines to each page will have the 1000 th line appearing after the 25 th page. So multiply 38 by 26 and then 38 by 27. Take the multiple of the number that gives an answer just above We can see that = This means the 1000 th line is on page 27. [38 25 = 950] (950 is less than 1000 lines) [38 26 = 988] (988 is less than 1000 lines) [38 (27) = 1026] (1026 is more than 1000 lines) [1000 th line in a 38 line per page book appears on = page 27] 1

2 Q Hour clock time 24-Hour clock time Q4. 10:10 a.m [10:10] Q5. 11:20 p.m [23:20] Q6. 1:01 a.m [01:01] Q7. 7:45 p.m [19:45] Q8-22. Look carefully at the shapes given below to determine the number of faces, vertices and edges. See how below. Name of Solid Number of faces Number of vertices Number of edges Triangular prism [ 5 ] [ 6 ] [ 9 ] Square prism [ 6 ] [ 8 ] [ 12 ] Triangular-based pyramid [ 4 ] [ 4 ] [ 6 ] Square-based pyramid [ 5 ] [ 5 ] [ 8 ] Cube [ 6 ] [ 8 ] [ 12 ] 2

3 Q23. Train time = 9.42 a.m. She gets to the station at 9:51 [9 mins late = (9: = 9:51)] Next train = a.m. Work out the difference between 9.51 and to find how long she will have to wait for the train. Use partitioning as shown below. 9:51 10:00 = (9 minutes) 10:00 10:27 = (27 minutes) Now total up the minutes to give you the total waiting time. [Waiting time = 36 minutes] Q These questions are asking you to change fractions into percentages. The easiest way to do this, is to turn the fraction into an equivalent fraction with a denominator of hundred. This gives the percentage. See the working out below. To turn the numbers into fractions, do: (No. taking part No. of members) and then percentage. 100 to change into Club Number of members Number taking part Fractions simplified Percentage (Q24) A (79/100) = 79/ % (Q25) B (36/50) = 72/ % (Q26) C (120/150) = 80/ % (Q27) D (49/70) = 70/ % (Q28) E (60/80) = 75/ % (See notes below on how to work out the percentage for the different clubs) Q24. To work out percentage for club A members: 79 [This is already 'over 100' which is the same as percentage] 100 [Percentage of club A members = 79%] 3

4 Q25. To work out percentage for club B members: 36 [ top/bottom by '2'] = [Percentage of club B members = 72%] Q26. To work out percentage for club C members: 120 [ top/bottom by '3'] = 40 [ top/bottom by '2'] = [Percentage of club C members = 80%] Q27. To work out percentage for club D members: 49 [ top/bottom by '7'] = 7 [ top/bottom by '10'] = [Percentage of club D members = 70%] Q28. To work out percentage for club E members: 60 [ top/bottom by '4'] = 15 [ top/bottom by '5'] = [Percentage of club E members = 75%] Q29. [a = 5] [b = 2] 4a = (4 5) [substitute in the values for 'a' and 'b'] 5b (5 2) [Be aware that in Maths: 4a = 4 a; 5b = 5 b] (4 5) = 20 = 2 (5 2) 10 [4a = 2] 5b 4

5 Q Starting from the end of the 5 th lesson (12:25pm), subtract 30 minutes first to work out the start of the 5 th lesson (11:55am). The start of the 5 th lesson is the same as the end of the 4 th lesson. Subtract 30 minutes again to get the start of the 4 th lesson (11:25am). This is the same as the end of the break period. Then from 11:25 am (when the break ends), subtract 15 minutes to work out the start of the break time (11:10 am). This is the same as end of 3 rd lesson. From here, subtract 30 minutes each time. See working below. Lesson begins Lesson ends 1 st Lesson 9:40a.m. 10:10a.m. 2 nd Lesson 10:10a.m. 10:40a.m. 3 rd Lesson 10:40a.m. 11:10a.m. Break 11:10a.m. 11:25a.m. 4 th Lesson 11:25a.m. 11:55a.m. 5 th Lesson 11:55a.m. 12:25p.m. Q w = 2475 Call the unknown number 'w' and follow the steps below to work it out. 275 w = 2475 [using algebra] w = [using inverse] 2475 [ top/bottom by '25' first] = 99 = [w = 9] 5

6 Q Prime factors of a number are prime numbers that times together to give the number. Follow the steps below to work this question out. Remember the question gives one of the prime numbers as '5'. So divide 2475 by 5 as shown below. Using your knowledge of factors, keep dividing all subsequent answers by prime numbers until you get a prime number as an answer. See below [5] = [5] = [11] = [3] = [3] The working out shows us that the prime numbers that times to give 2475 are: [(5 5) 11 (3 3) = 2475] [The three different prime numbers are: 3, 5, 11] Q Alternatively, the answer to question 41, gives a clue to completing this question. See how below. Q41 shows that: = 2475 This can be re-written as: = 2475 (5 5) 11 (3 3) = 2475 The prime factors that times together to give 2475 are: [3, 3, 5, 5, 11] (these 5 prime numbers times to give 2475) [The three different prime numbers are: 3, 5, 11] 6

7 Q The table shows the currency conversion rates of different currencies to the pound. Use direct proportion to work out the answers. [ 1.00] = 1.46 US Dollars [ 1.00] = 118 Ken. Shillings [ 1.00] = 1.42 Euros [ 1.00] = 2.13 Aus Dollars Q44. To change 3.00 into US Dollars: [times both sides by '3'] 1.00 = 1.46 US Dollars = [ 3.00 = 4.38 US Dollars] Q45. To change 1.50 into Ken. Shillings: [times both sides by '1.5'] 1.00 = 118 Ken. Shillings = [ 1.50 = 177 Ken. Shillings] Q46. To change into Euros: [times both sides by '13'] 1.00 = 1.42 Euros = [ = Euros] Q47. To change into Aus. Dollars: [times both sides by '50'] 1.00 = 2.13 Aus. Dollars = [ = Aus. Dollars] 7

8 Q Boys Girls 7 6 (ratios) 1. Add up the ratios [7 + 6 = 13] 2. Total number of children in school = Divide total number of children by total of ratio 4. [ = 27] 5. Multiply each of the ratios by '27' 6. The number of boys and girls should total '351' Boys Girls 7 6 (7 27 = 189) (6 27 = 162) [Boys = 189] [Girls = 162] Q50. Call the unknown number 'w' and follow the steps below to work it out. (w w) 2 = 242 [doubled means: ' 2'] w² 2 = 242 [using algebra] w² = [using inverse] w² = 121 w = 121 [w = 11] 8