Percentage means, a 'number over 100'. For example: 16% = 16 5% = 5 12% = 12 35% =

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1 Q1. [ = 0.04] The skill you need here is multiplications of decimal numbers. Count the total number of decimal places in the two numbers. Your answer should also have the same number of decimal places. Q To add fractions, find the LCM of the denominators. LCM of '2' and '4' = 4 Now work out the equivalent fractions and add them. [2 + 1 = 3 ] Percentage means, a 'number over 100'. For example: 16% = 16 5% = 5 12% = 12 35% = Q3. 50% of 30 = 50% 30 ['of' in Maths means ' '] (Use multiplication of fractions; simplify fraction by cancelling out the zeros) = 5 3 = [50% of 30 = 15] Q4. The skill you need here is division of fractions. This question is however so simple to do, you don't need to think too hard to solve work it out. [(10 ½) simply means how many halves can you get in 10?] [10 ½ = 20] 1

2 Q5. The skill you need here is division of decimals. This question is however so simple to do, you don't need to think too hard to work it out. [(5 0.5) simply means how many halves can you get in 5?] (Remember: 0.5 = ½) [5 0.5 = 10] Q6. [412 4 = 103] [The skill you need here is long division. See how below] Q To add fractions, find the LCM of the denominators. LCM of '8' and '2' = 8 Now work out the equivalent fractions and add them. [1 + 4 = 5 ] Q8. Work out the LCM of 5 mins, 15 mins and 12 mins to get the answer. The LCM = 60 minutes which is the same as 1 hour. [5]: [15]: [12]: (7:00 am + 60 minutes = 8:00am) [Buses are together again at: 8:00am] 2

3 When correcting numbers to the nearest 1000, look at the digit in the hundreds column. If the hundreds digit is '5' and above, round the digit in the thousands column up to the next See the examples below: Q ft = [ ft] nearest 1000 [(decider '8' is more than 5 so round up] Q ft = [ ft] nearest 1000 [(decider '0' is less than 5 so round down] Q ft = [ ft] nearest 1000 [(decider '2' is less than 5 so round down] Q ft = [ ft] nearest 1000 [(decider '3' is less than 5 so round down] Q ft = [ ft] nearest 1000 [(decider '3' is less than 5 so round down] Q ft = [ ft] nearest 1000 [(decider '7' is more than 5 so round up] [The deciders here are the numbers in the hundreds column] Q15. Call the unknown number 'w' and follow the steps below to work it out. w 10 = [using algebra] 10w = 180 w = [using inverse] [w = 18] 3

4 Q [Let's say Andy sold 'w' games.this means Steven sold 2w, (question says Andy sold ½ as many as Steven). If Steven sold '2w' games, then Michelle sold '4w', twice as many as Steven] Andy Steven Michelle w 2w 4w [Question says total number of laptops sold = 140] This means: ['w + 2w + 4w' = 140] w + 2w + 4w = 140 laptops 7w = 140 laptops [w = = 20] [using algebra] [w = 20 laptops] If [w = 20] then: Andy Steven Michelle w 2w 4w [1 x 20 = 20] [2 x 20 = 40] [4 x 20 = 80] [Andy sold 20 laptops] [Steven sold 40 laptops] [Michelle sold 80 laptops] Check: [If you add up all the laptops sold, they should total 140] Q Attendance Monday Tuesday Wednesday Thursday Friday AM PM Q19. Mean = [Total all the AM attendance numbers and divide by 5] [( ) 5 ] Mean = [Mean = 35] [Total up all the numbers and divide by number of numbers to get mean] 4

5 Q20. Median = [middle PM number when arranged in increasing order] [If there are 2 middle numbers, add them together and divide by '2'] [arranged in increasing order] [Median = 36] Q21. [Mode = 36] [most common/frequent PM number] Q When you multiply numbers by powers of 10 (numbers starting with '1' with zeros at the end e.g. 10, 100, 1000, etc.) the decimal point hops forwards (to the right). The number of hops corresponds with the number of zeros. Multiplying by 10 means the decimal point hops once because 10 has one zero. Multiplying by 100 means the decimal point hops twice because 100 has two zeros. Multiplying by 1000 means three hops; multiplying by means four hops and so on. Q = [37800] Q = [2450] Q = [47] Q = [25000] Q = [820] 5

6 Q Add the whole numbers first and place this on the side to use later: [7 + 5 = 12] Now add the fractions by working out the LCM: LCM of 8 and 16 = = 27 = 1 11 [change improper fraction] [to mixed fraction] Bring back the whole number and add to the 1 11 worked out. 16 [ = 13 11] Q Subtract the whole numbers first and place this on the side to use later: [7 3 = 4] Now subtract the fractions by working out the LCM: LCM of 5 and 15 = [You can't do (3 11)] So borrow '1' from the '4' on the side and add this '1' to 3 and then minus 11. Write down this '1' as 15 because 15 is the same as '1' [ ] [18 11 = 7 ] [Final answer = 3 7 ] [You have only 3 on the side now because] 15 [you borrowed '1' from the 4] 6

7 Q This question is testing your skill of working out Area and Perimeter of regular and irregular shapes. See working below: [Flag is a rectangle] [Area of a rectangle = length x width] [length of flag = 20 cm: (8 cm + 4 cm + 8 cm) [width of flag = 16 cm: (6 cm + 4 cm + 6 cm) Area of flag = 20 cm 16 cm Q29. [Area of flag = 320 cm²] Q30. To work out the area of the cross, work out the total area of the four shaded corners and subtract from area of whole flag. Length of each shaded corner = 8 cm Width of each shaded corner = 6 cm Area of each shaded corner = 8 cm 6 cm = 48 cm² Realise that there are '4' shaded corners in total in the flag! *[Area of the '4' shaded corners = (48 cm² 4 = 192 cm²)] Area of the cross = Area of flag Area of shaded corners [Area of the cross = = 128 cm²] 7

8 Q31. [Area of the '4' shaded corners = 192 cm²] See * above Q32. Perimeter of the flag is the total perimeter of the rectangle: [Perimeter of a rectangle = Adding up of all the sides] OR [Perimeter of a rectangle = (length x 2) + (width x 2)] Perimeter of rectangle flag = (20 2) + (16 2) Perimeter of rectangle flag = 40 cm + 32 cm [Perimeter of flag = 72 cm] Q33. Perimeter of the cross is adding the length of all the sides on the cross. Looking carefully, you can see 4 outer widths, 4 inside lengths and 4 inside widths. Add up all these sides together to get perimeter of the cross. 1. [outer width of cross = 4 cm: (4 4 cm)] 2. [inside length of cross = 8 cm: (4 8 cm)] 3. [inside width of cross = 6 cm: (4 6 cm)] Perimeter of cross = [(4 4) + (4 8) + (4 6)] Perimeter of cross = 16 cm + 32 cm + 24 cm [Perimeter of cross = 72 cm] 8

9 Q Can you work out the names of the four angles below? See answers below: Q34. [Angle A = Obtuse angle] Size of angle is between 90º and 180º. Q35. [Angle B = Right-angle] Size of angle is exactly 90º even with the shape tilted. Q36. [Angle C = Acute angle] Size of angle is between 0º and 90º. Q37. [Angle D = Reflex angle] Size of angle is between 180º and 360º. Q The number of dots in the triangles represent 'square numbers'. See the first 12 square numbers below: 1 st 2 nd 3 rd 4 th 5 th 6 th 7 th 8 th 9 th 10 th 11 th 12 th See below the pattern or the relationship between position, the number of rows and the number of dots as you move through the sequence. You will observe that 'squaring the number of rows' gives the number of dots. 9

10 1 st row = 1 row = 1² = 1 dot. 2 nd row = 2 rows = 2² = 4 dots. 3 rd row = 3 rows = 3² = 9 dots. 4 th row = 4 rows = 4² = 16 dots. 5 th row = 5 rows = 5² = 25 dots. 6 th row = 6 rows = 6² = 36 dots. 7 th row = 7 rows = 7² = 49 dots. 8 th row = 8 rows = 8² = 64 dots. 9 th row = 9 rows = 9² = 81 dots. 10 th row = 10 rows = 10² = 100 dots. Can you see the pattern? Now work out the answers to questions Q38. (number of rows)² = number of dots [5 rows = 5² = 25 dots] Q39. (number of rows)² = number of dots [7 rows = 7² = 49 dots] Q40. (number of rows)² = number of dots [11 rows = 11² = 121 dots] Q41. (number of rows)² = number of dots [20 rows = 20² = 400 dots] 10

11 Q42. [1 lb = 0.45 kg] and [1 kg = 2.2 lb] (by conversion) This means 1 pound in weight is equivalent to 0.45 kilogram or you will need 2.2 pounds of peas to make 1 kilogram of peas. Use direct proportion. 1 lb = 0.45 kg (Times both sides by '10' to find kg equivalent of 10 lb) 10 lb = 4.5 kg [10 lb < 10 kg] [10 kg mass is more] Q43. [1 km = 0.62 miles] and [1 mile = 1.6 km] (by conversion) This means 1 kilometre distance is equivalent to 0.62 miles or 1.6 kilometres is equivalent to 1 mile. Use direct proportion to complete this question. 1 km = 0.62 miles (Times both sides by '14' to find mile equivalent of 14 km) 14 km = 8.68 miles [14 km < 10 mile] [14 km distance is less] Q44. [1 litre = 1.8 pints] and [1 pint = 0.57 litres] (by conversion) This means 1 litre volume is equivalent to 1.8 pints or 0.57 litres is equivalent to 1 pint. Use direct proportion to complete this question. 1 litre = 1.8 pints (Times both sides by '2' to find pint equivalent of 2 litres) 2 litres = 3.6 pints [2 litres > 2 pints] [2 litre volume is more] 11

12 Q45. Number of poles Number of gaps Looking at the pattern above, you can see that the number of gaps is one less than the number of posts. Using this same deduction, we can see that: Number of poles Number of gaps 25 = 24 Size of 1 gap = 85 metres 24 gaps = 85 m 24 = 2040 m [Total gap between all 25 poles = 2040 metres] [5% = 5 = 1 = ( 20)] Q46. Original wage = 16, Percentage increase = 5 % Work out the percentage increase first. Then add this to the original wage. Increase in wage = 5 % of = 5 of = = Cross out the zeros in the fraction. Remember 'of' in Maths means ' ' [Increase in wage = ] Add this increase to the original wage. [New wage = ( ) = ] 12

13 Q47. Number of games = 6 games [Mean score of the games = 12 goals] Note: If you know the Mean, and you know how many games were played, multiply them together to get the Total number of goals. Find out more here. Multiply mean score by 6 (number of games) to get the total number of goals. Total number of goals in 6 games = 12 6 = [72] If the Mean score went up to '13' in the next game, this means number of games played has also gone up by one to '7' games. This means: Total number of goals in 7 games = 13 7 = [91] Score in seventh game = Total of 7 games Total of 6 games. [Score in seventh game = = 19] Q m [Line up the decimal points before adding] m m m [4.5 m m m = m] Q The easiest way to do this is to photocopy a few pages of the square paper with the shapes. Then carefully draw the reflections of the shapes. Replicate the exact point to point movement in the given shape, when drawing the reflections. See how to count the squares to draw the reflection of the first shape below. From the mirror line at the top, count: 1½ down, 2 right; then 1 left; then 1 down; then 1 right; then 1 down; then 2 left to meet the original half of the shape. Remember you are counting the big squares and not the very tiny squares. Good luck! 13