Tag Archives: difficult

Primary 5 CA1 Revision 12

P5-CA1-Ex12

Ans:

1–  $384

Christina –>  1u

Molly ->  3 u

Jack –>  1u + $65

5u + $65 = $705

5u –>  $705 – $65 = $640

1u –>  $640/5 = $128

$128 × 3 = $384

 

2–  235 paper clips

Before:                      Tom               :                   Jenny
1                   :                           5

——->     2                  :                         10

After:                             1                   :                           2

——>      5                  :                       10

5u – 2u = 4u

3u –>  141 clips

1u –>  47 clips

47 × 5 = 235 paper clips

 

3–  $60

3u –>  $36

1u –>  $12

$12 × 5 = $60

 

4–  9 years’ time

[Constant Difference]

3u –>  51 years

1u –>  17 years old

17 – 8 = 9 years’ time

 

5–  See belowQn 5

 

 

 

 

 

 

 

 

 

6–  18 coins

Multiples of 5 –>  5         10           15
+ 3  ->  8         13           18

Multiples of 4 –>   4         8             12            16
+ 2 ->   6         10          14           18

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Primary 6 Algebra Level 3 Ex 3

P6-Algebra-L3-Ex3

Ans:

1–  (20 + 5n) cm

1st piece –>  1u

2nd piece –>  2u

3u –>  60 cm

1u –>  20 cm (1st piece)

20 cm + 5 cm = (20 + 5n) cm

 

2–  96z cm

Length of longest side –>  24× 2 = 48cm

24+ 24+ 4896z cm

 

3–  $(5 – 0.50d)

Cost of 5 pencils –>  $0.50 × = $0.50d

$5 – $0.50$(5 – 0.50d)

 

4–  a–>  (8+ 10) sweets ,   b –>  (20 + 10)/3 sweets 

Number of sweets Rebecca had –>  4f × 2 = 8sweets

Number of sweets Tanya had –>  (8 + 10)  ———– (a)

Total number of sweets –>  4f + 8f + 8+ 10 = (20 + 10)

(20+ 10) ÷ 3 = (20+ 10)/3 sweets  ————–(b)

 

5–  a –>  $(– 16)/2 ,   b –>  $34

2u –>  $(y – $16)

1u  (sandals) –>  $(y – 16)/2    ———— (a)

Cost of sandals ->  $(52-16)/2 = $18

$18 + $16 = $34   —————–(b)

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Primary 6 August Problem Sums 9

P6-PSP-Aug-Ex 9

Ans:

1– 28 cm

Square numbers are 1, 4, 9, 16, 25, 36, 49, 64, 81, etc …

The two possible square numbers that add to 74 are 25 and 49

5 cm × 5 cm = 25 cm²

7 cm × 7 cm = 49 cm²

7 cm × 4 = 28 cm

 

2–  355 more marbles

Number of boys –>  3 + 5 = 8

Units of marbles each girl received –>  1u

Units of marbles each boy received –>  1u + 30

Total received by the 8 children –>  1u × 3 + (1u + 30) × 5 = 8u + 150

8u + 150 marbles ->  570 marbles

8u –>  570 – 150 = 420 marbles

1u –>  102.5 marbles

(5u + 150) – 3u = 2u + 150

(102.5 × 2) + 150 = 355 more marbles

 

3–  $71.50

7 durians + 10 mangoes –>  $57

[1 durian + 1 mango –>  $7.50] × 7
–>  7 durians + 7 mangoes –>  $52.50

Therefore, $57 – $52.50 = $4.50 –>  3 mangoes

1 mango–>  $4.50/ 3 = $1.50

1 durian –>  $7.50 – $1.50 = $6

4 durians + 3 mangoes –>  $6 × 4+ $1.50 × 3 = $28.50

$100 – $28.50 = $71.50

 

4–  15 : 6 : 10

Red   :  Blue                      Blue   :   Purple
5      :     2                             3      :      5

–>  15    :     6                             6      :    10

Red   :   Blue   :   Purple
15   :    6    :   10

 

5–  56 cm

Height of water level at first –>  5/8 × 64 cm = 40 cm

1600 cm³ ÷ (10 × 10) cm² = 16 cm

16 cm + 40 cm = 56 cm

 

6–  200 cookies

[Constant Difference]

At first:

Joanna –>  250 cookies

Sharon ->  350 cookies

In the end –>        Joanna  :  Sharon
3       :         5

2u –>  100

1u –>  50

8u –>  50 × 8 = 400 cookies left

600 – 400 = 200 cookies

 

7–  $13.50

5 small towels + 6 big towels –>  $34.50

6 small towels + 5 bog towels –>  $34.50 – $4 = $31.50

11 small towels + 11 big towels –>  $34.50 + $31.50 = $66

1 small towel + 1 big towel –> $66/ 11 = $6

5 small towels + 5 big towels –>  $6 × 5 = $30

1 big towel –> $34.50 – $30 = $4.50

$4.50 × 3 = $13.50

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Primary 6 Prelims Revision 9

P6-Prelims-Ex 9

Ans:

1– $45

Julian –>  1u

Frederick –>  2u

Marcus –>  6u

5u –> $25

1u –>  $5

$5 × 9u = $45

 

2–  16 more tricycles

Assume all are tricycles –> 56 × 3 = 168 wheels

168 – 148 = 20 wheels extra

Each bicycle has 1 lesser wheel than each tricycle.

Therefore, 20 ÷ 1 = 20 bicycles

56 – 20 00= 36 tricycles

36 – 20 = 16 more tricycles than bicycles

 

3–  $44

4–  22.5 km/h faster

Marcus’ speed –>  270 /4 = 67.5 km/h

Marcus’ new speed –>  270/3 = 90 km/h

90 km/h – 67.5 km/h = 22.5 km/h faster

 

5–  396 boys

Girls –>  1u × 5 = 5u

Boys –>  (1u + 16) × 3 = 3u + 48

8u + 48 –>  976 pupils

8u –>  928

1u –>  116

116 × 3 + 48 = 396 boys

 

6–  $2945

7 handbags + 5 watches = 3 handbags + 11 watches

7 handbags – 3 handbags = 11 watches – 5 watches

4 handbags = 6 watches

6 watches –>  $285 × 4 = $1140

1 watch –>  $1140 ÷ 6 = $190

$285 × 7 + $190 × 5 = $2945

 

7–  300 stickers

Maxwell –> 100%

Jeanetter –>  120%

20/100 × 120% = 24%

120%  – 24% = 96% left

96% –>  288 stickers

1% — 3 stickers

3 × 100 = 300 stickers

 

8–  153 cm

17 + 13 = 30 cm – 3 pieces

1 piece –>  10 cm

14 × 10 cm + 13 cm = 153 cm

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Primary 6 Prelims Revision 6

P6-Prelims-Ex 6

Ans:

1–  $1225

18% = 9/50

90% = 9/10

Therefore,

Brandon   :   Charles
50        :     10
5          :        1

6u –>  $1470

1u –>  $245

$245 × 5u = $1225

 

2–  9/10 h

Time taken to fill 1/9 of the tank –>  2/5 ÷ 4 = 1/10 h

1/10 h × 9 = 9/10 h

 

3–  8 pentagons

3 × 5 = 15 matchsticks for the 3 extra pentagons

60 – 15 = 45 matchsticks (The number of squares and pentagons are now the                                                              same)

Number of matchsticks needed to make 1 square and 1 pentagon -> 4 + 5
= 9

45/9 = 5

5 + 3 = 8 pentagons

 

4–  10 hours

55 min = 11/12 h

11/12 h + 3/4 h = 1   2/3 h

5  1/2 h ÷ 11/12 h = 6 sets

6 × 1   2/3 h = 10 hours

 

5–  $40

85% – 55% = 30%

30% –>  $12

100% –>  12/30 × 100 = $40

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Primary 6 Prelims Revision 3

P6-Prelims-Ex 3

Ans:

1–  3 : 12 : 17

2–  4.95 cm

Length of the tank –>  180 cm³ ÷ 12 edges = 15 cm

33/100 × 15% = 4.95 cm

 

3–  100 balls

Total units of balls –>  5u + 4u = 9u

Units of balls in each bag in the end –>  9u/2 = 4.5u

5u – 4.5u = 0.5u —>  10 balls

1u –>  10 × 2 = 20 balls

20 × 5u = 100 balls

 

4–  540 km

5–  $24

1 blouse –>  1u

1 pair of jeans –>  1u + $12

3 pairs of jeans + 4 blouses –>  (1u + $12) × 3 + 4u = 7u + $36

7u + $36 ->  $204

7u –>  $204 – $36 = $168

1u –>  $24

 

6–  891 beads

Red : Blue + Green
4   :      5

Blue : Green
3    :    8     –>  11u

Adjust the units for the blue and green beads such that they are the same in both cases.

Common multiple of 5 and 11 is 55u

Therefore,

Red  :  Blue + Green
44   :      55

Blue  :  Green
15   :  40

Red  :  Blue  :  Green
44 :    15   :      40

44u – 40u = 4u –>  36 beads

1u –>  9 beads

44u + 55u = 99u —->  9 beads × 99 = 891 beads

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Primary 2 Whole Numbers Level 3 Ex 2

P2-Whole Numbers-L3-Ex 2

Ans:

1–  8 markers

 

2–  8 stamps

3–  569 stickers

4–  776 stamps

5–  40 pupils

Qn 5

Number of girls –> 30 ÷ 3 = 10

30 + 10 = 40 pupils

 

6–  9 beads

Total number of beads they had –>  76 + 45 = 121

130 – 121 = 9 beads

 

7–  720 stickers

Number of stickers Tanya has –>  341 + 38 = 379

379 + 341 = 720 stickers

 

8–  537 stamps

Primary 6 SA1 Revision 12

P6-SA1-Ex 12

Ans:

1–  175

2–  $43.50

70% of the price –>  $101.50

30% –>  $101.50/70 × 30 = $43.50

 

3–  (3+ 6) kg

Alan’s mass ->  (+ 3) kg

Nicholas’ mass ->  (m + 3) – 2 = (+ 1) kg

Brett’s mass ->  (+ 1) + 1 = (+ 2) kg

(m + 3) + (+ 1) + (+ 2) = (3+ 6) kg

 

4–  195 km

1  1/2 h× 80 km/h = 120 km

45/60 h × 100 km/h = 75 kg

120 km + 75 km = 195 km

 

5–  $6441.60

Earnings in January –>  122/100 × $6000 = $7320

Earnings in February –>  88/100 × $7320 = $6441.60

 

6–  30 people

Fraction of men  –>  30/100 = 3/10 = 9/30

Fraction of men if 10 women alighted –>  45/100 = 9/20

Women –>  30u – 9u = 21u

20u – 9u = 11u

10u –>  10 women

30 u –>  30 people

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Primary 2 Whole Numbers Level 3 Ex 1

P2-Whole Numbers-L3-Ex 1

Ans:

1–  241 marbles

2–  538 stamps

Number of stamps Irene has –>  325 – 112 = 213

325 + 213 = 538 stamps

 

3–  202 marbles

4–  40 pupils

5-  30 apples

Number of apples in each basket –>  2 + 3 = 5

5 × 6 = 30 apples

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Primary 6 April Problem Sums 5

P6-PSP-Apr-Ex 5

Ans:

1–  30 m

Spaces between 100 trees –> 99

Distance between each tree –> 297 m ÷ 99 = 3 m

3 m × 10 spaces = 30 m

 

2–  28 pupils

Number of pupils who passed one or both subjects –> 40 – 2 = 38

30 + 36 = 66

66 – 38 = 28 pupils

 

3–  a ->  (18s + 24) kg ,   b ->   16 kg

Mass of chicken –>  3s kg

Mass of puppy –>  (3s + 4) kg

Mass of dog –>  (3+ 3s + 4) kg × 2 = (12+ 8) kg

3s + 3s + 4 + 12s + 8 = (18s + 12) kg                   (a)

18 × 2 + 12 = 48 kg

48 kg ÷ 3 = 16 kg                           (b)

 

4–  $51.30

Total cost of 5 apples and 5 mangoes –>  $3.25 × 5 = $16.25

Cost of 3 apples –>  $17.60 – $16.25 = $1.35

Cost of 1 apple –> $1.35 ÷ 3 = $0.45

Cost of 1 mango –> $3.25 – $0.45 = $2.80

Cost of 2 mangoes and 7 apples –>  $2.80 × 2 + $0.45 × 7 = $8.70

$50 – $8.70 = $51.30

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