NOTE: In examinations, all questions MUST HAVE FINAL STATEMENTS, if not 1 MARK WILL BE DEDUCTED AWAY even if you get the right answer. The blank provided for each question doesn't mean you do not have to write your final statement.
FINAL STATEMENTS SHOW MARKERS THAT YOU KNOW WHAT YOU MUST FIND TO SOLVE THE PROBLEM SUMS.
Question 1 to 5 carry 2 marks each.
Q1:
Answer: 8 photo frames
She bought equal number of photo frames and stuffed toy meaning 1 photo frame for every stuffed toy
Cost of 1 photo frame and 1 stuffed toy -> $12 + $34 = $46 (M1)
Sets of 1 photo frame and 1 stuffed toy she could buy with $368 -> $368 ÷ 46 = 8 sets
8 sets -> 8 photo frames (A1)
She bought 8 photo frames.
Q2:
Answer: 1/10
1 whole -> all the vegetables the grocer had before selling.
Amount left for afternoon after 5/6 of vegetables sold in morning -> 1 - 5/6 = 1/6.
2/5 of the remainder was sold in afternoon means -> 3/5 of 1/6 left.
3/5 of 1/6 = 3/5 × 1/6 (M1)
= 1/10 (A1)
1/10 of the vegetables was left.
Q3:
Answer: 1/50m2
Perimeter of square -> 4/5m
1 side of square -> 4/5m ÷ 4 = 1/5m(M1)
Area of shaded triangle = 1/2 × base × height
= 1/2 × 1/5 × 1/5
= 1/50 m2 (A1)
The area of the shaded triangle is 1/50 m2.
Q4:
Answer: 0.45m
Piece of tape used to wrap length of box twice and the height of box twice.
Height of box = 15cm = 0.15m
So:
1.2m = 2 × length of box + 2 × height of box
2 × Length of box = 1.2m - 0.15m - 0.15m
= 0.9m (M1)
Length of box in metres = 0.9m ÷ 2
= 0.45m (A1)
The length of the box is 0.45m
Q5:
Answer: 116.8kg
Weight of Chew Meng -> 55.88kg + 5kg = 60.88kg
Total weight of the two -> 55.88kg + 60.88kg (M1)= 116.76kg ≈ 116.8kg (A1)(corrected to 1 decimal place)
Their total weight is about 116.8kg
Number of marks for each question is shown in the brackets at the each of each question or part-question. Marks are given for workings and answers. (M1) stands for method marks while (A1) stands for answer marks.
Q6: 3marks
Answer: 12 people
Mr Tan and his 4 family members = 5 people
5 people -> $143
1 person -> $143 ÷ 5 = $28.60 (M1)
Total number of people -> $343.20 ÷ $28.60 (M1) = 12 people
There were 12 people in the group. (A1)
Q7: 3marks
Answer: $180
1 whole -> all the money she had
Fraction of money left after buying blouse -> 1 - 1/5 =4/5
Fraction of money left after buying shoes with 1/2 of the remaining money -> 1/2 × 4/5 = 2/5 (M1)
2 units out of 5 units -> $72
1 unit -> $72 ÷ 2 = $36 (M1)
Money she had at first -> 5 units -> $36 × 5 = $180
She had $180 at first (A1)
Q8: 3 marks
Answer: 280 pages
Fraction of the book read on Monday together with 1/2 of the pages of book remaining which are not read -> 2/5 + 1/2 = 4/10 + 5/10
= 9/10 of the book (M1)
Fraction of the pages of book read on Tuesday -> 1 whole - 9/10 = 1/10
1/10 of the book -> 1 unit -> 28 pages (M1)
10 units -> 1 full book = 28 × 10 pages
There were 280 pages in the book.(A1)
Q9: 3 marks
Answer: 49 pupils
Step 1:
List multiples of 3, 4 and 7 respectively. Add 1 to the multiple of 3 and 4 since 1 is left out.
Step 2: Look out for the smallest common number in the 3 sets of numbers.
Multiples of 3:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54
Add 1:
4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55
Multiples of 4:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56
Add 1:
5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57
Multiples of 7:
7, 14, 21, 28, 35, 42, 49, 56, 63, 70
The least possible number of pupils in the class would be 49 pupils.
Q10: 3 marks
Answer: 72cm2
Area of shaded part = Area of big triangle - Area of small triangle (unshaded)
Area of big triangle = 1/2 × base × height
= 1/2 × 18 × 14
= 126cm2 (M1)
Area of small triangle = 1/2 × base of small triangle × height of small triangle
= 1/2 × 18 × 6
=54cm2 (M1)
Area of shaded part = 126 - 54 = 72cm2
The area of the shaded part is 72cm2.(A1)
Q11: 3 marks
Answer: 300 people
Ratio of men to women before 105 men left = 3 : 2
Ratio of men to women after 105 men left = 5 : 8
Number of women in the party remained unchanged.
3 : 2 (multiplied by 4)= 12 : 8
Compare 12 : 8 to 5 : 8
Units of men leaving the party = 12 - 5 = 7 units
7 units -> 105 men(M1)
1 unit -> 15 men
Total number of people at the part at first -> 12 + 8 = 20 units(M1)
20 units -> 20 × 15 = 300 people (A1)
300 people were at the party at first.
Q12: 4 marks
Answer: 39 questions
Use guess and check method:
You should arrive at 39 questions answered correctly, and 11 questions answered wrongly. If guess and check workings were shown, (M3) will be awarded.
She answered 39 questions correctly. (A1)
To check:
39 correct answers -> 39 × 3 = 117 points
11 wrong answers -> 11 × 3 = 33 points
Total score = 117 - 33 = 84 points
Q13: 4 marks
Answer: 444 eggs
1 whole -> Total number of eggs at first
Fraction of eggs left after baking butter cake with 1/6 of the eggs = 1 whole - 1/6 = 5/6
Fraction of the total number of eggs used for baking chocolate cakes -> 3/10 of 5/6 of the total eggs he had at first -> 3/10 × 5/6 = 1/4(M1)
Total fraction of egg used -> 185 eggs since the number of eggs was the same as the first after buying 185 eggs.
Fraction of eggs used ->1/4 + 1/6 = 3/12 + 2/12 = 5/12(M1)
5 units -> 185
1 unit -> 185 ÷ 5 = 37 eggs (M1)
Eggs at first -> 12 units -> 37 × 12 = 444 eggs (A1)
He had 444 eggs at first.
Q14: 4 marks
Answer:
Intervals between 2nd and 5th seed -> 3 intervals (M1)
3 intervals -> 180cm or 1.8m
1 intervals -> 60cm or 0.6m(M1)
9.6m = 960cm
Number of intervals within 9.6m or 960cm -> 9.6m ÷ 0.6m or 960cm ÷ 60cm = 16 intervals.(M1)
Number of seedings planted -> 16 + 1 = 17 seedlings (A1)
He planted 17 seedlings in all.
Q15: 5 marks
Answer: $1 800
1 whole = Prize money which is $12 000
Fraction of money left after giving wife 2/5 of it -> 1 whole - 2/5 = 3/5
Fraction of the prize money Mr Wong kept for himself -> 4/9 × 3/5 = 4/15
Fraction of prize money given to John and Mark -> 1 - 4/15 - 2/5
= 15/15 - 4/15 - 6/15(M1)
= 11/15 - 6/15
= 5/15
15 units -> $12 000
1 unit -> $12 000 ÷ 15 = $800 (M1)
5 units -> Money that the 2 brothers shared -> $800 × 5 = $4 000 (M1)
Money that Mark received -> ($4 000 - $400) ÷ 2 = $3 600 ÷ 2
= $ 1 800 (A1)
Mark received $1 800.
Q16: 5 marks
Answer: 540cm2
Area of triangle = 384cm2
384cm2 = 1/2 × base of triangle × height of triangle
= 1/2 × 24cm × height of triangle
= 12cm × height of triangle
Height of triangle = 384 ÷ 12 = 32cm (M1)
Perimeter of triangle = 32 + 24 + 40 = 96cm (M1)
Rectangle has same perimeter as triangle.
Ratio of 1 length of rectangle to 1 breadth of triangle = 5:3
A rectangle has 2 lengths and 2 breadths, so total units -> 5 + 5 + 3 + 3 = 16 units (M1)
16 units -> perimeter of rectangle -> 96cm
1 unit -> 96 ÷ 16 = 6cmlength -> 5 × 6 = 30cm
3 units -> breadth -> 3 × 6 = 18cm
Area of rectangle -> length × breadth = 30 × 18 = 540cm2 (A1)
The area of the rectangle is 540cm2.
Q17:
Answer: 140 packets
Ratio of green to blue = 5:4
Unit of green beads more than blue beads -> 5-4 = 1 unit
1 unit -> 480
5 units -> green beads -> 480 × 5 = 2400 green beads (M1)
4 units -> blue beads -> 480 × 4 = 1920 blue beads (M1)
Ratio of pink to blue = 2:3
3 units of blue beads -> 1920 beads
1 unit = 1920 ÷ 3 = 640 beads
Number of pink beads -> 2 units -> 2 × 640 beads = 1280 pink beads (M1)
Total number of beads -> pink + blue + green_> 1 280 + 1 920 + 2 400 = 5 600 beads(M1)
Number of packets with 40 beads each -> 5600 ÷ 40 = 140 packets (A1)
She had 140 packets of beads.
Q18a:
Answer: 16 triangles formed (A1)
Always make relationship between the number of patterns to the other thing you want to find out. So an example will be:
Pattern # -> # × 1 = # triangle formed -> (Sum of pattern number #) × 3 matches
Pattern 1 -> 1 × 1 = 1 triangle formed -> (1) × 3 = 1 × 3 = 3 matches
Pattern 2 -> 2 × 2 = 4 triangles formed -> (1 + 2) × 3 = 3 × 3 = 9matches
Pattern 3 -> 3 × 3 = 9 triangles formed -> (1 + 2 + 3) × 3 = 6 × 3 = 18 matches
Pattern 4 -> 4 × 4 = 16 triangles formed -> (1 + 2 + 3 + 4) × 3 = 10 × 3 = 30 matches
...
Pattern 10 -> 10 × 10 = 100 triangles formed -> (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) × 3 = 55 × 3 = 165 matches (M1)
...
Pattern 15 -> 15 × 15 = 225 triangles formed (M1)
NOTE: METHOD AND WORKINGS ARE 2 MARKS, NO WORKINGS NO MARKS
Q18b:
Answer: 225 triangles formed (A1)
Q18c:
Answer: 165 matchsticks (A1)
FINAL STATEMENTS SHOW MARKERS THAT YOU KNOW WHAT YOU MUST FIND TO SOLVE THE PROBLEM SUMS.
Question 1 to 5 carry 2 marks each.
Q1:
Answer: 8 photo frames
She bought equal number of photo frames and stuffed toy meaning 1 photo frame for every stuffed toy
Cost of 1 photo frame and 1 stuffed toy -> $12 + $34 = $46 (M1)
Sets of 1 photo frame and 1 stuffed toy she could buy with $368 -> $368 ÷ 46 = 8 sets
8 sets -> 8 photo frames (A1)
She bought 8 photo frames.
Q2:
Answer: 1/10
1 whole -> all the vegetables the grocer had before selling.
Amount left for afternoon after 5/6 of vegetables sold in morning -> 1 - 5/6 = 1/6.
2/5 of the remainder was sold in afternoon means -> 3/5 of 1/6 left.
3/5 of 1/6 = 3/5 × 1/6 (M1)
= 1/10 (A1)
1/10 of the vegetables was left.
Q3:
Answer: 1/50m2
Perimeter of square -> 4/5m
1 side of square -> 4/5m ÷ 4 = 1/5m(M1)
Area of shaded triangle = 1/2 × base × height
= 1/2 × 1/5 × 1/5
= 1/50 m2 (A1)
The area of the shaded triangle is 1/50 m2.
Q4:
Answer: 0.45m
Piece of tape used to wrap length of box twice and the height of box twice.
Height of box = 15cm = 0.15m
So:
1.2m = 2 × length of box + 2 × height of box
2 × Length of box = 1.2m - 0.15m - 0.15m
= 0.9m (M1)
Length of box in metres = 0.9m ÷ 2
= 0.45m (A1)
The length of the box is 0.45m
Q5:
Answer: 116.8kg
Weight of Chew Meng -> 55.88kg + 5kg = 60.88kg
Total weight of the two -> 55.88kg + 60.88kg (M1)= 116.76kg ≈ 116.8kg (A1)(corrected to 1 decimal place)
Their total weight is about 116.8kg
Number of marks for each question is shown in the brackets at the each of each question or part-question. Marks are given for workings and answers. (M1) stands for method marks while (A1) stands for answer marks.
Q6: 3marks
Answer: 12 people
Mr Tan and his 4 family members = 5 people
5 people -> $143
1 person -> $143 ÷ 5 = $28.60 (M1)
Total number of people -> $343.20 ÷ $28.60 (M1) = 12 people
There were 12 people in the group. (A1)
Q7: 3marks
Answer: $180
1 whole -> all the money she had
Fraction of money left after buying blouse -> 1 - 1/5 =4/5
Fraction of money left after buying shoes with 1/2 of the remaining money -> 1/2 × 4/5 = 2/5 (M1)
2 units out of 5 units -> $72
1 unit -> $72 ÷ 2 = $36 (M1)
Money she had at first -> 5 units -> $36 × 5 = $180
She had $180 at first (A1)
Q8: 3 marks
Answer: 280 pages
Fraction of the book read on Monday together with 1/2 of the pages of book remaining which are not read -> 2/5 + 1/2 = 4/10 + 5/10
= 9/10 of the book (M1)
Fraction of the pages of book read on Tuesday -> 1 whole - 9/10 = 1/10
1/10 of the book -> 1 unit -> 28 pages (M1)
10 units -> 1 full book = 28 × 10 pages
There were 280 pages in the book.(A1)
Q9: 3 marks
Answer: 49 pupils
Step 1:
List multiples of 3, 4 and 7 respectively. Add 1 to the multiple of 3 and 4 since 1 is left out.
Step 2: Look out for the smallest common number in the 3 sets of numbers.
Multiples of 3:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54
Add 1:
4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55
Multiples of 4:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56
Add 1:
5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57
Multiples of 7:
7, 14, 21, 28, 35, 42, 49, 56, 63, 70
The least possible number of pupils in the class would be 49 pupils.
Q10: 3 marks
Answer: 72cm2
Area of shaded part = Area of big triangle - Area of small triangle (unshaded)
Area of big triangle = 1/2 × base × height
= 1/2 × 18 × 14
= 126cm2 (M1)
Area of small triangle = 1/2 × base of small triangle × height of small triangle
= 1/2 × 18 × 6
=54cm2 (M1)
Area of shaded part = 126 - 54 = 72cm2
The area of the shaded part is 72cm2.(A1)
Q11: 3 marks
Answer: 300 people
Ratio of men to women before 105 men left = 3 : 2
Ratio of men to women after 105 men left = 5 : 8
Number of women in the party remained unchanged.
3 : 2 (multiplied by 4)= 12 : 8
Compare 12 : 8 to 5 : 8
Units of men leaving the party = 12 - 5 = 7 units
7 units -> 105 men(M1)
1 unit -> 15 men
Total number of people at the part at first -> 12 + 8 = 20 units(M1)
20 units -> 20 × 15 = 300 people (A1)
300 people were at the party at first.
Q12: 4 marks
Answer: 39 questions
Use guess and check method:
You should arrive at 39 questions answered correctly, and 11 questions answered wrongly. If guess and check workings were shown, (M3) will be awarded.
She answered 39 questions correctly. (A1)
To check:
39 correct answers -> 39 × 3 = 117 points
11 wrong answers -> 11 × 3 = 33 points
Total score = 117 - 33 = 84 points
Q13: 4 marks
Answer: 444 eggs
1 whole -> Total number of eggs at first
Fraction of eggs left after baking butter cake with 1/6 of the eggs = 1 whole - 1/6 = 5/6
Fraction of the total number of eggs used for baking chocolate cakes -> 3/10 of 5/6 of the total eggs he had at first -> 3/10 × 5/6 = 1/4(M1)
Total fraction of egg used -> 185 eggs since the number of eggs was the same as the first after buying 185 eggs.
Fraction of eggs used ->1/4 + 1/6 = 3/12 + 2/12 = 5/12(M1)
5 units -> 185
1 unit -> 185 ÷ 5 = 37 eggs (M1)
Eggs at first -> 12 units -> 37 × 12 = 444 eggs (A1)
He had 444 eggs at first.
Q14: 4 marks
Answer:
Intervals between 2nd and 5th seed -> 3 intervals (M1)
3 intervals -> 180cm or 1.8m
1 intervals -> 60cm or 0.6m(M1)
9.6m = 960cm
Number of intervals within 9.6m or 960cm -> 9.6m ÷ 0.6m or 960cm ÷ 60cm = 16 intervals.(M1)
Number of seedings planted -> 16 + 1 = 17 seedlings (A1)
He planted 17 seedlings in all.
Q15: 5 marks
Answer: $1 800
1 whole = Prize money which is $12 000
Fraction of money left after giving wife 2/5 of it -> 1 whole - 2/5 = 3/5
Fraction of the prize money Mr Wong kept for himself -> 4/9 × 3/5 = 4/15
Fraction of prize money given to John and Mark -> 1 - 4/15 - 2/5
= 15/15 - 4/15 - 6/15(M1)
= 11/15 - 6/15
= 5/15
15 units -> $12 000
1 unit -> $12 000 ÷ 15 = $800 (M1)
5 units -> Money that the 2 brothers shared -> $800 × 5 = $4 000 (M1)
Money that Mark received -> ($4 000 - $400) ÷ 2 = $3 600 ÷ 2
= $ 1 800 (A1)
Mark received $1 800.
Q16: 5 marks
Answer: 540cm2
Area of triangle = 384cm2
384cm2 = 1/2 × base of triangle × height of triangle
= 1/2 × 24cm × height of triangle
= 12cm × height of triangle
Height of triangle = 384 ÷ 12 = 32cm (M1)
Perimeter of triangle = 32 + 24 + 40 = 96cm (M1)
Rectangle has same perimeter as triangle.
Ratio of 1 length of rectangle to 1 breadth of triangle = 5:3
A rectangle has 2 lengths and 2 breadths, so total units -> 5 + 5 + 3 + 3 = 16 units (M1)
16 units -> perimeter of rectangle -> 96cm
1 unit -> 96 ÷ 16 = 6cm
3 units -> breadth -> 3 × 6 = 18cm
Area of rectangle -> length × breadth = 30 × 18 = 540cm2 (A1)
The area of the rectangle is 540cm2.
Q17:
Answer: 140 packets
Ratio of green to blue = 5:4
Unit of green beads more than blue beads -> 5-4 = 1 unit
1 unit -> 480
5 units -> green beads -> 480 × 5 = 2400 green beads (M1)
4 units -> blue beads -> 480 × 4 = 1920 blue beads (M1)
Ratio of pink to blue = 2:3
3 units of blue beads -> 1920 beads
1 unit = 1920 ÷ 3 = 640 beads
Number of pink beads -> 2 units -> 2 × 640 beads = 1280 pink beads (M1)
Total number of beads -> pink + blue + green_> 1 280 + 1 920 + 2 400 = 5 600 beads(M1)
Number of packets with 40 beads each -> 5600 ÷ 40 = 140 packets (A1)
She had 140 packets of beads.
Q18a:
Answer: 16 triangles formed (A1)
Always make relationship between the number of patterns to the other thing you want to find out. So an example will be:
Pattern # -> # × 1 = # triangle formed -> (Sum of pattern number #) × 3 matches
Pattern 1 -> 1 × 1 = 1 triangle formed -> (1) × 3 = 1 × 3 = 3 matches
Pattern 2 -> 2 × 2 = 4 triangles formed -> (1 + 2) × 3 = 3 × 3 = 9matches
Pattern 3 -> 3 × 3 = 9 triangles formed -> (1 + 2 + 3) × 3 = 6 × 3 = 18 matches
Pattern 4 -> 4 × 4 = 16 triangles formed -> (1 + 2 + 3 + 4) × 3 = 10 × 3 = 30 matches
...
Pattern 10 -> 10 × 10 = 100 triangles formed -> (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) × 3 = 55 × 3 = 165 matches (M1)
...
Pattern 15 -> 15 × 15 = 225 triangles formed (M1)
NOTE: METHOD AND WORKINGS ARE 2 MARKS, NO WORKINGS NO MARKS
Q18b:
Answer: 225 triangles formed (A1)
Q18c:
Answer: 165 matchsticks (A1)
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