Yes, the mid year examinations are over... For some, there are reasons to rejoice and to celebrate...
Yet for some, they will enter into moments of weeping and grieving... Perhaps weeping over their lack of focus and attention during lessons, and not showing self control to revise enough for examinations.
No matter, we all learn from mistakes... If CA 1 was not the turning point for some of you, perhaps these SA 1 results will be...
I vaguely remembered how some were seen crying or weeping over the CA 1 results...
I remembered how each of you promised to put in your best and to set the right targets for SA 1... Yet, sad to say, for some, I do not see the effort nor the actions...
It is really time to get serious with your studies...
My advice: Take a good break for a week or two during your holidays, but spend the rest of the time revising all the topics done so far since January...
Don't waste time away anymore...
Don't be so short sighted, to think about play, play and play...
I have always said this, and I will say it again:
There is a season for everything, a time to play, a time to rest, and a time to work.
Can I really beg you all to learn this, and know when to put in your focus, attention and hard work.
I am not saying you should not play at all, but hey, really some of you have been playing around through out this whole term too much...
When examinations were nearing that time,would you please touch your heart and ask if you have really put in your best?
For some, I am disappointed to see you wasting the time after school to be loitering around in school, to be playing in the field...
For some, I am discouraged to hear about how you will hog the computer and play online games all day long without restrictions...
In the end, you ended up not doing your homework properly, did not have time to revise, and to resort to copying homework...
It is a clear sign that for some of you, whatever you have been doing so far, is not helping you much in your studies...
DON'T LIVE TO REGRET... YOU HAVE ONE LIFE TO LIVE IT RIGHT. IT IS OKAY TO TRY AND FAIL, BUT NOT OKAY TO FAIL TRYING AGAIN...
Keep your focus on SA 2...
If you put in your effort, and work with the teachers, I am sure you will see improvements...
It is STILL NOT TOO LATE to make it right now...
Remember the video I have shown you before? Same question again...
ARE YOU GOING TO FINISH STRONG?
Our days of 5.7 since we've met...
Time's Ticking...
Monday, May 18, 2009
Monday, May 11, 2009
Checking of answers and corrections
Hi 5.7 pupils,
Here are a few reminders before you get to see the answers.
Please:
1. Do not copy the answers. You are supposed to do your work BEFORE you check the answers here. If you have not completed the work and attempted all the questions. Come back later, then do the corrections accordingly. IF YOU ARE CAUGHT COPYING, ANOTHER SET WILL BE PRINTED FOR YOU TO BE DONE.
2. If you have the CORRECT answer, put a tick in PENCIL.
3. If you have the WRONG answer, please do your CORRECTIONS in GREEN PEN with FULL ANSWERS (Includes model diagrams and workings, if any)
4. Look through the answers, revise and learn from the mistakes made.
5. Complete the surveys which will give me information on what questions I have to go through with you all.
6. Difficult questions will be discussed on this coming Tuesday and Wednesday.
7. Practice papers will be collected, marked straight after your Maths examinations.
Answers for Practice Paper 5 - Paper 1
Practice Paper 5, Paper 1:
Total marks: 40
Question 1 to 10 carries 1 mark each.
Question:
Q1:
Answer: 3
4 212 ÷ 4 = 1 053 (no remainders)
4 122 ÷ 4 = 1 030 R 2 (not correct)
4 126 ÷ 4 = 1 031 R 2 (not correct)
4 218 ÷ 4 = 1 054 R 2 (not correct)
Q2:
Answer: 2
The first shape in the pattern will be in the 1st, 5th,9th,13th… 49th position.
Every pattern repeats itself after 4 counts.
Hence the 50th position will be the next pattern in line which is the rectangle.
Q3:
Answer: 2
4.05 × 200 is the same as:
4.05 × 2 × 100 = 8.10 × 100
= 810
Q4:
Answer: 2
Monday -> 2.4km
Tuesday -> 1 650m = 1.65km
Total -> 2.4km + 1.65km
= 4.05km
Q5:
Answer: 3
Common sense: There cannot be a packet of orange juice which contains 750 ℓ of orange juice! That will be too heavy and too much for anyone to carry and drink! We don’t measure amount of orange juice in cm or m as well! They are for measuring length and distance. So the most reasonable answer is ml!
Q6:
Answer: 3
Express 1/3 as a like fraction to all the options provided.
1/3 = 3/9 = 5/15 = 6/18 = 7/21
Only option 3 which is 7/18 will be greater than 6/18 which is also equivalent to 1/3 .
Q7:
Answer: 4
DC is 4 times the length of ED. This means that we can make 8 equal triangles like triangle CDE out of the square ABCD.
So since one triangle is shaded out of 8 possible triangles, the fraction is 1/8.
Q8:
Answer: 1
6 children -> 3/4 of a pizza
1 children -> ¾ ÷ 6 = ¾ × 1/6
= 1/8
Q9:
Answer: 1
Base of shaded triangle = length of YZ
= 9cm - 5cm
= 4cm
Height of shaded triangle = 12cm
Area of shaded triangle = 1/2 × base × height
= 1/2 × 4 × 12
= 2 × 12
= 24cm2
Q10:
Answer: 3
Girls -> 22
Boys -> 18
Total -> 40
Ratio of girls to total number of pupils in class
= 22 : 40
divided by common factor 2)
= 11 : 20
Question 11 to 15 carries 2 marks each.
Q11:
Answer: 4
15 - 5 × 0 + 20 ÷ 5
= 15 - 0 + 4
= 15 + 4
= 19
Q12:
Answer: 4
10 divisions between 1.6 to 1.7, so each division represents 0.01. Y is at the 8th division and closer to 1.7
So it is simply:
1.6 + (8 × 0.01)
= 1.6 + 0.08
= 1.68
Q13:
Answer: 2
Ratio of Leela to Janice before Janice gave $40 to Leela
= L : J
= 3 : 7
After Janice gave $40 to Leela, the ratio of Leela to Janice should be
= L : J
= 5 : 5 since they would have same amount of money.
So units of money Janice gave to Leela would be = 7 - 5 = 2 units
2 units -> $40
1 unit -> $20
Janice had 7 units at first:
7 units -> $20 × 7 = $140
Q14:
Answer: 3
6.97 is 0.03 away from 7 (2nd nearest)
6.89 is 0.11 away from 7 (farthest)
7.02 is 0.02 away from 7 (nearest)
7.10 is 0.10 away from 7 (2nd farthest)
Q15:
Answer: 4
3/4 is greater than 2/3. So if we multiply 3/4 by the larger number, the number can only be greater than the product of the smaller number multiplied by 2/3.
For example:
3/4 (greater than 2/3) × greater number cannot be equal to 2/3 (smaller than 3/4) × smaller number.
So for the product of both numbers to be equal:
3/4 × small number = 2/3 × 36
3/4 × small number = 24
Small number = 24 ÷ 3/4
= 24 × 4/3
= 32
Question 16 to 25 carries 1 mark each.
Q16:
Answer: 8 0000
Missing number = 80 × 1 000 = 80 000
Q17:
Answer: 909 099
nine hundred and nine thousand is 909 000
ninety-nine is 99
So 909 000 + 99 = 909 099
Q18:
Answer: 1/40
0.025 = 25/1000 (divided by common factor 25) = 1/40
Q19:
Answer: 30.07kg
1 000g = 1kg = 1.0kg
1 g = 1/1000 kg = 0.001kg
70 g = 70/1000 kg = 0.070kg
30kg 70 g = 30.070 kg = 30.07kg
Q20:
Answer: 1.55ℓ
1 000ml = 1.0ℓ
1 450ml = 1.45ℓ
Difference in capacity -> 3.00ℓ - 1.45ℓ = 1.55ℓ
Q21:
Answer: 2/15
1 whole -> the plot of land
Garden -> 2/5 of the land
Roses -> 1/3 of the garden
Fraction of land used by roses -> 1/3 of the garden which is 2/5 of the land
= 1/3 × 2/5
= 2/15
Q22:
Answer: 11
3 × 7/12 = 21/12
The numbers at the top must add up to 21.
So the missing number in the box is:
21 - 5 - 5 = 11
Q23:
Answer: 2/27
8/9 ÷ 12
= 8/9 × 1/12
= 2/27
Q24:
Answer: 1/2
When the base and the height of a triangle is the length and the breadth of a rectangle, then the area of that triangle is half of the area of the given rectangle.
So 1/2 of the rectangle ABCD is shaded.
Q25:
Answer 5:11
Length of PQ -> 5 units
Length of PS -> 11 units
Ratio of PQ to PS = 5: 11
Question 26 to 30 carries 2 marks each.
Q26:
Answer: 5/16
Half way between 1/8 and 3/8 is 2/8.
Half way between 2/8 and 3/8 will be changing 2/8 and 3/8 to smaller denominators to compare.
So:
2/8 (multiplied top and bottom by 2)= 4/16
3/8 (multiplied top and bottom by 2)= 6/16
In between 4/16 and 6/16 will be 5/16.
Q27:
Answer: $40
For Wei Li to give $20 to Alex and for them to have equal amount of money, it means that Wei Li has twice the amount of $20 to give away.
So:
$20 × 2 = $40.
Q28a:
Answer: 8 499 (1 mark)
7 999 can be rounded up to 8 000, but it is not the largest possible number. Remember also that 8 499 can be rounded off and downwards to 8 000 as the nearest thousand.
Q28b:
Answer: 7 500 (1 mark)
Smallest possible number will be 7 500 since we are asked to round off to the nearest thousand. We need only to consider the digit in the hundreds place value.
Q29:
Answer:22
$15 can buy 2 sets of apples at $6.50 per set with $2 left.
$6.50 × 2 = $13
$15 - $13 = $2
$2 can buy 2 more apples at $0.80 with $0.40 left.
Number of apples in 2 sets of $6.50 apples -> 2 × 10 = 20 apples
Number of apples at $0.80 each -> 1 × 2 = 2 apples
Maximum number of apples -> 22 apples.
Q30:
Answer: Q and R OR Q and S
PQRS is a square made up of 4 parts namely P, Q, R and S
If R and S are squares and each is 1/4 of the figure, then they add up to half of the area of rectangle PQRS.
Q and P will also add up to half of the area of the figure. Notice P is just a small triangle while Q is a square added with a small triangle. So if we cut up all squares to be like P, we will have 8 equal triangles like P. Each triangle like P will be 1/8 of the figure.
To get 5/8, we can see that Q is 3/8 (3 equal pieces of triangle) and either R or S is 2/8.
Together Q and S or Q and R will form 5/8 of the figure.
Total marks: 40
Question 1 to 10 carries 1 mark each.
Question:
Q1:
Answer: 3
4 212 ÷ 4 = 1 053 (no remainders)
4 122 ÷ 4 = 1 030 R 2 (not correct)
4 126 ÷ 4 = 1 031 R 2 (not correct)
4 218 ÷ 4 = 1 054 R 2 (not correct)
Q2:
Answer: 2
The first shape in the pattern will be in the 1st, 5th,9th,13th… 49th position.
Every pattern repeats itself after 4 counts.
Hence the 50th position will be the next pattern in line which is the rectangle.
Q3:
Answer: 2
4.05 × 200 is the same as:
4.05 × 2 × 100 = 8.10 × 100
= 810
Q4:
Answer: 2
Monday -> 2.4km
Tuesday -> 1 650m = 1.65km
Total -> 2.4km + 1.65km
= 4.05km
Q5:
Answer: 3
Common sense: There cannot be a packet of orange juice which contains 750 ℓ of orange juice! That will be too heavy and too much for anyone to carry and drink! We don’t measure amount of orange juice in cm or m as well! They are for measuring length and distance. So the most reasonable answer is ml!
Q6:
Answer: 3
Express 1/3 as a like fraction to all the options provided.
1/3 = 3/9 = 5/15 = 6/18 = 7/21
Only option 3 which is 7/18 will be greater than 6/18 which is also equivalent to 1/3 .
Q7:
Answer: 4
DC is 4 times the length of ED. This means that we can make 8 equal triangles like triangle CDE out of the square ABCD.
So since one triangle is shaded out of 8 possible triangles, the fraction is 1/8.
Q8:
Answer: 1
6 children -> 3/4 of a pizza
1 children -> ¾ ÷ 6 = ¾ × 1/6
= 1/8
Q9:
Answer: 1
Base of shaded triangle = length of YZ
= 9cm - 5cm
= 4cm
Height of shaded triangle = 12cm
Area of shaded triangle = 1/2 × base × height
= 1/2 × 4 × 12
= 2 × 12
= 24cm2
Q10:
Answer: 3
Girls -> 22
Boys -> 18
Total -> 40
Ratio of girls to total number of pupils in class
= 22 : 40
divided by common factor 2)
= 11 : 20
Question 11 to 15 carries 2 marks each.
Q11:
Answer: 4
15 - 5 × 0 + 20 ÷ 5
= 15 - 0 + 4
= 15 + 4
= 19
Q12:
Answer: 4
10 divisions between 1.6 to 1.7, so each division represents 0.01. Y is at the 8th division and closer to 1.7
So it is simply:
1.6 + (8 × 0.01)
= 1.6 + 0.08
= 1.68
Q13:
Answer: 2
Ratio of Leela to Janice before Janice gave $40 to Leela
= L : J
= 3 : 7
After Janice gave $40 to Leela, the ratio of Leela to Janice should be
= L : J
= 5 : 5 since they would have same amount of money.
So units of money Janice gave to Leela would be = 7 - 5 = 2 units
2 units -> $40
1 unit -> $20
Janice had 7 units at first:
7 units -> $20 × 7 = $140
Q14:
Answer: 3
6.97 is 0.03 away from 7 (2nd nearest)
6.89 is 0.11 away from 7 (farthest)
7.02 is 0.02 away from 7 (nearest)
7.10 is 0.10 away from 7 (2nd farthest)
Q15:
Answer: 4
3/4 is greater than 2/3. So if we multiply 3/4 by the larger number, the number can only be greater than the product of the smaller number multiplied by 2/3.
For example:
3/4 (greater than 2/3) × greater number cannot be equal to 2/3 (smaller than 3/4) × smaller number.
So for the product of both numbers to be equal:
3/4 × small number = 2/3 × 36
3/4 × small number = 24
Small number = 24 ÷ 3/4
= 24 × 4/3
= 32
Question 16 to 25 carries 1 mark each.
Q16:
Answer: 8 0000
Missing number = 80 × 1 000 = 80 000
Q17:
Answer: 909 099
nine hundred and nine thousand is 909 000
ninety-nine is 99
So 909 000 + 99 = 909 099
Q18:
Answer: 1/40
0.025 = 25/1000 (divided by common factor 25) = 1/40
Q19:
Answer: 30.07kg
1 000g = 1kg = 1.0kg
1 g = 1/1000 kg = 0.001kg
70 g = 70/1000 kg = 0.070kg
30kg 70 g = 30.070 kg = 30.07kg
Q20:
Answer: 1.55ℓ
1 000ml = 1.0ℓ
1 450ml = 1.45ℓ
Difference in capacity -> 3.00ℓ - 1.45ℓ = 1.55ℓ
Q21:
Answer: 2/15
1 whole -> the plot of land
Garden -> 2/5 of the land
Roses -> 1/3 of the garden
Fraction of land used by roses -> 1/3 of the garden which is 2/5 of the land
= 1/3 × 2/5
= 2/15
Q22:
Answer: 11
3 × 7/12 = 21/12
The numbers at the top must add up to 21.
So the missing number in the box is:
21 - 5 - 5 = 11
Q23:
Answer: 2/27
8/9 ÷ 12
= 8/9 × 1/12
= 2/27
Q24:
Answer: 1/2
When the base and the height of a triangle is the length and the breadth of a rectangle, then the area of that triangle is half of the area of the given rectangle.
So 1/2 of the rectangle ABCD is shaded.
Q25:
Answer 5:11
Length of PQ -> 5 units
Length of PS -> 11 units
Ratio of PQ to PS = 5: 11
Question 26 to 30 carries 2 marks each.
Q26:
Answer: 5/16
Half way between 1/8 and 3/8 is 2/8.
Half way between 2/8 and 3/8 will be changing 2/8 and 3/8 to smaller denominators to compare.
So:
2/8 (multiplied top and bottom by 2)= 4/16
3/8 (multiplied top and bottom by 2)= 6/16
In between 4/16 and 6/16 will be 5/16.
Q27:
Answer: $40
For Wei Li to give $20 to Alex and for them to have equal amount of money, it means that Wei Li has twice the amount of $20 to give away.
So:
$20 × 2 = $40.
Q28a:
Answer: 8 499 (1 mark)
7 999 can be rounded up to 8 000, but it is not the largest possible number. Remember also that 8 499 can be rounded off and downwards to 8 000 as the nearest thousand.
Q28b:
Answer: 7 500 (1 mark)
Smallest possible number will be 7 500 since we are asked to round off to the nearest thousand. We need only to consider the digit in the hundreds place value.
Q29:
Answer:22
$15 can buy 2 sets of apples at $6.50 per set with $2 left.
$6.50 × 2 = $13
$15 - $13 = $2
$2 can buy 2 more apples at $0.80 with $0.40 left.
Number of apples in 2 sets of $6.50 apples -> 2 × 10 = 20 apples
Number of apples at $0.80 each -> 1 × 2 = 2 apples
Maximum number of apples -> 22 apples.
Q30:
Answer: Q and R OR Q and S
PQRS is a square made up of 4 parts namely P, Q, R and S
If R and S are squares and each is 1/4 of the figure, then they add up to half of the area of rectangle PQRS.
Q and P will also add up to half of the area of the figure. Notice P is just a small triangle while Q is a square added with a small triangle. So if we cut up all squares to be like P, we will have 8 equal triangles like P. Each triangle like P will be 1/8 of the figure.
To get 5/8, we can see that Q is 3/8 (3 equal pieces of triangle) and either R or S is 2/8.
Together Q and S or Q and R will form 5/8 of the figure.
Answers for Practice Paper 5 - Paper 2
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)
Answers for Practice Paper 8 - Paper 1
Practice Paper 5, Paper 1:
Total marks: 40
Question 1 to 10 carries 1 mark each.
Question:
Q1:
Answer: 4
Digit 7 is in ten thousands place value, so the value of it is 7 × 10 000 = 70 000
Q2:
Answer: 4
2 350 × 80
= 2350 × 8 × 10
= 1 8800 × 10
= 188 000
Q3:
Answer: 2
Volume = length × breadth × height
= 14 × 7 × 9
= 882 cm3
Q4:
Answer: 2
Change 5 and 3/4 to be improper fraction with 3 wholes and 11/4. The missing number is 11.
Q5:
Answer: 2
7 and 8/9 as improper fraction will be 71/9.
How do we get 71? We take 7 wholes multiplied by denominator 9 to be 63. Then we take 63 + 7 to be 71.
Q6:
Answer: 2
Tessellation should be repeated patterns following a sequence which leaves no gaps in between shapes.
Only option 2 leaves a gap and is not repeated by following a sequence.
Q7:
Answer: 2
thousandths refer to the 3rd decimal place. 1 thousandths is 0.001.
So the digit in the thousandths place value would be 2
Q8:
Answer: 2
0.125 = 125 / 1000
(divide numerator and denominator by common factor 125)
= 1/8
Q9:
Answer: 1
Equivalent ratio of 24 : 32 is 6 : 8 when we divide 24 and 32 by common factor 4.
Missing number will be 6 which is option 1.
Q10:
Answer: 4
MULTIPLY 19 912 BY 5 FIRST BEFORE ROUNDING OFF TO THE NEAREST THOUSAND.
19 912 × 5
= 99 560
≈ 100 000 (Round off to nearest thousand)
NEVER ROUND OFF 19 912 TO THE NEAREST THOUSAND BEFORE YOU MULTIPLY! That is the WRONG METHOD. SOMETIMES YOU WILL GET THE WRONG AND DIFFERENT ANSWER.
Wrong method:
19 912 ≈ 20 000
20 000 × 5 = 100 000
You may get to the right answer this time round with the number 19 912 but if the number if 19 499 it will be wrong. For example:
19 499 ≈ 19 000 (round off to nearest thousand)
19 000 × 5 = 95 000
as compared to:
19 499 × 5 = 97 495
97 495 ≈ 97 000 (round off to nearest thousand)
Can you see that the 2 different methods will give two different answers. So make sure you multiply first before rounding off!
Question 11 to 15 carries 2 marks each.
Q11:
Answer: 4
Instead of trying your luck by counting the number of squares and possibly getting it wrong, you can be sure by finding the area of the big rectangle of 12cm2 first.
Then find the area of the 3 small triangles and take them away from the area of the big rectangle.
Area of small triangle 1 = 1/2 × 2 × 3 = 3 cm2
Area of small triangle 2 = 1/2 × 2 × 1 = 1 cm2
Area of small triangle 3 = 1/2 × 2 × 4 = 4 cm2
So area of triangle ABC = 12 - 3 - 1 - 4
= 4 cm2
Q12:
Answer: 3
No matter how you would draw a line of symmetry to cut the parallelogram, it will not have an exact reflection of a half.
Q13:
Answer: 3
Multiples of 4:
4, 8, 12, 16, 20, 24...
Multiples of 6:
6, 12, 18, 24...
1st two common multiples of 4 and 6 are 12 and 24.
12 × 24 = 288
Q14:
Answer: 4
Volume of 1 cube = 1 × 1 × 1 = 1cm3
Number of cubes -> 6 + 6 + 4 + 3 = 19 cubes
Volume of 19 cubes -> 19 × 1 = 19cm3
Q15:
Answer: 3
2/9 is represented by 28 pages
1/9 is represented by 28 ÷ 2 = 14 pages
1 whole book-> 14 × 9 = 126 pages
Question 16 to 25 carries 1 mark each.
Q16:
Answer: 2 718
Each number is lesser than the previous one progressively with one more taken away.
For example 2 741 to 2 730 is 11 taken away.
2 705 to 2 691 is 14 taken away.
2 691 to 2 676 is 15 taken away.
So what number after 2730 is 12 taken away, and that this number, by taking away 13 will be 2 705.
2 730 - 12 = 2 718
2718 - 13 = 2 705
Q17:
Answer: 0.87
2 tenths = 0.20
67 hundredths = 6 tenths and 7 hundredths = 0.67
Total -> 0.20 + 0.67
= 0.87
Q18:
Answer: 0.200
10 divisions -> 0.25ℓ
1 division -> 0.25 ÷ 10 = 0.025ℓ
8 divisions -> 8 × 0.025ℓ = 0.200ℓ
= 0.2ℓ
Q19:
Answer: To be shown on Tuesday
Q20:
Answer: To be shown on Tuesday
Q21:
Answer: 5 and 17/40
Change denominator to be like fractions with common denominator of 40.
3 and 4/5 + 1 and 5/8 = 3 and 32/40 + 1 and 25/40
= 4 and 57/40
= 5 and 17/40
Q22:
Answer: 5 and 31/125
5.248 = 5 and 248/1000 (divide numerator and denominator by common factor 8)
= 5 and 31/125
Q23:
Answer: $1.50
5 pens -> $2.50
1 pen -> $2.50 ÷ 5 = $0.50
3 pens -> $0.50 × 3 = $1.50
Q24:
Answer -> 5.6
Number X is likely to be 5.647 or 5.648, but we are asked to round the number off to 1 decimal place, so we looked at the digit in the hundredths place.
5.64 ≈ 5.6 (round off to 1 decimal place)
Q25:
Answer -> 3 : 4
24 out of 42 pupils are girls.
Boys -> 42 - 24 = 18 boys
Ratio of boys to girls = 18 : 24 (greatest common factor is 6)
= 3 : 4
Question 26 to 30 carries 2 marks each.
Q26:
Answer: 12
Marbles David had after winning and before giving away -> 28 + 17 = 45 marbles.
Marbles he had before winning 33 -> 45 - 33 = 12
Q27:
Answer: 112
B DM AS means brackets first, then depending on which one comes first from the left, division and multiplication, followed by, again, depending on which one comes first from the left to the right, addition and subtraction.
120 - 60 ÷ (11 + 4) × 2
= 120 - 60 ÷ 15 × 2
= 120 - 4 × 2
= 120 - 8
= 112
Q28:
Answer: 48
Volume of one 3-cm cube = length × base × height
= 3 × 3 × 3
= 27 cm3
Volume of rectangular tank = length × base × height
= 20 × 6 × 12
= 1 440 cm3
HOWEVER IT IS NOT POSSIBLE TO CUT UP CUBES TO FIT NICELY IN THIS RECTANGULAR TANK. So we must consider the number of cubes which can fit in by considering the 3 dimensions.
Along the length, we can fit in only 6 cubes in a row which have a length of 18cm.
Along the breadth, we can fit in 2 rows of cubes with 6cm.
Along the height, we can fit in 4 rows of cubes with 12cm.
So when we multiply the rows in 3 dimension, we can find the maximum number of 3-cm cubes which will fit into this tank.
6 × 2 × 4
= 48 cubes
Q29:
Answer: 4 080cm3
Length and breadth of tank did not change, what changes would be the height which affects the volume of water in tank.
Height of tank = 10cm
Height of water = 8cm
If water is filled up to 10cm , the volume of water will be capacity of tank which is 5 100cm3.
So for every 1 cm of height of tank, volume of water will be 5 100 ÷ 10 = 510 cm3
8cm height -> 8 × 510 = 4080 cm3
Q30:
Answer: 25 tiles
1 square is made up of 4 triangular tiles.
1 triangular tile -> 1/4 of a square
Empty spaces is about 6 and 1/4 square missing.
6 and 1/4 = 25/4 = 25 × 1/4 of a square
= 25 × triangular tiles
Total marks: 40
Question 1 to 10 carries 1 mark each.
Question:
Q1:
Answer: 4
Digit 7 is in ten thousands place value, so the value of it is 7 × 10 000 = 70 000
Q2:
Answer: 4
2 350 × 80
= 2350 × 8 × 10
= 1 8800 × 10
= 188 000
Q3:
Answer: 2
Volume = length × breadth × height
= 14 × 7 × 9
= 882 cm3
Q4:
Answer: 2
Change 5 and 3/4 to be improper fraction with 3 wholes and 11/4. The missing number is 11.
Q5:
Answer: 2
7 and 8/9 as improper fraction will be 71/9.
How do we get 71? We take 7 wholes multiplied by denominator 9 to be 63. Then we take 63 + 7 to be 71.
Q6:
Answer: 2
Tessellation should be repeated patterns following a sequence which leaves no gaps in between shapes.
Only option 2 leaves a gap and is not repeated by following a sequence.
Q7:
Answer: 2
thousandths refer to the 3rd decimal place. 1 thousandths is 0.001.
So the digit in the thousandths place value would be 2
Q8:
Answer: 2
0.125 = 125 / 1000
(divide numerator and denominator by common factor 125)
= 1/8
Q9:
Answer: 1
Equivalent ratio of 24 : 32 is 6 : 8 when we divide 24 and 32 by common factor 4.
Missing number will be 6 which is option 1.
Q10:
Answer: 4
MULTIPLY 19 912 BY 5 FIRST BEFORE ROUNDING OFF TO THE NEAREST THOUSAND.
19 912 × 5
= 99 560
≈ 100 000 (Round off to nearest thousand)
NEVER ROUND OFF 19 912 TO THE NEAREST THOUSAND BEFORE YOU MULTIPLY! That is the WRONG METHOD. SOMETIMES YOU WILL GET THE WRONG AND DIFFERENT ANSWER.
Wrong method:
19 912 ≈ 20 000
20 000 × 5 = 100 000
You may get to the right answer this time round with the number 19 912 but if the number if 19 499 it will be wrong. For example:
19 499 ≈ 19 000 (round off to nearest thousand)
19 000 × 5 = 95 000
as compared to:
19 499 × 5 = 97 495
97 495 ≈ 97 000 (round off to nearest thousand)
Can you see that the 2 different methods will give two different answers. So make sure you multiply first before rounding off!
Question 11 to 15 carries 2 marks each.
Q11:
Answer: 4
Instead of trying your luck by counting the number of squares and possibly getting it wrong, you can be sure by finding the area of the big rectangle of 12cm2 first.
Then find the area of the 3 small triangles and take them away from the area of the big rectangle.
Area of small triangle 1 = 1/2 × 2 × 3 = 3 cm2
Area of small triangle 2 = 1/2 × 2 × 1 = 1 cm2
Area of small triangle 3 = 1/2 × 2 × 4 = 4 cm2
So area of triangle ABC = 12 - 3 - 1 - 4
= 4 cm2
Q12:
Answer: 3
No matter how you would draw a line of symmetry to cut the parallelogram, it will not have an exact reflection of a half.
Q13:
Answer: 3
Multiples of 4:
4, 8, 12, 16, 20, 24...
Multiples of 6:
6, 12, 18, 24...
1st two common multiples of 4 and 6 are 12 and 24.
12 × 24 = 288
Q14:
Answer: 4
Volume of 1 cube = 1 × 1 × 1 = 1cm3
Number of cubes -> 6 + 6 + 4 + 3 = 19 cubes
Volume of 19 cubes -> 19 × 1 = 19cm3
Q15:
Answer: 3
2/9 is represented by 28 pages
1/9 is represented by 28 ÷ 2 = 14 pages
1 whole book-> 14 × 9 = 126 pages
Question 16 to 25 carries 1 mark each.
Q16:
Answer: 2 718
Each number is lesser than the previous one progressively with one more taken away.
For example 2 741 to 2 730 is 11 taken away.
2 705 to 2 691 is 14 taken away.
2 691 to 2 676 is 15 taken away.
So what number after 2730 is 12 taken away, and that this number, by taking away 13 will be 2 705.
2 730 - 12 = 2 718
2718 - 13 = 2 705
Q17:
Answer: 0.87
2 tenths = 0.20
67 hundredths = 6 tenths and 7 hundredths = 0.67
Total -> 0.20 + 0.67
= 0.87
Q18:
Answer: 0.200
10 divisions -> 0.25ℓ
1 division -> 0.25 ÷ 10 = 0.025ℓ
8 divisions -> 8 × 0.025ℓ = 0.200ℓ
= 0.2ℓ
Q19:
Answer: To be shown on Tuesday
Q20:
Answer: To be shown on Tuesday
Q21:
Answer: 5 and 17/40
Change denominator to be like fractions with common denominator of 40.
3 and 4/5 + 1 and 5/8 = 3 and 32/40 + 1 and 25/40
= 4 and 57/40
= 5 and 17/40
Q22:
Answer: 5 and 31/125
5.248 = 5 and 248/1000 (divide numerator and denominator by common factor 8)
= 5 and 31/125
Q23:
Answer: $1.50
5 pens -> $2.50
1 pen -> $2.50 ÷ 5 = $0.50
3 pens -> $0.50 × 3 = $1.50
Q24:
Answer -> 5.6
Number X is likely to be 5.647 or 5.648, but we are asked to round the number off to 1 decimal place, so we looked at the digit in the hundredths place.
5.64 ≈ 5.6 (round off to 1 decimal place)
Q25:
Answer -> 3 : 4
24 out of 42 pupils are girls.
Boys -> 42 - 24 = 18 boys
Ratio of boys to girls = 18 : 24 (greatest common factor is 6)
= 3 : 4
Question 26 to 30 carries 2 marks each.
Q26:
Answer: 12
Marbles David had after winning and before giving away -> 28 + 17 = 45 marbles.
Marbles he had before winning 33 -> 45 - 33 = 12
Q27:
Answer: 112
B DM AS means brackets first, then depending on which one comes first from the left, division and multiplication, followed by, again, depending on which one comes first from the left to the right, addition and subtraction.
120 - 60 ÷ (11 + 4) × 2
= 120 - 60 ÷ 15 × 2
= 120 - 4 × 2
= 120 - 8
= 112
Q28:
Answer: 48
Volume of one 3-cm cube = length × base × height
= 3 × 3 × 3
= 27 cm3
Volume of rectangular tank = length × base × height
= 20 × 6 × 12
= 1 440 cm3
HOWEVER IT IS NOT POSSIBLE TO CUT UP CUBES TO FIT NICELY IN THIS RECTANGULAR TANK. So we must consider the number of cubes which can fit in by considering the 3 dimensions.
Along the length, we can fit in only 6 cubes in a row which have a length of 18cm.
Along the breadth, we can fit in 2 rows of cubes with 6cm.
Along the height, we can fit in 4 rows of cubes with 12cm.
So when we multiply the rows in 3 dimension, we can find the maximum number of 3-cm cubes which will fit into this tank.
6 × 2 × 4
= 48 cubes
Q29:
Answer: 4 080cm3
Length and breadth of tank did not change, what changes would be the height which affects the volume of water in tank.
Height of tank = 10cm
Height of water = 8cm
If water is filled up to 10cm , the volume of water will be capacity of tank which is 5 100cm3.
So for every 1 cm of height of tank, volume of water will be 5 100 ÷ 10 = 510 cm3
8cm height -> 8 × 510 = 4080 cm3
Q30:
Answer: 25 tiles
1 square is made up of 4 triangular tiles.
1 triangular tile -> 1/4 of a square
Empty spaces is about 6 and 1/4 square missing.
6 and 1/4 = 25/4 = 25 × 1/4 of a square
= 25 × triangular tiles
Answers for Practice Paper 8 - Paper 2
Paper 2
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: 4/25
1 whole -> the whole cake
Remaining cake to be shared among 5 children -> 1 whole - 1/5 = 4/5
4/5 shared among 5 children
Fraction of cake each child got -> 4/5 ÷ 5 (M1)
= 4/5 × 1/5
= 4/25 (A1)
Each child got 4/25 of the cake.
Q2:
Answer: 87
7th multiple of 13
= 7 × 13 = 91 (M)1/2
Factors of 8:
1, 2, 4, 8
Factors of 36:
1, 2, 3, 4, 6, 9, 12, 18, 36
Common factor of 8 and 36:
1, 2, 4
Largest common factor of 8 and 36:
4 (M1/2)
Difference between 91 and 4 = 91 - 4 = 87
The difference is 87 (A1)
Q3:
Answer: 5 and 3/7, 5 and 5/7, 5 and 7/5, 5 and 5/3 (A2)
Ascending order means putting from the least to the greatest
Least: 5 and 3/7
2nd: 5 and 5/7
3rd: 5 and 7/5 which is also 6 and 2/5
Greatest: 5 and 5/3 which is 6 and 2/3
Q4:
Answer: 3 060
Ratio of female to male teachers -> 5 : 1
Units of female teachers more than male teachers -> 5 - 1 = 4 units
4 units -> 68
1 unit -> 68 ÷ 4 = 17
Total number of teachers -> 6 units -> 6 × 17 = 102 teachers(M1)
Ratio of teachers to pupils -> 1: 30
1 unit -> 102 teachers
Number of pupils -> 30 units -> 30 × 102 = 3 060 (A1)
The number of pupils would be 3 060
Q5:
Answer: 21 cm2
Area of Triangle DEF and Area of Triangle BCF = Half of Area of Rectangle ABCD
Area of Rectangle ABCD = 714cm2
Half of area of Rectangle ABCD -> 714 ÷ 2 = 357cm2
Area of Triangle DEF = 336cm2
Area of Triangle BCF = 357 - 336 = 21cm2
The area of Triangle BCF is 21cm2.
Q6: 3marks
Answer: 5 304cm3
Shaded area of 1 cuboid -> 780 ÷ 5 = 156cm2 (M1)
Volume of 1 cuboid -> 156 × 34 = 5 304cm3 (M1A1) [Deduct 1m for wrong units]
The volume of 1 cuboid is 5 304cm3
Q7: 3marks
Answer: 250
Ratio of English books to the rest of the books = 4 : 1
Number of units of English books more = 4 - 1 = 3 units
3 units -> 2 400
1 unit -> 2 400 ÷ 3 = 800 (M1)
Ratio of Chinese to Malay to Tamil books = 7 : 5 : 4
Total units = 7 + 5 + 4 = 16 units
16 units -> 800 books (M1)
1 unit -> 800 ÷ 16 = 50
Malay books -> 5 units -> 5 × 50 = 250 (A1)
There are 250 Malay books.
Q8: 3 marks
Answer: 104cm2
Area of Square A = 64cm2 = L × L
= 8cm × 8cm
Length of Square A = 8cm = Base of Triangle B and Base of Triangle C
Height of Triangle B = 25 - 8 = 17cm
Height of Triangle C = 17 - 8 = 9 cm
Area of Triangle B = 1/2 × base of B × height of B
= 1/2 × 8 × 17
= 68cm2 (M1)
Area of Triangle C = 1/2 × base of C × height of C
= 1/2 × 8 × 9
= 36cm2 (M1)
Total area of Triangle B and C = 68cm2 + 36cm2 = 104cm2 (A1)
Q9: 3 marks
Answer: 264
Assume that Mary has 1 unit of stickers.
Then Jane would have 3 times as many as Mary which is 3 units.
Devi has half as many as Jane which is 1/2 × 3 units = 1.5 units
Total number of units -> 1 + 3 + 1.5 = 5.5 units (M1)
5.5 units -> 726 stickers (M1)
1 unit -> 132 stickers
Units Jane has more than Mary -> 3 - 1 = 2 units
2 units -> 132 × 2 = 264 stickers (A1)
Jane has 264 stickers more than Mary.
Q10: 4 marks
Answer: 38
Number of questions answered -> 5/6 of 150 = 5/6 × 150 = 125 questions
Number of correct answers added with number of wrong answers should be equal to 125 questions.
Use guess and check method. (M3)
You should arrive at 87 correct answers and 38 (A2) wrong answers.
To check:
87 correct answers -> 87 × 5 marks = 435 marks
38 wrong answers, with 2 marks deducted for each wrong answer -> 38 × 2 = 76 marks
Total marks -> 435 - 76 = 359 marks.
Q11: 3 marks
Answer: 189cm3
Capacity of tank -> 16cm × 8cm × 7cm = 896cm3
Volume of water with 4 metal balls filled to height of 6cm -> 16cm × 8cm × 6cm = 768cm3
Volume to fill the tank to the max before overflowing -> 896cm3 - 768cm3 = 128cm3 (M1)
Volume of 2 metal balls -> 128cm3 + 250cm3 = 378 cm3 (M1)
Volume of 1 such metal ball -> 378cm3 ÷ 2 - 189cm3 (A1)
Q12: 4 marks
Answer: $960
Model Diagram Method:
To be shown in class.
Ratio Method:
Ratio of Lily to Cindy at first = 5:7
Total units -> 5 + 7 = 12 units
Ratio of Lily to Cindy after Cindy gave $288 to Lily = 13 : 11 since Cindy had 11/13 of Lily's money after giving her $288.
Total units -> 13 + 11 = 24 units
However, the total amount of money they have altogether should not change and should be the same amount before and after Cindy gave $288 to Lily.
So change the first ratio to be the same units as the second one by multiplying both by 2.
5 : 7 = 10 : 14
At first, L : C = 10: 14
After, L : C = 13: 11
Changes in units for Cindy -> 14 - 11 = 3 units
3 units -> $288
1 unit -> $96
Units Lily had at first -> 10 units -> 10 × $96 = $960
Lily had $960 at first.
Q13a and 13b: Error in question, so no answer.
Q14: 4 marks
Answer -> X:26 (A1), Y:26 (A1), Z:624 (A2)
Q15: 5 marks
Answer: 14
Q16a: 5 marks
Answer: $19
Q16b: marks
Answer: $8
Q17:
Answer: 161
Q18a:
Answer: 48
Q18b:
Answer: 420
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: 4/25
1 whole -> the whole cake
Remaining cake to be shared among 5 children -> 1 whole - 1/5 = 4/5
4/5 shared among 5 children
Fraction of cake each child got -> 4/5 ÷ 5 (M1)
= 4/5 × 1/5
= 4/25 (A1)
Each child got 4/25 of the cake.
Q2:
Answer: 87
7th multiple of 13
= 7 × 13 = 91 (M)1/2
Factors of 8:
1, 2, 4, 8
Factors of 36:
1, 2, 3, 4, 6, 9, 12, 18, 36
Common factor of 8 and 36:
1, 2, 4
Largest common factor of 8 and 36:
4 (M1/2)
Difference between 91 and 4 = 91 - 4 = 87
The difference is 87 (A1)
Q3:
Answer: 5 and 3/7, 5 and 5/7, 5 and 7/5, 5 and 5/3 (A2)
Ascending order means putting from the least to the greatest
Least: 5 and 3/7
2nd: 5 and 5/7
3rd: 5 and 7/5 which is also 6 and 2/5
Greatest: 5 and 5/3 which is 6 and 2/3
Q4:
Answer: 3 060
Ratio of female to male teachers -> 5 : 1
Units of female teachers more than male teachers -> 5 - 1 = 4 units
4 units -> 68
1 unit -> 68 ÷ 4 = 17
Total number of teachers -> 6 units -> 6 × 17 = 102 teachers(M1)
Ratio of teachers to pupils -> 1: 30
1 unit -> 102 teachers
Number of pupils -> 30 units -> 30 × 102 = 3 060 (A1)
The number of pupils would be 3 060
Q5:
Answer: 21 cm2
Area of Triangle DEF and Area of Triangle BCF = Half of Area of Rectangle ABCD
Area of Rectangle ABCD = 714cm2
Half of area of Rectangle ABCD -> 714 ÷ 2 = 357cm2
Area of Triangle DEF = 336cm2
Area of Triangle BCF = 357 - 336 = 21cm2
The area of Triangle BCF is 21cm2.
Q6: 3marks
Answer: 5 304cm3
Shaded area of 1 cuboid -> 780 ÷ 5 = 156cm2 (M1)
Volume of 1 cuboid -> 156 × 34 = 5 304cm3 (M1A1) [Deduct 1m for wrong units]
The volume of 1 cuboid is 5 304cm3
Q7: 3marks
Answer: 250
Ratio of English books to the rest of the books = 4 : 1
Number of units of English books more = 4 - 1 = 3 units
3 units -> 2 400
1 unit -> 2 400 ÷ 3 = 800 (M1)
Ratio of Chinese to Malay to Tamil books = 7 : 5 : 4
Total units = 7 + 5 + 4 = 16 units
16 units -> 800 books (M1)
1 unit -> 800 ÷ 16 = 50
Malay books -> 5 units -> 5 × 50 = 250 (A1)
There are 250 Malay books.
Q8: 3 marks
Answer: 104cm2
Area of Square A = 64cm2 = L × L
= 8cm × 8cm
Length of Square A = 8cm = Base of Triangle B and Base of Triangle C
Height of Triangle B = 25 - 8 = 17cm
Height of Triangle C = 17 - 8 = 9 cm
Area of Triangle B = 1/2 × base of B × height of B
= 1/2 × 8 × 17
= 68cm2 (M1)
Area of Triangle C = 1/2 × base of C × height of C
= 1/2 × 8 × 9
= 36cm2 (M1)
Total area of Triangle B and C = 68cm2 + 36cm2 = 104cm2 (A1)
Q9: 3 marks
Answer: 264
Assume that Mary has 1 unit of stickers.
Then Jane would have 3 times as many as Mary which is 3 units.
Devi has half as many as Jane which is 1/2 × 3 units = 1.5 units
Total number of units -> 1 + 3 + 1.5 = 5.5 units (M1)
5.5 units -> 726 stickers (M1)
1 unit -> 132 stickers
Units Jane has more than Mary -> 3 - 1 = 2 units
2 units -> 132 × 2 = 264 stickers (A1)
Jane has 264 stickers more than Mary.
Q10: 4 marks
Answer: 38
Number of questions answered -> 5/6 of 150 = 5/6 × 150 = 125 questions
Number of correct answers added with number of wrong answers should be equal to 125 questions.
Use guess and check method. (M3)
You should arrive at 87 correct answers and 38 (A2) wrong answers.
To check:
87 correct answers -> 87 × 5 marks = 435 marks
38 wrong answers, with 2 marks deducted for each wrong answer -> 38 × 2 = 76 marks
Total marks -> 435 - 76 = 359 marks.
Q11: 3 marks
Answer: 189cm3
Capacity of tank -> 16cm × 8cm × 7cm = 896cm3
Volume of water with 4 metal balls filled to height of 6cm -> 16cm × 8cm × 6cm = 768cm3
Volume to fill the tank to the max before overflowing -> 896cm3 - 768cm3 = 128cm3 (M1)
Volume of 2 metal balls -> 128cm3 + 250cm3 = 378 cm3 (M1)
Volume of 1 such metal ball -> 378cm3 ÷ 2 - 189cm3 (A1)
Q12: 4 marks
Answer: $960
Model Diagram Method:
To be shown in class.
Ratio Method:
Ratio of Lily to Cindy at first = 5:7
Total units -> 5 + 7 = 12 units
Ratio of Lily to Cindy after Cindy gave $288 to Lily = 13 : 11 since Cindy had 11/13 of Lily's money after giving her $288.
Total units -> 13 + 11 = 24 units
However, the total amount of money they have altogether should not change and should be the same amount before and after Cindy gave $288 to Lily.
So change the first ratio to be the same units as the second one by multiplying both by 2.
5 : 7 = 10 : 14
At first, L : C = 10: 14
After, L : C = 13: 11
Changes in units for Cindy -> 14 - 11 = 3 units
3 units -> $288
1 unit -> $96
Units Lily had at first -> 10 units -> 10 × $96 = $960
Lily had $960 at first.
Q13a and 13b: Error in question, so no answer.
Q14: 4 marks
Answer -> X:26 (A1), Y:26 (A1), Z:624 (A2)
Q15: 5 marks
Answer: 14
Q16a: 5 marks
Answer: $19
Q16b: marks
Answer: $8
Q17:
Answer: 161
Q18a:
Answer: 48
Q18b:
Answer: 420
Sunday, May 10, 2009
Regarding Exams...
Dear all,
It's time for our mid year examinations... All the effort you have been putting in so far, have to be heightened and be displayed in all your papers this coming week...
I pray that each of you who have put in all the hard work will be rewarded, and that you will enjoy the fruits of your effort.
Do all that you can within these few days to stay healthy, stress free and be well prepared. It is important to study, but also important to stay healthy.
So eat wise, rest well, and stay focus to make full use of your time effectively and efficiently...
Remember: "Goals are just dreams if we go about them without actions..."
Put your goals down and get into actions!
I pray for the best for your examinations and health!
It's time for our mid year examinations... All the effort you have been putting in so far, have to be heightened and be displayed in all your papers this coming week...
I pray that each of you who have put in all the hard work will be rewarded, and that you will enjoy the fruits of your effort.
Do all that you can within these few days to stay healthy, stress free and be well prepared. It is important to study, but also important to stay healthy.
So eat wise, rest well, and stay focus to make full use of your time effectively and efficiently...
Remember: "Goals are just dreams if we go about them without actions..."
Put your goals down and get into actions!
I pray for the best for your examinations and health!
Saturday, May 02, 2009
Quiet Moments...
It's raining again at this point in time...
Outside my window, I could have a clear view and see how storms could be so terrifying, yet so tantalising... There is some kind of 'charm' in a storm which can mesmerise me...
Yes, I just love the night time, especially when it drizzles or pours! It can be so quiet, so calm... It can be loud, cooling and dark...
Yet, the fast pace you see in day time where everyone is rushing to school, to work or to do something, will not be noticeable during the night time...
You do not have to rush... and everything sort of comes to a standstill...
Today, I spent my whole day marking, marking and more marking...
I went down to school to mark, I went down to town to mark, I went down to Changi Airport to mark...
I marked and marked and marked...
Yet, I would not forget to pamper myself with a short getaway to the rustic feel of nature... I went to have a sumptuous dinner at Changi Village, and I stopped over at the bridge over the river canal and overlooked into the vastness of the sea... It was a great feeling...
It was a reminder to me: "Everything's gonna be alright... Rockabye... Rockabye..."
Reminds me of a song though...
We have tough moments at different times, but these are only seasons, like a storm, it will come and go. Everything will be alright, when we brave through it...
Don't forget to smile at the storms in your life, be brave, and learn to take good breaks once in a while, but not too much.
Hang in there, children...
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