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
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