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.
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