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
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