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Mathematics questions, chapter 2
Nama / NameKelas / ClassTarikh / Date

Standard Form

44 marks. Use Practice to check each answer as you go, or Exam to answer everything first. Show your working for Section B.

Section A: objective questions

12 marks
Choose the correct answer. Each question carries 1 mark.
1

Question 1

How many significant figures does 0.004 050 have?
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C
The zeros before 4 only fix the place value. The digits 4, 0, 5, 0 count: a zero between non-zero digits and a zero at the end of a decimal are both significant. So 4 s.f. (6 counts every digit; 2 ignores both zeros).
For the teacher: Remembering, low difficulty, standard 2.1.1
Textbook p. 34
2

Question 2

Which number has exactly 3 significant figures?
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B
0.0305 has 3, 0, 5. 0.030 50 has 4 (end zero of a decimal counts), and 3.005 and 3 005 have 4 (zeros between non-zero digits).
For the teacher: Understanding, low difficulty, standard 2.1.1
Textbook p. 34
3

Question 3

Round off 0.007 048 2 to 3 significant figures.
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A
The first s.f. is 7; the three s.f. are 7, 0, 4 and the next digit is 8 ≥ 5, so 4 becomes 5: 0.00705. 0.00704 forgets to round up.
For the teacher: Applying, low difficulty, standard 2.1.2
Textbook p. 35
4

Question 4

Round off 45 986 to 2 significant figures.
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D
Keep 4 and 5; the next digit 9 ≥ 5, so 45 becomes 46. Fill the rest with zeros: 46 000. 46 loses the place value.
For the teacher: Applying, low difficulty, standard 2.1.2
Textbook p. 35
5

Question 5

Which of the following is in standard form?
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C
In standard form A × 10n, 1 ≤ A < 10. Only 6.2 satisfies this; 62, 0.62 and 10 do not.
For the teacher: Remembering, low difficulty, standard 2.2.1
Textbook p. 37
6

Question 6

Write 0.000 072 in standard form.
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B
The decimal point moves 5 places to the right to sit after 7, so the index is −5. 72 × 10−6 has A ≥ 10.
For the teacher: Applying, low difficulty, standard 2.2.1
Textbook p. 37
7

Question 7

Write 3.08 × 104 as a single number.
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C
Positive index 4: move the point 4 places to the right. 3.08 → 30 800.
For the teacher: Applying, low difficulty, standard 2.2.1
Textbook p. 38
8

Question 8

Convert 0.85 nanometre to metres. State the answer in standard form. (1 nanometre = 10−9 m)
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A
0.85 × 10−9 = 8.5 × 10−1 × 10−9 = 8.5 × 10−10 m. 8.5 × 10−9 forgets the 0.85 is smaller than 1.
For the teacher: Applying, low difficulty, standard 2.2.1
Textbook p. 38
9

Question 9

Calculate 6.3 × 105 + 4.5 × 106. State the answer in standard form.
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B
6.3 × 105 = 0.63 × 106. 0.63 + 4.5 = 5.13, so 5.13 × 106. Adding the A values (10.8) and the indices wrongly gives the other options.
For the teacher: Applying, low difficulty, standard 2.2.2
Textbook p. 40
10

Question 10

Calculate 8.4 × 10−3 − 2.1 × 10−4. State the answer in standard form.
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D
2.1 × 10−4 = 0.21 × 10−3. 8.4 − 0.21 = 8.19, so 8.19 × 10−3. 6.3 comes from subtracting 2.1 without matching the indices.
For the teacher: Applying, medium difficulty, standard 2.2.2
Textbook p. 41
11

Question 11

Calculate (4.5 × 10−3) × (6 × 105). State the answer in standard form.
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B
4.5 × 6 = 27 and −3 + 5 = 2, so 27 × 102. Since 27 is more than 10, write 2.7 × 103. 27 × 102 is not in standard form.
For the teacher: Applying, medium difficulty, standard 2.2.2
Textbook p. 42
12

Question 12

Calculate (9.6 × 10−5) ÷ (1.2 × 10−2). State the answer in standard form.
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D
9.6 ÷ 1.2 = 8. For division subtract the indices: −5 − (−2) = −3. So 8 × 10−3.
For the teacher: Applying, medium difficulty, standard 2.2.2
Textbook p. 42

Section B: structured questions

32 marks
Answer all questions. Show your working.
13

Question 13

Significant figures.
[2 marks] (a)State the number of significant figures in (i) 6 008 (ii) 0.0420.
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Tick each point you got.
[1 mark] (b)Round off 0.005 972 6 to 3 significant figures.
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Tick each point you got.
For the teacher: Applying, low difficulty, standard 2.1.2
Textbook p. 35
14

Question 14

Change between single numbers and standard form.
[1 mark] (a)Write 540 000 000 in standard form.
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Tick each point you got.
[1 mark] (b)Write 0.000 000 306 in standard form.
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Tick each point you got.
[2 marks] (c)The width of a hair is 450 micrometres. Express it in metres, in standard form. (1 micrometre = 10−6 m)
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Tick each point you got.
For the teacher: Understanding, low difficulty, standard 2.2.1
Textbook p. 38
15

Question 15

Calculate each of the following. State your answers in standard form.
[2 marks] (a)5.2 × 105 + 3.8 × 104
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Tick each point you got.
[2 marks] (b)6.1 × 10−3 − 4.5 × 10−4
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Tick each point you got.
[2 marks] (c)(2.4 × 104) × (3.5 × 10−6)
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Tick each point you got.
[2 marks] (d)(7.2 × 10−5) ÷ (1.8 × 10−8)
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Tick each point you got.
For the teacher: Applying, low difficulty, standard 2.2.2
Textbook p. 41
16

Question 16

Aiman writes: 4.2 × 105 + 3.1 × 104 = 7.3 × 109.
[1 mark] (a)Explain what mistake Aiman made.
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Tick each point you got.
[2 marks] (b)Show the correct answer in standard form.
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Tick each point you got.
For the teacher: Evaluating, medium difficulty, standard 2.2.2
Textbook p. 40
17

Question 17

A grain of sand has mass 2.5 × 10−4 g. A bag of sand has mass 20 kg.
[1 mark] (a)Express the mass of the bag in grams, in standard form.
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Tick each point you got.
[2 marks] (b)Calculate the number of sand grains in the bag. State your answer in standard form.
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Tick each point you got.
For the teacher: Analysing, medium difficulty, standard 2.2.3
Textbook p. 43
18

Question 18

Light travels a distance of 3.0 × 105 km in one second.
[2 marks] (a)Calculate the distance light travels in one hour, in km. State your answer in standard form.
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Tick each point you got.
[2 marks] (b)The distance from the Sun to the Earth is 1.496 × 108 km. How long does light take to travel this distance? State your answer in seconds, in standard form correct to 3 significant figures.
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Tick each point you got.
For the teacher: Analysing, medium difficulty, standard 2.2.3
Textbook p. 43
19

Question 19

A rectangular piece of land measures 2.4 × 103 m by 5 × 102 m. The land costs RM3.50 per square metre.
[2 marks] (a)Calculate the area of the land in m2, in standard form.
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Tick each point you got.
[1 mark] (b)Calculate the total cost of the land in RM, in standard form.
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Tick each point you got.
For the teacher: Applying, medium difficulty, standard 2.2.3
Textbook p. 43
20

Question 20

The diameter of the Moon is 3.474 × 103 km. Surface area of a sphere = 4πr². Use π = 3.142.
[1 mark] (a)State the radius of the Moon in km.
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Tick each point you got.
[3 marks] (b)Calculate the surface area of the Moon in km2. State your answer in standard form correct to 4 significant figures.
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Tick each point you got.
For the teacher: Applying, high difficulty, standard 2.2.3
Textbook p. 44