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( i ) Find the value of .

1. ( i ) Find the value of. (ii) Simplify ( s 3 ) 4. ( s 3 ) 4. = s 3×4. = s 12. 1. (iii) Find the value of without using your calculator. 2. ( i ) Write 3 × 3 × 3 × 3 × 3 × 3 in the form 3 x , where x ∈ ℕ. 3 × 3 × 3 × 3 × 3 × 3 = 3 6. 3 p × 3 4 = 3 −2.

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( i ) Find the value of .

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  1. 1. (i) Find the value of . (ii) Simplify (s3)4. (s3)4 = s3×4 = s12

  2. 1. (iii) Find the value of without using your calculator.

  3. 2. (i) Write 3 × 3 × 3 × 3 × 3 × 3 in the form 3x, where x ∈ ℕ. 3 × 3 × 3 × 3 × 3 × 3 = 36 3p × 34 = 3−2 (ii) If 3p × 34 = 3−2, write down the value of p. 3p + 4 = 3−2 p + 4 = –2 p = –2 – 4 p = –6

  4. 2. (iii) Write in the form 3n, where n ∈ ℤ.

  5. 3. The mass of water on the earth’s surface is 1·41 × 1018tonnes. The total mass of the earth is 5·97 × 1021tonnes Find the order of magnitude comparison for the mass of water to the total mass of the earth. (i) Mass of water on Earth = 1⋅41 × 1018 Since 1·41 < 5 Order of magnitude = n = 18

  6. 3. The mass of water on the earth’s surface is 1·41 × 1018tonnes. The total mass of the earth is 5·97 × 1021tonnes Find the order of magnitude comparison for the mass of water to the total mass of the earth. (i) Mass of earth = 5⋅97 × 1021 Since 5·97 > 5 Order of magnitude = n + 1 = 21 + 1 = 22

  7. 3. The mass of water on the earth’s surface is 1·41 × 1018tonnes. The total mass of the earth is 5·97 × 1021tonnes Find the order of magnitude comparison for the mass of water to the total mass of the earth. (i)

  8. 3. The mass of water on the earth’s surface is 1·41 × 1018tonnes. The total mass of the earth is 5·97 × 1021tonnes Express the mass of water on the earth’s surface as a percentage of the total mass of the earth. Express your answer in scientific form. (ii)

  9. 4. The speed of light is 299,792,458 metres per second. (i) Write this number in the form a × 10n, where 1 ≤ a ≤ 10 and n ∈ ℤ, correct to one significant figure. Speed of light = 299,792,458 = 2⋅99792458 × 108 = 3 × 108 (correct to one significant figure)

  10. 4. The speed of light is 299,792,458 metres per second. (ii) Find the order of magnitude estimate for the speed of light. Speed of light = 2⋅99792458 × 108 Since 2·99… < 5 Order of magnitude = n = 8

  11. 5. Simplify (n2)3 × n−10. Give your answer with a positive power. (n2)3 × n−10 = n2×3 × n−10 = n6 × n−10 = n6 + (− 10) = n−4 =

  12. 6. Calculate the value of Write your answer in the form a × 10n, where 1 ≤ ≤ 10 and n ∈ ℤ, correct to three significant figures.

  13. 7. (i) The earth is approximately spherical with a radius of 6,400 km. Calculate the volume of the earth, giving your answer in scientific notation, correct to two significant figures. Volume of sphere

  14. 7. • The approximate volume of the moon is 2·2 × 1010cubic kilometres. • Calculate how many times the earth’s volume is greater than the moon’s. Therefore, the Earth’s volume is 50 times greater than the Moon’s.

  15. 8. (i) Express 9 and 27 in the form 3n where n ∈ ℤ. 9 = 32 27 = 33

  16. 8. 9(3x) = 27x − 1 (ii) Hence or otherwise, solve for if x 9(3x) = 27x − 1 32(3x) = (33)x – 1 32 + x = 33x – 3 2 + x = 3x – 3 –3x + x = –3 – 2 –2x = –5 = =

  17. 9. Solve for x in the following equation:

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