Hong Kong · Grade 12 · Practice Sheet 42

1. 1.

   Find the sum of the first 10 terms of an arithmetic series with first term a = 9 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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2. 2.

   A force of 217 N acts on an area of 4.8 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

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3. 3.

   A current of 3.1 A flows through a 15 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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4. 4.

   An object with initial velocity 14 m/s accelerates at 2.3 m/s² for 8 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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5. 5.

   Find the sum of the first 5 terms of a geometric series with first term a = 7 and common ratio r = 2.

   Formula:Sum of a Geometric Series

   $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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6. 6.

   An object with initial velocity 12 m/s accelerates at 3.9 m/s² for 10 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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7. 7.

   A force of 439 N acts on an area of 8.7 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

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8. 8.

   A force of 78 N moves an object 2 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   Find the gravitational potential energy of a 22 kg object raised 18 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    A force of 19 N moves an object 30 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    Find the gravitational potential energy of a 28 kg object raised 21 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    A force of 50 N moves an object 25 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    A cone has base radius 9 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

    $V = \tfrac{1}{3} \pi r^2 h$

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14. 14.

    Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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15. 15.

    Find the sum of the first 4 terms of a geometric series with first term a = 3 and common ratio r = 2.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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16. 16.

    A population of 4,500 grows 2% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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17. 17.

    HK$ 500 is invested at 6% compound interest per annum for 2 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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18. 18.

    Find the population standard deviation of: 7, 16, 6, 3, 15 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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19. 19.

    Find the sum of the first 7 terms of an arithmetic series with first term a = 4 and common difference d = 5.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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20. 20.

    A wave has frequency 842 Hz and wavelength 1.41 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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