China · Grade 12 · Practice Sheet 4

1. 1.

   A population of 8,800 grows 3% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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2. 2.

   A force of 433 N acts on an area of 3.8 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   Two masses 1,600 kg and 800 kg are 18 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

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4. 4.

   Find the sum of the first 5 terms of a geometric series with first term a = 6 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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5. 5.

   A force of 204 N acts on an area of 9.7 m². Find the pressure.

   Formula:Pressure

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

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6. 6.

   Find the population standard deviation of: 4, 17, 14, 5, 5 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   A 23 kg object moves at 22 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2} m v^2$

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8. 8.

   Find the sum of the first 8 terms of an arithmetic series with first term a = 5 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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9. 9.

   A wave has frequency 443 Hz and wavelength 0.67 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    Find the force needed to accelerate a 52 kg mass at 1.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    An object with initial velocity 10 m/s accelerates at 2.1 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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12. 12.

    Find the momentum of a 44 kg object moving at 11 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    ¥3,500 is invested at 6% compound interest per annum for 4 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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14. 14.

    Find the sum of the first 3 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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15. 15.

    Find the force needed to accelerate a 33 kg mass at 4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    A wave has frequency 100 Hz and wavelength 3.09 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    Find the gravitational potential energy of a 10 kg object raised 15 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    Find the sum of the first 5 terms of a geometric series with first term a = 6 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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19. 19.

    A 12 kg object moves at 21 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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20. 20.

    A triangle has sides a = 17 cm and b = 7 cm with an included angle C = 90°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

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