South Africa · Grade 12 · Practice Sheet 18

1. 1.

   Find the gravitational potential energy of a 23 kg object raised 11 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   A population of 6,500 grows 5% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   A 39 kg object moves at 12 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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4. 4.

   Find the sum of the first 8 terms of a geometric series with first term a = 5 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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5. 5.

   Find the sum of the first 10 terms of an arithmetic series with first term a = 9 and common difference d = 1.

   Formula:Sum of an Arithmetic Series

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

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6. 6.

   A wave has frequency 265 Hz and wavelength 2.77 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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8. 8.

   A device runs at 214 V drawing 9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   A force of 271 N acts on an area of 0.8 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    A wave has frequency 423 Hz and wavelength 4.41 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    Find the gravitational potential energy of a 23 kg object raised 34 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    A current of 6.8 A flows through a 16 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    In a triangle, a = 16, b = 5 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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14. 14.

    Find the population standard deviation of: 9, 16, 16, 20, 10 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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15. 15.

    A wave has frequency 51 Hz and wavelength 0.85 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    Solve using the quadratic formula: x² − 6x + 5 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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17. 17.

    R3,300 is invested at 3% 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.

    An object with initial velocity 10 m/s accelerates at 2.3 m/s² for 4 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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19. 19.

    A current of 4.2 A flows through a 46 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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20. 20.

    Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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