Algeria · Grade 12 · Practice Sheet 42

1. 1.

   Find the sum of the first 6 terms of a geometric series with first term a = 6 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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2. 2.

   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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3. 3.

   A wave has frequency 154 Hz and wavelength 1.38 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   A device runs at 29 V drawing 8.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   Find the population standard deviation of: 12, 11, 15, 11, 3 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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6. 6.

   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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7. 7.

   A wave has frequency 82 Hz and wavelength 4.26 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   A body starts at 9 m/s and accelerates at 4.2 m/s² for 4 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   A population of 5,200 grows 2% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

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10. 10.

    Find the population standard deviation of: 20, 18, 4, 13, 20 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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11. 11.

    Solve using the quadratic formula: x² + 7x + 6 = 0.

    Formula:Quadratic Formula

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

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12. 12.

    A force of 386 N acts on an area of 4.2 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    Find the force needed to accelerate a 50 kg mass at 4.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    Two masses 7,000 kg and 820 kg are 11 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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15. 15.

    Find the momentum of a 38 kg object moving at 2 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

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

    Formula:Sum of a Geometric Series

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

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17. 17.

    DA 700 is invested at 4% compound interest per annum for 5 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 force needed to accelerate a 33 kg mass at 7.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A wave has frequency 886 Hz and wavelength 0.29 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    Find the gravitational potential energy of a 38 kg object raised 32 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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