Egypt · Grade 12 · Practice Sheet 28

1. 1.

   A device runs at 224 V drawing 3.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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2. 2.

   Solve using the quadratic formula: x² − 3x − 10 = 0.

   Formula:Quadratic Formula

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

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3. 3.

   A population of 2,300 grows 3% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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4. 4.

   Find the force needed to accelerate a 20 kg mass at 7.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   A wave has frequency 295 Hz and wavelength 2.11 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   Find the population standard deviation of: 5, 6, 2, 9, 17 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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8. 8.

   A current of 3.7 A flows through a 14 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   A 35 kg object moves at 5 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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10. 10.

    Find the force needed to accelerate a 39 kg mass at 5.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A force of 12 N moves an object 14 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    A current of 5.8 A flows through a 55 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    Find the gravitational potential energy of a 29 kg object raised 4 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    A body starts at 6 m/s and accelerates at 4.5 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    Find the force needed to accelerate a 38 kg mass at 0.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    In a triangle, a = 10, b = 15 and the included angle C = 100°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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17. 17.

    A current of 7.2 A flows through a 20 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    A device runs at 222 V drawing 6.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A population of 6,600 grows 10% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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20. 20.

    E£ 2,600 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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