United Arab Emirates · Grade 12 · Practice Sheet 32

1. 1.

   Two masses 4,900 kg and 490 kg are 8 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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2. 2.

   An object with initial velocity 2 m/s accelerates at 3.2 m/s² for 5 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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3. 3.

   Solve using the quadratic formula: x² + 3x + 2 = 0.

   Formula:Quadratic Formula

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

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4. 4.

   A force of 438 N acts on an area of 3.3 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   A device runs at 223 V drawing 1.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   Find the gravitational potential energy of a 29 kg object raised 2 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   AED 3,000 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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8. 8.

   A wave has frequency 418 Hz and wavelength 0.58 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   A force of 421 N acts on an area of 3.1 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    Find the momentum of a 9 kg object moving at 30 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    A population of 8,600 grows 10% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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12. 12.

    A current of 2.3 A flows through a 41 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 8 kg object raised 8 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    In a triangle, a = 5, b = 13 and the included angle C = 40°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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15. 15.

    A current of 5.1 A flows through a 28 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    Solve using the quadratic formula: x² − 2x − 3 = 0.

    Formula:Quadratic Formula

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

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17. 17.

    Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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18. 18.

    An object with initial velocity 12 m/s accelerates at 4.5 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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19. 19.

    A population of 1,800 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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20. 20.

    Find the gravitational potential energy of a 2 kg object raised 13 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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