Morocco · Grade 12 · Practice Sheet 40

1. 1.

   A wave has frequency 323 Hz and wavelength 4.81 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   A force of 271 N acts on an area of 5.7 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   A cone has base radius 2 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

   $V = \tfrac{1}{3} \pi r^2 h$

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4. 4.

   A population of 5,100 grows 10% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

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

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5. 5.

   Find the momentum of a 23 kg object moving at 27 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   In a triangle, a = 8, b = 7 and the included angle C = 50°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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7. 7.

   Two masses 4,800 kg and 720 kg are 4 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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8. 8.

   A force of 402 N acts on an area of 4 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   A device runs at 56 V drawing 8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    MAD 2,500 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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11. 11.

    Solve using the quadratic formula: x² − 2x − 24 = 0.

    Formula:Quadratic Formula

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

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12. 12.

    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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13. 13.

    In a triangle, a = 11, b = 11 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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14. 14.

    A body starts at 12 m/s and accelerates at 2.6 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

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

    Formula:Quadratic Formula

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

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16. 16.

    A current of 7 A flows through a 57 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    Find the momentum of a 40 kg object moving at 15 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    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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19. 19.

    A force of 38 N moves an object 26 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    A force of 186 N acts on an area of 8.2 m². Find the pressure.

    Formula:Pressure

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

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