Cambodia · Grade 12 · Practice Sheet 10

1. 1.

   Find the force needed to accelerate a 51 kg mass at 4.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   A body starts at 12 m/s and accelerates at 1.7 m/s² for 12 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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3. 3.

   In a triangle, a = 9, b = 17 and the included angle C = 60°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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4. 4.

   A wave has frequency 535 Hz and wavelength 4.72 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   A triangle has sides a = 7 cm and b = 11 cm with an included angle C = 30°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

   $A = \tfrac{1}{2} ab\sin C$

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6. 6.

   A current of 6 A flows through a 60 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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7. 7.

   A 39 kg object moves at 22 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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8. 8.

   A device runs at 138 V drawing 9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   Solve using the quadratic formula: x² + 1x − 12 = 0.

   Formula:Quadratic Formula

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

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10. 10.

    A force of 369 N acts on an area of 5.8 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    An object with initial velocity 14 m/s accelerates at 1.3 m/s² for 7 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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12. 12.

    Solve using the quadratic formula: x² + 6x + 8 = 0.

    Formula:Quadratic Formula

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

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13. 13.

    Find the population standard deviation of: 14, 4, 6, 8, 2 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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14. 14.

    A body starts at 14 m/s and accelerates at 2.2 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    A current of 6.5 A flows through a 40 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    Find the momentum of a 48 kg object moving at 11 m/s.

    Formula:Momentum

    $p = mv$

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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.

    Solve using the quadratic formula: x² + 1x − 2 = 0.

    Formula:Quadratic Formula

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

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19. 19.

    A population of 1,200 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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20. 20.

    Find the sum of the first 20 terms of an arithmetic series with first term a = 10 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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