Cambodia · Grade 11 · Practice Sheet 3

1. 1.

   Find the force needed to accelerate a 8 kg mass at 8.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   Find the sum of the first 13 terms of an arithmetic series with first term a = 8 and common difference d = 2.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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3. 3.

   Find the population standard deviation of: 10, 7, 14, 3, 18 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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4. 4.

   ៛ 2,700 is invested at 5% compound interest per annum for 3 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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5. 5.

   Find the momentum of a 1 kg object moving at 13 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A 18 kg object moves at 21 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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7. 7.

   Solve using the quadratic formula: x² + 8x + 12 = 0.

   Formula:Quadratic Formula

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

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8. 8.

   A triangle has sides a = 11 cm and b = 19 cm with an included angle C = 120°. 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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9. 9.

   A cylinder has radius 5 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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10. 10.

    A triangle has sides a = 10 cm and b = 14 cm with an included angle C = 45°. 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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11. 11.

    A body starts at 2 m/s and accelerates at 4.9 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    In a triangle, a = 9, b = 16 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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13. 13.

    Two masses 6,200 kg and 270 kg are 12 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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14. 14.

    An object has mass 40.3 g and volume 31 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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15. 15.

    A force of 96 N moves an object 37 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    A force of 53 N acts on an area of 5.8 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    Find the force needed to accelerate a 28 kg mass at 4.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    Find the sum of the first 9 terms of an arithmetic series with first term a = 3 and common difference d = 6.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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19. 19.

    A triangle has sides a = 6 cm and b = 15 cm with an included angle C = 90°. 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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20. 20.

    A force of 70 N acts on an area of 1.1 m². Find the pressure.

    Formula:Pressure

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

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