Malaysia · Year 11 · Practice Sheet 13

1. 1.

   A triangle has sides a = 20 cm and b = 19 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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2. 2.

   A body starts at 11 m/s and accelerates at 1.5 m/s² for 11 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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3. 3.

   A population of 9,000 grows 10% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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4. 4.

   Find the gravitational potential energy of a 9 kg object raised 20 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   Find the population standard deviation of: 8, 3, 14, 15, 3 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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6. 6.

   A force of 327 N acts on an area of 1.5 m². Find the pressure.

   Formula:Pressure

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

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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 14 kg object moves at 11 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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9. 9.

   Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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10. 10.

    Find the momentum of a 20 kg object moving at 14 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

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

    Formula:Quadratic Formula

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

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12. 12.

    A force of 188 N acts on an area of 5.9 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A wave has frequency 603 Hz and wavelength 3.46 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    An object has mass 165 g and volume 25 cm³. Find its density.

    Formula:Density

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

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15. 15.

    Find the sum of the first 5 terms of an arithmetic series with first term a = 2 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

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

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16. 16.

    Find the population standard deviation of: 6, 15, 11, 5, 14 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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17. 17.

    Find the gravitational potential energy of a 36 kg object raised 26 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    An object has mass 79.2 g and volume 33 cm³. Find its density.

    Formula:Density

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

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19. 19.

    A triangle has sides a = 11 cm and b = 18 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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20. 20.

    Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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