Vietnam · Grade 11 · Practice Sheet 32

1. 1.

   An object with initial velocity 2 m/s accelerates at 3.1 m/s² for 9 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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2. 2.

   Find the sum of the first 18 terms of an arithmetic series with first term a = 7 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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3. 3.

   Find the force needed to accelerate a 10 kg mass at 3.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   A 33 kg object moves at 24 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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5. 5.

   A cylinder has radius 6 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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6. 6.

   A current of 2.6 A flows through a 22 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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7. 7.

   A cylinder has radius 7 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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8. 8.

   A device runs at 78 V drawing 6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   Two masses 3,600 kg and 260 kg are 20 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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10. 10.

    A current of 1.2 A flows through a 43 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    A wave has frequency 820 Hz and wavelength 1.26 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    An object has mass 34.1 g and volume 11 cm³. Find its density.

    Formula:Density

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

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13. 13.

    A 9 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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14. 14.

    Solve using the quadratic formula: x² + 0x − 9 = 0.

    Formula:Quadratic Formula

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

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15. 15.

    A triangle has sides a = 5 cm and b = 16 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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16. 16.

    A wave has frequency 407 Hz and wavelength 4.9 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    Find the force needed to accelerate a 50 kg mass at 1.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A cone has base radius 7 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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19. 19.

    A body starts at 9 m/s and accelerates at 5.8 m/s² for 12 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    Find the population standard deviation of: 6, 9, 17, 16, 5 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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