China · Grade 11 · Practice Sheet 33

1. 1.

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

   Formula:Quadratic Formula

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

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2. 2.

   Find the momentum of a 22 kg object moving at 15 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   An object with initial velocity 1 m/s accelerates at 3.6 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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4. 4.

   A 35 kg object moves at 5 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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5. 5.

   An object with initial velocity 15 m/s accelerates at 4 m/s² for 8 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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6. 6.

   A force of 100 N moves an object 13 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   A wave has frequency 282 Hz and wavelength 2.63 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   Two masses 1,900 kg and 710 kg are 10 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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9. 9.

   A 37 kg object moves at 20 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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10. 10.

    Solve using the quadratic formula: x² − 10x + 24 = 0.

    Formula:Quadratic Formula

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

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11. 11.

    In a triangle, a = 6, b = 7 and the included angle C = 40°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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12. 12.

    A right-angled triangle has legs of 3 cm and 15 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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13. 13.

    Find the population standard deviation of: 5, 9, 4, 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.

    Find the momentum of a 24 kg object moving at 18 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    Two masses 4,200 kg and 580 kg are 6 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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16. 16.

    A device runs at 221 V drawing 7.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    Find the gravitational potential energy of a 16 kg object raised 18 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    Two masses 7,400 kg and 750 kg are 2 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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19. 19.

    In a triangle, a = 11, b = 18 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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20. 20.

    A body starts at 9 m/s and accelerates at 5.6 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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