Kenya · Grade 11 · Practice Sheet 16

1. 1.

   A triangle has sides a = 15 cm and b = 13 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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2. 2.

   A force of 107 N moves an object 26 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   An object has mass 64.8 g and volume 24 cm³. Find its density.

   Formula:Density

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

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4. 4.

   Find the sum of the first 4 terms of a geometric series with first term a = 6 and common ratio r = 4.

   Formula:Sum of a Geometric Series

   $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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5. 5.

   A wave has frequency 81 Hz and wavelength 3.32 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   An object with initial velocity 10 m/s accelerates at 2.3 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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7. 7.

   Find the population standard deviation of: 3, 17, 8, 20, 4 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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8. 8.

   Solve using the quadratic formula: x² − 5x + 6 = 0.

   Formula:Quadratic Formula

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

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9. 9.

   A current of 3.3 A flows through a 35 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    Find the sum of the first 7 terms of a geometric series with first term a = 1 and common ratio r = 4.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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11. 11.

    A body starts at 6 m/s and accelerates at 1.4 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    Find the force needed to accelerate a 30 kg mass at 7.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    Find the sum of the first 11 terms of an arithmetic series with first term a = 3 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

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

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14. 14.

    A wave has frequency 897 Hz and wavelength 4.76 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    Solve using the quadratic formula: x² + 8x + 15 = 0.

    Formula:Quadratic Formula

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

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16. 16.

    Find the momentum of a 28 kg object moving at 19 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

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

    A wave has frequency 128 Hz and wavelength 2.62 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    Find the gravitational potential energy of a 12 kg object raised 25 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    Two masses 8,200 kg and 420 kg are 4 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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