Kenya · Grade 11 · Practice Sheet 38

1. 1.

   In a triangle, a = 14, b = 5 and the included angle C = 60°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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2. 2.

   An object with initial velocity 5 m/s accelerates at 1 m/s² for 10 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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3. 3.

   Two masses 3,000 kg and 550 kg are 17 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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4. 4.

   Find the momentum of a 6 kg object moving at 29 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   A triangle has sides a = 12 cm and b = 5 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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6. 6.

   Solve using the quadratic formula: x² − 9x + 18 = 0.

   Formula:Quadratic Formula

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

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7. 7.

   Find the force needed to accelerate a 48 kg mass at 5.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   An object has mass 62.4 g and volume 16 cm³. Find its density.

   Formula:Density

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

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9. 9.

   Find the population standard deviation of: 3, 7, 11, 14, 18 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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10. 10.

    Find the gravitational potential energy of a 31 kg object raised 39 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    Find the momentum of a 23 kg object moving at 5 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    A force of 24 N moves an object 20 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    A force of 30 N acts on an area of 1.5 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    Find the sum of the first 4 terms of a geometric series with first term a = 1 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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15. 15.

    Solve using the quadratic formula: x² − 3x − 18 = 0.

    Formula:Quadratic Formula

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

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16. 16.

    In a triangle, a = 17, b = 12 and the included angle C = 70°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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17. 17.

    A wave has frequency 208 Hz and wavelength 4.84 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    Solve using the quadratic formula: x² + 1x − 2 = 0.

    Formula:Quadratic Formula

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

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19. 19.

    Find the gravitational potential energy of a 47 kg object raised 30 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    KSh 1,300 is invested at 4% 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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