Uganda · Grade 12 · Practice Sheet 21

1. 1.

   Find the sum of the first 4 terms of a geometric series with first term a = 8 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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2. 2.

   A wave has frequency 261 Hz and wavelength 2.37 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   In a triangle, a = 6, b = 17 and the included angle C = 110°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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4. 4.

   Two masses 2,800 kg and 310 kg are 11 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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5. 5.

   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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6. 6.

   Find the population standard deviation of: 9, 8, 17, 6, 18 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   Find the momentum of a 11 kg object moving at 18 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

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

   Formula:Sum of a Geometric Series

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

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9. 9.

   A wave has frequency 868 Hz and wavelength 1.6 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    Find the force needed to accelerate a 58 kg mass at 1.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A triangle has sides a = 5 cm and b = 15 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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12. 12.

    A wave has frequency 611 Hz and wavelength 3.9 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    A force of 328 N acts on an area of 9.5 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    A cone has base radius 8 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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15. 15.

    Solve using the quadratic formula: x² − 1x − 12 = 0.

    Formula:Quadratic Formula

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

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16. 16.

    Find the force needed to accelerate a 45 kg mass at 6.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A force of 42 N moves an object 30 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

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

    Formula:Sum of a Geometric Series

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

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19. 19.

    Find the force needed to accelerate a 18 kg mass at 7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    Find the sum of the first 20 terms of an arithmetic series with first term a = 11 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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