Italy · Classe 12 · Practice Sheet 44

1. 1.

   Find the sum of the first 7 terms of a geometric series with first term a = 6 and common ratio r = 2.

   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 783 Hz and wavelength 3.08 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   Two masses 8,100 kg and 870 kg are 9 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 30 kg object moving at 8 m/s.

   Formula:Momentum

   $p = mv$

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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.

   An object with initial velocity 15 m/s accelerates at 2.4 m/s² for 2 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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7. 7.

   A force of 108 N acts on an area of 8.6 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   A device runs at 22 V drawing 1.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   A triangle has sides a = 19 cm and b = 13 cm with an included angle C = 90°. 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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10. 10.

    In a triangle, a = 7, b = 17 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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11. 11.

    A cone has base radius 6 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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12. 12.

    Find the momentum of a 59 kg object moving at 10 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    A force of 335 N acts on an area of 4.7 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    Find the sum of the first 20 terms of an arithmetic series with first term a = 2 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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15. 15.

    A 19 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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16. 16.

    Find the population standard deviation of: 5, 11, 19, 12, 11 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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17. 17.

    A population of 4,600 grows 8% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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18. 18.

    A force of 100 N moves an object 5 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    Find the force needed to accelerate a 39 kg mass at 3.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    Find the momentum of a 2 kg object moving at 27 m/s.

    Formula:Momentum

    $p = mv$

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