Italy · Classe 12 · Practice Sheet 20

1. 1.

   Find the force needed to accelerate a 40 kg mass at 3.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   In a triangle, a = 11, b = 14 and the included angle C = 80°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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3. 3.

   A cone has base radius 10 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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4. 4.

   A body starts at 13 m/s and accelerates at 4.9 m/s² for 8 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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5. 5.

   An object with initial velocity 4 m/s accelerates at 1.2 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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6. 6.

   Find the sum of the first 12 terms of an arithmetic series with first term a = 6 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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7. 7.

   Find the sum of the first 4 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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8. 8.

   A current of 3 A flows through a 43 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   In a triangle, a = 9, b = 10 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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10. 10.

    A body starts at 13 m/s and accelerates at 1.3 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    A cone has base radius 6 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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12. 12.

    Find the sum of the first 5 terms of a geometric series with first term a = 1 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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13. 13.

    In a triangle, a = 9, b = 7 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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14. 14.

    A device runs at 220 V drawing 3.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    Two masses 3,200 kg and 860 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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16. 16.

    A wave has frequency 694 Hz and wavelength 3.42 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    A force of 149 N acts on an area of 5.9 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    A force of 16 N moves an object 24 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    A wave has frequency 342 Hz and wavelength 2.25 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    A force of 192 N acts on an area of 3 m². Find the pressure.

    Formula:Pressure

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

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