Iraq · Grade 12 · Practice Sheet 36

1. 1.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 5 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

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

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2. 2.

   A wave has frequency 547 Hz and wavelength 3.19 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

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4. 4.

   A force of 38 N moves an object 19 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

   An object with initial velocity 7 m/s accelerates at 4.6 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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6. 6.

   Two masses 7,200 kg and 660 kg are 14 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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7. 7.

   A cone has base radius 2 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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8. 8.

   A device runs at 173 V drawing 9.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   Find the force needed to accelerate a 11 kg mass at 4.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    Find the gravitational potential energy of a 18 kg object raised 37 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    Solve using the quadratic formula: x² − 11x + 30 = 0.

    Formula:Quadratic Formula

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

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12. 12.

    A device runs at 24 V drawing 0.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    Find the gravitational potential energy of a 6 kg object raised 29 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    Find the force needed to accelerate a 16 kg mass at 1.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A device runs at 21 V drawing 7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    A population of 5,100 grows 10% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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17. 17.

    A current of 7 A flows through a 9 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    A body starts at 20 m/s and accelerates at 5.3 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    In a triangle, a = 6, b = 15 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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20. 20.

    A device runs at 225 V drawing 2.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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