United Arab Emirates · Grade 12 · Practice Sheet 14

1. 1.

   Find the sum of the first 19 terms of an arithmetic series with first term a = 4 and common difference d = 8.

   Formula:Sum of an Arithmetic Series

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

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2. 2.

   A current of 6.8 A flows through a 35 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   A force of 225 N acts on an area of 1.4 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   A triangle has sides a = 20 cm and b = 20 cm with an included angle C = 60°. 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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5. 5.

   Two masses 8,200 kg and 200 kg are 6 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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6. 6.

   A triangle has sides a = 18 cm and b = 12 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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7. 7.

   A body starts at 13 m/s and accelerates at 3 m/s² for 6 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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8. 8.

   A current of 5.9 A flows through a 15 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   A force of 85 N moves an object 17 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    Solve using the quadratic formula: x² + 0x − 4 = 0.

    Formula:Quadratic Formula

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

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11. 11.

    A force of 29 N moves an object 7 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    A wave has frequency 605 Hz and wavelength 1.08 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    A device runs at 195 V drawing 4.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    A force of 231 N acts on an area of 6 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    A device runs at 91 V drawing 5.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    Find the force needed to accelerate a 7 kg mass at 3.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    Find the gravitational potential energy of a 8 kg object raised 7 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    A triangle has sides a = 9 cm and b = 12 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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19. 19.

    Solve using the quadratic formula: x² − 1x − 20 = 0.

    Formula:Quadratic Formula

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

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20. 20.

    A triangle has sides a = 16 cm and b = 18 cm with an included angle C = 60°. 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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