Hungary · Grade 12 · Practice Sheet 23

1. 1.

   In a triangle, a = 14, b = 12 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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2. 2.

   Find the population standard deviation of: 11, 10, 6, 19, 7 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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3. 3.

   A body starts at 5 m/s and accelerates at 1.4 m/s² for 2 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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5. 5.

   A device runs at 240 V drawing 1.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   A wave has frequency 376 Hz and wavelength 2.02 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   Find the force needed to accelerate a 23 kg mass at 6.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A 36 kg object moves at 23 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2} m v^2$

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9. 9.

   Find the momentum of a 48 kg object moving at 3 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    In a triangle, a = 6, b = 13 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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11. 11.

    Find the momentum of a 1 kg object moving at 19 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    A current of 4.8 A flows through a 13 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    Find the sum of the first 7 terms of a geometric series with first term a = 3 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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14. 14.

    A device runs at 7 V drawing 4.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    Find the sum of the first 5 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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16. 16.

    Find the population standard deviation of: 7, 6, 9, 12, 15 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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17. 17.

    A wave has frequency 419 Hz and wavelength 2.09 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    A force of 55 N moves an object 31 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    Solve using the quadratic formula: x² + 10x + 24 = 0.

    Formula:Quadratic Formula

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

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20. 20.

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