Hungary · Grade 12 · Practice Sheet 22

1. 1.

   Find the population standard deviation of: 18, 12, 4, 9, 12 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   A cone has base radius 6 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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3. 3.

   A device runs at 148 V drawing 7.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   A current of 7.7 A flows through a 5 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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5. 5.

   A wave has frequency 70 Hz and wavelength 3.64 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   A body starts at 6 m/s and accelerates at 1.3 m/s² for 10 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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7. 7.

   An object with initial velocity 15 m/s accelerates at 3.4 m/s² for 6 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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8. 8.

   A force of 11 N moves an object 34 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   Find the sum of the first 10 terms of an arithmetic series with first term a = 7 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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10. 10.

    A triangle has sides a = 14 cm and b = 11 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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11. 11.

    Find the sum of the first 18 terms of an arithmetic series with first term a = 10 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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12. 12.

    In a triangle, a = 17, b = 18 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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13. 13.

    A triangle has sides a = 9 cm and b = 9 cm with an included angle C = 45°. 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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14. 14.

    Solve using the quadratic formula: x² − 3x − 4 = 0.

    Formula:Quadratic Formula

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

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15. 15.

    A cone has base radius 8 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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16. 16.

    A wave has frequency 720 Hz and wavelength 1.67 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    Find the momentum of a 3 kg object moving at 6 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    In a triangle, a = 17, b = 13 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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19. 19.

    Find the gravitational potential energy of a 16 kg object raised 2 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    A force of 64 N moves an object 20 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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