Hungary · Grade 12 · Practice Sheet 47

1. 1.

   Find the force needed to accelerate a 60 kg mass at 4.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   A current of 0.6 A flows through a 13 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   In a triangle, a = 14, b = 11 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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4. 4.

   Find the force needed to accelerate a 20 kg mass at 6.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   In a triangle, a = 18, b = 18 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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6. 6.

   Find the population standard deviation of: 9, 4, 13, 17, 11 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   Find the sum of the first 8 terms of a geometric series with first term a = 6 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.

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

   Formula:Quadratic Formula

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

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9. 9.

   In a triangle, a = 5, b = 17 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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10. 10.

    Two masses 7,100 kg and 420 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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11. 11.

    A device runs at 91 V drawing 0.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    An object with initial velocity 4 m/s accelerates at 3.7 m/s² for 4 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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13. 13.

    Find the sum of the first 5 terms of a geometric series with first term a = 7 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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14. 14.

    A force of 47 N moves an object 37 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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15. 15.

    A cone has base radius 10 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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16. 16.

    In a triangle, a = 14, b = 7 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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17. 17.

    Two masses 8,200 kg and 250 kg are 3 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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18. 18.

    Find the momentum of a 31 kg object moving at 23 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A triangle has sides a = 11 cm and b = 10 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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20. 20.

    A body starts at 7 m/s and accelerates at 2.8 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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