Indonesia · Grade 12 · Practice Sheet 30

1. 1.

   Find the sum of the first 17 terms of an arithmetic series with first term a = 10 and common difference d = 1.

   Formula:Sum of an Arithmetic Series

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

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2. 2.

   A 26 kg object moves at 10 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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3. 3.

   A force of 224 N acts on an area of 2.9 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   A current of 0.7 A flows through a 48 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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5. 5.

   A 39 kg object moves at 15 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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6. 6.

   Two masses 9,000 kg and 280 kg are 12 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.

   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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8. 8.

   Find the force needed to accelerate a 23 kg mass at 4.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   Find the gravitational potential energy of a 11 kg object raised 12 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    Two masses 9,000 kg and 760 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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11. 11.

    In a triangle, a = 6, b = 14 and the included angle C = 100°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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12. 12.

    Find the sum of the first 13 terms of an arithmetic series with first term a = 4 and common difference d = 6.

    Formula:Sum of an Arithmetic Series

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

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13. 13.

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

    Find the momentum of a 25 kg object moving at 21 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    Solve using the quadratic formula: x² − 5x + 0 = 0.

    Formula:Quadratic Formula

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

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16. 16.

    A body starts at 17 m/s and accelerates at 5.2 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    Find the force needed to accelerate a 8 kg mass at 1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A force of 35 N moves an object 22 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    A current of 6.4 A flows through a 31 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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20. 20.

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

    Formula:Sum of a Geometric Series

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

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