Japan · Grade 12 · Practice Sheet 32

1. 1.

   Find the sum of the first 9 terms of an arithmetic series with first term a = 10 and common difference d = 4.

   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 2.7 A flows through a 30 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   Two masses 8,800 kg and 610 kg are 18 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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4. 4.

   A population of 2,900 grows 3% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

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5. 5.

   Find the momentum of a 38 kg object moving at 26 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   Two masses 2,100 kg and 230 kg are 11 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.

   In a triangle, a = 9, b = 7 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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8. 8.

   A body starts at 15 m/s and accelerates at 5.3 m/s² for 6 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   A wave has frequency 40 Hz and wavelength 0.29 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    A triangle has sides a = 15 cm and b = 16 cm with an included angle C = 90°. 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.

    A 12 kg object moves at 4 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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12. 12.

    A body starts at 9 m/s and accelerates at 1.5 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    A population of 3,400 grows 5% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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14. 14.

    Find the sum of the first 6 terms of a geometric series with first term a = 7 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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15. 15.

    A triangle has sides a = 17 cm and b = 19 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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16. 16.

    A cone has base radius 10 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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17. 17.

    Find the momentum of a 19 kg object moving at 21 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A device runs at 225 V drawing 3.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    Find the force needed to accelerate a 59 kg mass at 1.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A force of 72 N moves an object 23 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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