Switzerland · Grade 12 · Practice Sheet 26

1. 1.

   A device runs at 29 V drawing 6.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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2. 2.

   A 31 kg object moves at 16 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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3. 3.

   A cone has base radius 5 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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4. 4.

   Find the force needed to accelerate a 29 kg mass at 7.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   Find the sum of the first 13 terms of an arithmetic series with first term a = 3 and common difference d = 3.

   Formula:Sum of an Arithmetic Series

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

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6. 6.

   Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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7. 7.

   In a triangle, a = 11, b = 6 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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8. 8.

   Find the population standard deviation of: 20, 19, 7, 9, 8 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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9. 9.

   Find the force needed to accelerate a 30 kg mass at 1.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A force of 71 N moves an object 29 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    A device runs at 8 V drawing 2.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    Find the gravitational potential energy of a 45 kg object raised 13 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

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

    Formula:Sum of a Geometric Series

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

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14. 14.

    CHF 2,900 is invested at 3% compound interest per annum for 3 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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15. 15.

    A body starts at 11 m/s and accelerates at 4.4 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    Two masses 7,400 kg and 480 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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17. 17.

    Find the momentum of a 15 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A current of 6 A flows through a 26 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    A population of 7,600 grows 10% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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20. 20.

    Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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