Singapore · Grade 12 · Practice Sheet 40

1. 1.

   An object with initial velocity 2 m/s accelerates at 3.9 m/s² for 9 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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2. 2.

   A device runs at 127 V drawing 6.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   A current of 6.8 A flows through a 21 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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4. 4.

   Find the sum of the first 11 terms of an arithmetic series with first term a = 12 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

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

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5. 5.

   A body starts at 15 m/s and accelerates at 3.9 m/s² for 8 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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6. 6.

   Find the momentum of a 14 kg object moving at 28 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A force of 23 N moves an object 14 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   $2,500 is invested at 6% compound interest per annum for 4 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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9. 9.

   A triangle has sides a = 17 cm and b = 5 cm with an included angle C = 30°. 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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10. 10.

    Find the population standard deviation of: 8, 12, 11, 4, 11 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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11. 11.

    A population of 4,600 grows 2% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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12. 12.

    A 12 kg object moves at 17 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

    A device runs at 84 V drawing 7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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15. 15.

    A force of 54 N moves an object 6 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    In a triangle, a = 17, b = 11 and the included angle C = 80°. 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.

    A 8 kg object moves at 19 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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18. 18.

    A current of 1.5 A flows through a 51 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    Find the sum of the first 7 terms of a geometric series with first term a = 2 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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20. 20.

    Two masses 8,900 kg and 710 kg are 19 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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