Taiwan · Grade 11 · Practice Sheet 42

1. 1.

   Find the force needed to accelerate a 49 kg mass at 8.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   A population of 3,600 grows 3% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   A current of 6.3 A flows through a 39 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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4. 4.

   A body starts at 15 m/s and accelerates at 2.9 m/s² for 4 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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5. 5.

   A triangle has sides a = 5 cm and b = 15 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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6. 6.

   Find the sum of the first 6 terms of a geometric series with first term a = 1 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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7. 7.

   An object with initial velocity 0 m/s accelerates at 1.1 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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8. 8.

   NT$ 1,300 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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9. 9.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 12 and common difference d = 8.

   Formula:Sum of an Arithmetic Series

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

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10. 10.

    A wave has frequency 51 Hz and wavelength 3.58 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    An object with initial velocity 2 m/s accelerates at 2.7 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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12. 12.

    Find the force needed to accelerate a 51 kg mass at 1.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    A device runs at 147 V drawing 3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    An object has mass 59.8 g and volume 23 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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15. 15.

    Two masses 2,600 kg and 470 kg are 9 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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16. 16.

    Find the gravitational potential energy of a 25 kg object raised 20 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    Find the sum of the first 8 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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18. 18.

    A force of 119 N moves an object 3 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    An object has mass 109.2 g and volume 39 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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20. 20.

    Find the gravitational potential energy of a 49 kg object raised 19 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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