Cambodia · Grade 11 · Practice Sheet 1

1. 1.

   Find the population standard deviation of: 10, 15, 11, 4, 8 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   A force of 364 N acts on an area of 2 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   An object with initial velocity 5 m/s accelerates at 4.3 m/s² for 3 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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4. 4.

   Two masses 2,000 kg and 130 kg are 20 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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5. 5.

   Find the gravitational potential energy of a 10 kg object raised 5 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   An object with initial velocity 0 m/s accelerates at 4.7 m/s² for 4 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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7. 7.

   A force of 80 N moves an object 36 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

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

   Formula:Sum of a Geometric Series

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

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9. 9.

   A wave has frequency 79 Hz and wavelength 3.93 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    ៛ 900 is invested at 6% 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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11. 11.

    Find the gravitational potential energy of a 50 kg object raised 10 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    A current of 2.9 A flows through a 20 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    Find the sum of the first 4 terms of a geometric series with first term a = 5 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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14. 14.

    Find the sum of the first 18 terms of an arithmetic series with first term a = 7 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

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

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15. 15.

    Find the force needed to accelerate a 13 kg mass at 0.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    A device runs at 134 V drawing 2.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    Find the sum of the first 7 terms of a geometric series with first term a = 8 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.

    Find the population standard deviation of: 15, 10, 7, 12, 7 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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19. 19.

    A population of 9,000 grows 3% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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20. 20.

    A right-angled triangle has legs of 10 cm and 19 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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