Russia · Grade 12 · Practice Sheet 34

1. 1.

   Find the population standard deviation of: 17, 20, 5, 11, 9 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   Two masses 2,500 kg and 150 kg are 10 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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3. 3.

   Find the sum of the first 17 terms of an arithmetic series with first term a = 8 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

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4. 4.

   Find the force needed to accelerate a 52 kg mass at 7.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   ₽900 is invested at 4% 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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6. 6.

   A force of 146 N acts on an area of 0.9 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   Find the sum of the first 14 terms of an arithmetic series with first term a = 1 and common difference d = 1.

   Formula:Sum of an Arithmetic Series

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

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8. 8.

   A wave has frequency 77 Hz and wavelength 1.87 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   Find the gravitational potential energy of a 7 kg object raised 2 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    ₽1,000 is invested at 8% compound interest per annum for 2 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.

    A wave has frequency 255 Hz and wavelength 0.71 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    Find the momentum of a 60 kg object moving at 23 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    Find the population standard deviation of: 3, 7, 20, 13, 2 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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14. 14.

    Find the force needed to accelerate a 5 kg mass at 5.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    Two masses 5,600 kg and 220 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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16. 16.

    A wave has frequency 20 Hz and wavelength 2.84 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    A force of 98 N moves an object 20 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    In a triangle, a = 12, b = 11 and the included angle C = 100°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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19. 19.

    A population of 2,100 grows 3% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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20. 20.

    A wave has frequency 241 Hz and wavelength 2.92 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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