Mongolia · Grade 12 · Practice Sheet 49

1. 1.

   A body starts at 6 m/s and accelerates at 3.9 m/s² for 10 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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2. 2.

   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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3. 3.

   Find the population standard deviation of: 9, 8, 12, 16, 3 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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4. 4.

   A wave has frequency 74 Hz and wavelength 0.89 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   Find the force needed to accelerate a 20 kg mass at 3.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A wave has frequency 663 Hz and wavelength 3.05 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   A population of 4,600 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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8. 8.

   Find the momentum of a 51 kg object moving at 27 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   A force of 55 N moves an object 16 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    Find the force needed to accelerate a 36 kg mass at 0.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    ₮1,300 is invested at 5% compound interest per annum for 5 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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12. 12.

    Find the force needed to accelerate a 19 kg mass at 3.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    ₮1,900 is invested at 4% 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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14. 14.

    Two masses 2,000 kg and 430 kg are 13 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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15. 15.

    ₮2,000 is invested at 4% compound interest per annum for 5 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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16. 16.

    A cone has base radius 8 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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17. 17.

    Two masses 8,800 kg and 370 kg are 18 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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18. 18.

    Find the sum of the first 13 terms of an arithmetic series with first term a = 3 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

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

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19. 19.

    A cone has base radius 4 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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20. 20.

    A current of 7.1 A flows through a 28 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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