Egypt · Grade 12 · Practice Sheet 46

1. 1.

   A wave has frequency 293 Hz and wavelength 1.43 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   Two masses 3,100 kg and 300 kg are 15 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 = 5 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

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

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4. 4.

   A device runs at 135 V drawing 4.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   E£ 600 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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6. 6.

   A triangle has sides a = 5 cm and b = 7 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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7. 7.

   Find the force needed to accelerate a 59 kg mass at 3.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A population of 2,800 grows 10% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

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9. 9.

   Find the momentum of a 31 kg object moving at 18 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    E£ 3,700 is invested at 6% 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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11. 11.

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

    Formula:Sum of a Geometric Series

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

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12. 12.

    A body starts at 14 m/s and accelerates at 4.8 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    Find the momentum of a 3 kg object moving at 18 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    Find the population standard deviation of: 10, 4, 4, 17, 20 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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15. 15.

    Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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16. 16.

    Find the sum of the first 8 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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17. 17.

    A wave has frequency 616 Hz and wavelength 1.03 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    Find the momentum of a 23 kg object moving at 19 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A device runs at 128 V drawing 0.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    A wave has frequency 225 Hz and wavelength 2.99 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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