Ethiopia · Grade 12 · Practice Sheet 20

1. 1.

   Find the sum of the first 14 terms of an arithmetic series with first term a = 11 and common difference d = 3.

   Formula:Sum of an Arithmetic Series

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

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2. 2.

   A body starts at 10 m/s and accelerates at 1.8 m/s² for 6 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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3. 3.

   A 3 kg object moves at 22 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2} m v^2$

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4. 4.

   A current of 3.6 A flows through a 35 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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5. 5.

   A cone has base radius 8 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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6. 6.

   Br 800 is invested at 8% 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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7. 7.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 7 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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8. 8.

   A wave has frequency 736 Hz and wavelength 4.95 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   Find the momentum of a 50 kg object moving at 14 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    A population of 4,500 grows 5% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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11. 11.

    A force of 69 N moves an object 29 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    Find the sum of the first 4 terms of a geometric series with first term a = 2 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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13. 13.

    In a triangle, a = 17, b = 8 and the included angle C = 110°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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14. 14.

    Find the gravitational potential energy of a 10 kg object raised 33 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    Find the sum of the first 7 terms of an arithmetic series with first term a = 5 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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16. 16.

    A cone has base radius 11 cm and height 12 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.

    Find the population standard deviation of: 11, 7, 11, 16, 8 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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18. 18.

    Find the gravitational potential energy of a 34 kg object raised 40 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    An object with initial velocity 9 m/s accelerates at 1.6 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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20. 20.

    A device runs at 29 V drawing 3.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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