Tunisia · Grade 12 · Practice Sheet 34

1. 1.

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

   Formula:Sum of a Geometric Series

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

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2. 2.

   An object with initial velocity 8 m/s accelerates at 4 m/s² for 6 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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3. 3.

   A cone has base radius 8 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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4. 4.

   A wave has frequency 78 Hz and wavelength 1.62 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   Find the momentum of a 7 kg object moving at 16 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A body starts at 2 m/s and accelerates at 5.9 m/s² for 8 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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7. 7.

   An object with initial velocity 2 m/s accelerates at 1.5 m/s² for 6 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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8. 8.

   A current of 2.4 A flows through a 55 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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10. 10.

    Find the force needed to accelerate a 22 kg mass at 2.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A body starts at 9 m/s and accelerates at 3.5 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    A wave has frequency 145 Hz and wavelength 3.92 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    DT 1,500 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.

    Find the momentum of a 53 kg object moving at 22 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    A device runs at 62 V drawing 4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    Two masses 5,200 kg and 420 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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17. 17.

    A triangle has sides a = 13 cm and b = 13 cm with an included angle C = 45°. 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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18. 18.

    A population of 7,600 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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19. 19.

    A current of 6.7 A flows through a 59 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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20. 20.

    A 39 kg object moves at 2 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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