Qatar · Grade 12 · Practice Sheet 14

1. 1.

   A 37 kg object moves at 3 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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2. 2.

   A wave has frequency 366 Hz and wavelength 3.55 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   Find the force needed to accelerate a 28 kg mass at 6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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5. 5.

   An object with initial velocity 1 m/s accelerates at 1.2 m/s² for 10 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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6. 6.

   A device runs at 105 V drawing 5.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   Solve using the quadratic formula: x² + 1x + 0 = 0.

   Formula:Quadratic Formula

   $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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8. 8.

   Find the sum of the first 9 terms of an arithmetic series with first term a = 6 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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9. 9.

   A device runs at 40 V drawing 4.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    Find the force needed to accelerate a 16 kg mass at 5.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A current of 7.9 A flows through a 50 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    Two masses 3,000 kg and 290 kg are 14 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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13. 13.

    An object with initial velocity 9 m/s accelerates at 4.5 m/s² for 7 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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14. 14.

    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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15. 15.

    A device runs at 14 V drawing 8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    An object with initial velocity 9 m/s accelerates at 1.1 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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17. 17.

    A body starts at 8 m/s and accelerates at 4.6 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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18. 18.

    A device runs at 111 V drawing 2.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A cone has base radius 7 cm and height 20 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.

    QAR 3,800 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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