Iraq · Grade 12 · Practice Sheet 23

1. 1.

   Solve using the quadratic formula: x² + 9x + 20 = 0.

   Formula:Quadratic Formula

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

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2. 2.

   Find the momentum of a 13 kg object moving at 6 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   A body starts at 12 m/s and accelerates at 2 m/s² for 11 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   A 30 kg object moves at 6 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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5. 5.

   A cone has base radius 7 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.

   Two masses 6,900 kg and 560 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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7. 7.

   A population of 6,600 grows 10% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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8. 8.

   A force of 108 N acts on an area of 3.1 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

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9. 9.

   A wave has frequency 730 Hz and wavelength 4.27 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    Find the force needed to accelerate a 13 kg mass at 7.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A cone has base radius 3 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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12. 12.

    An object with initial velocity 3 m/s accelerates at 2.2 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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13. 13.

    Find the population standard deviation of: 11, 18, 4, 20, 12 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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14. 14.

    Find the gravitational potential energy of a 13 kg object raised 38 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    A force of 189 N acts on an area of 2.2 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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16. 16.

    A force of 25 N moves an object 38 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    A device runs at 198 V drawing 4.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    Find the sum of the first 4 terms of a geometric series with first term a = 6 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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19. 19.

    A body starts at 8 m/s and accelerates at 5.1 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    Solve using the quadratic formula: x² + 1x − 12 = 0.

    Formula:Quadratic Formula

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

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