Oman · Grade 12 · Practice Sheet 21

1. 1.

   A body starts at 9 m/s and accelerates at 4.6 m/s² for 6 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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2. 2.

   A population of 6,500 grows 5% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   Find the force needed to accelerate a 44 kg mass at 3.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   An object with initial velocity 2 m/s accelerates at 2 m/s² for 8 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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5. 5.

   A cone has base radius 6 cm and height 24 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.

   A device runs at 46 V drawing 0.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   OMR 2,100 is invested at 3% 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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8. 8.

   In a triangle, a = 13, b = 9 and the included angle C = 70°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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9. 9.

   Solve using the quadratic formula: x² − 4x − 5 = 0.

   Formula:Quadratic Formula

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

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10. 10.

    A force of 73 N moves an object 17 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    In a triangle, a = 9, b = 8 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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12. 12.

    Two masses 2,600 kg and 230 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.

    A force of 223 N acts on an area of 5.3 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    A wave has frequency 650 Hz and wavelength 4.88 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    Solve using the quadratic formula: x² − 2x − 3 = 0.

    Formula:Quadratic Formula

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

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16. 16.

    Find the force needed to accelerate a 54 kg mass at 5.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    Two masses 3,800 kg and 680 kg are 18 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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18. 18.

    A population of 5,800 grows 2% 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 wave has frequency 552 Hz and wavelength 0.55 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    Find the population standard deviation of: 12, 8, 11, 6, 8 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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