Oman · Grade 12 · Practice Sheet 2

1. 1.

   A body starts at 15 m/s and accelerates at 5.3 m/s² for 7 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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2. 2.

   A force of 99 N acts on an area of 8.5 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   Find the sum of the first 5 terms of an arithmetic series with first term a = 12 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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4. 4.

   A population of 8,300 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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5. 5.

   OMR 1,400 is invested at 5% 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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6. 6.

   Two masses 6,700 kg and 180 kg are 8 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 wave has frequency 42 Hz and wavelength 3.86 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   Find the gravitational potential energy of a 38 kg object raised 16 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   Solve using the quadratic formula: x² − 1x − 20 = 0.

   Formula:Quadratic Formula

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

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10. 10.

    A force of 89 N acts on an area of 6.8 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    Find the force needed to accelerate a 23 kg mass at 5.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    Two masses 6,100 kg and 660 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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13. 13.

    A triangle has sides a = 12 cm and b = 7 cm with an included angle C = 90°. 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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14. 14.

    Find the momentum of a 32 kg object moving at 2 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    Find the force needed to accelerate a 40 kg mass at 5.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    A force of 53 N moves an object 9 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    OMR 3,900 is invested at 8% 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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18. 18.

    A cone has base radius 3 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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19. 19.

    A triangle has sides a = 16 cm and b = 18 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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20. 20.

    Find the force needed to accelerate a 48 kg mass at 7.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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