Tunisia · Grade 12 · Practice Sheet 16

1. 1.

   Find the force needed to accelerate a 21 kg mass at 3.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   A body starts at 7 m/s and accelerates at 4.2 m/s² for 10 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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3. 3.

   Find the force needed to accelerate a 49 kg mass at 2.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   Find the sum of the first 14 terms of an arithmetic series with first term a = 5 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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5. 5.

   A force of 183 N acts on an area of 4.9 m². Find the pressure.

   Formula:Pressure

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

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6. 6.

   Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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7. 7.

   A wave has frequency 238 Hz and wavelength 1.16 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   Find the force needed to accelerate a 15 kg mass at 2.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A wave has frequency 734 Hz and wavelength 0.35 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    A body starts at 15 m/s and accelerates at 5.7 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    Find the force needed to accelerate a 31 kg mass at 4.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    Two masses 7,300 kg and 860 kg are 10 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.

    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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14. 14.

    Find the momentum of a 45 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    A force of 242 N acts on an area of 2.8 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    A population of 2,300 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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17. 17.

    Find the sum of the first 6 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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18. 18.

    A cone has base radius 9 cm and height 21 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 = 10 cm and b = 12 cm with an included angle C = 60°. 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.

    A 6 kg object moves at 11 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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