Switzerland · Grade 11 · Practice Sheet 38

1. 1.

   A force of 464 N acts on an area of 5 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   Find the force needed to accelerate a 43 kg mass at 5.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   Find the gravitational potential energy of a 4 kg object raised 22 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   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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5. 5.

   A force of 249 N acts on an area of 4.2 m². Find the pressure.

   Formula:Pressure

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

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6. 6.

   A body starts at 10 m/s and accelerates at 1.7 m/s² for 5 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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7. 7.

   Find the momentum of a 53 kg object moving at 11 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   Find the population standard deviation of: 11, 2, 17, 16, 14 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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9. 9.

   A triangle has sides a = 14 cm and b = 14 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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10. 10.

    In a triangle, a = 8, b = 9 and the included angle C = 100°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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11. 11.

    A body starts at 8 m/s and accelerates at 1.5 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    A force of 56 N moves an object 5 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    In a triangle, a = 5, b = 18 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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14. 14.

    Find the gravitational potential energy of a 33 kg object raised 22 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    Solve using the quadratic formula: x² − 2x − 24 = 0.

    Formula:Quadratic Formula

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

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16. 16.

    A population of 4,700 grows 5% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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17. 17.

    CHF 3,100 is invested at 6% 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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18. 18.

    Two masses 2,100 kg and 610 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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19. 19.

    Find the gravitational potential energy of a 26 kg object raised 16 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    Find the population standard deviation of: 15, 10, 12, 12, 18 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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