Sweden · Grade 11 · Practice Sheet 41

1. 1.

   A 16 kg object moves at 16 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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2. 2.

   A right-angled triangle has legs of 15 cm and 19 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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3. 3.

   A force of 440 N acts on an area of 3 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   Two masses 4,500 kg and 520 kg are 2 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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5. 5.

   An object has mass 273 g and volume 35 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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6. 6.

   Find the gravitational potential energy of a 25 kg object raised 17 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   A wave has frequency 648 Hz and wavelength 0.53 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   Find the force needed to accelerate a 21 kg mass at 0.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A force of 311 N acts on an area of 6.9 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    Find the sum of the first 4 terms of a geometric series with first term a = 8 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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11. 11.

    A cylinder has radius 3 cm and height 25 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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12. 12.

    Find the population standard deviation of: 8, 17, 8, 14, 4 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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13. 13.

    A cone has base radius 2 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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14. 14.

    Find the sum of the first 8 terms of a geometric series with first term a = 1 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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15. 15.

    A cone has base radius 3 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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16. 16.

    An object with initial velocity 3 m/s accelerates at 4.3 m/s² for 2 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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17. 17.

    Find the momentum of a 19 kg object moving at 19 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    An object with initial velocity 12 m/s accelerates at 4.5 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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19. 19.

    Solve using the quadratic formula: x² − 7x + 12 = 0.

    Formula:Quadratic Formula

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

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20. 20.

    A population of 6,800 grows 3% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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