Norway · Grade 11 · Practice Sheet 19

1. 1.

   A 24 kg object moves at 8 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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2. 2.

   A cone has base radius 7 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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3. 3.

   Two masses 8,700 kg and 290 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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4. 4.

   An object has mass 120 g and volume 24 cm³. Find its density.

   Formula:Density

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

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5. 5.

   In a triangle, a = 8, b = 10 and the included angle C = 110°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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6. 6.

   A force of 64 N acts on an area of 6.9 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   An object with initial velocity 9 m/s accelerates at 2.2 m/s² for 6 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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8. 8.

   Find the gravitational potential energy of a 18 kg object raised 4 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   An object has mass 81 g and volume 10 cm³. Find its density.

   Formula:Density

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

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10. 10.

    Find the sum of the first 15 terms of an arithmetic series with first term a = 5 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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11. 11.

    Find the force needed to accelerate a 14 kg mass at 6.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    Find the sum of the first 5 terms of a geometric series with first term a = 7 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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13. 13.

    In a triangle, a = 5, b = 11 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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14. 14.

    An object with initial velocity 12 m/s accelerates at 2.4 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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15. 15.

    A force of 187 N acts on an area of 8.9 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    A wave has frequency 385 Hz and wavelength 4.71 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    Find the sum of the first 11 terms of an arithmetic series with first term a = 1 and common difference d = 6.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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18. 18.

    Find the population standard deviation of: 18, 12, 20, 12, 10 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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19. 19.

    In a triangle, a = 17, b = 17 and the included angle C = 110°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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20. 20.

    Two masses 5,100 kg and 210 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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