Sweden · Grade 11 · Practice Sheet 12

1. 1.

   Find the gravitational potential energy of a 7 kg object raised 25 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   An object has mass 168.1 g and volume 41 cm³. Find its density.

   Formula:Density

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

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3. 3.

   In a triangle, a = 14, b = 13 and the included angle C = 50°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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4. 4.

   A force of 272 N acts on an area of 7 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   Two masses 3,400 kg and 120 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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6. 6.

   In a triangle, a = 12, b = 13 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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7. 7.

   A wave has frequency 160 Hz and wavelength 3.51 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   Find the force needed to accelerate a 32 kg mass at 5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   Find the momentum of a 21 kg object moving at 20 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    kr 2,800 is invested at 4% compound interest per annum for 4 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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11. 11.

    A cylinder has radius 10 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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12. 12.

    In a triangle, a = 14, b = 17 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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13. 13.

    A population of 4,500 grows 2% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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14. 14.

    kr 3,700 is invested at 3% compound interest per annum for 2 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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15. 15.

    Find the force needed to accelerate a 23 kg mass at 3.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    A 4 kg object moves at 6 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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17. 17.

    A wave has frequency 289 Hz and wavelength 4.3 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    Solve using the quadratic formula: x² − 13x + 42 = 0.

    Formula:Quadratic Formula

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

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19. 19.

    A device runs at 177 V drawing 7.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    An object with initial velocity 13 m/s accelerates at 4.8 m/s² for 9 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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