Switzerland · Grade 12 · Practice Sheet 29

1. 1.

   A force of 82 N moves an object 32 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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2. 2.

   A force of 188 N acts on an area of 9.5 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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4. 4.

   Solve using the quadratic formula: x² − 5x + 4 = 0.

   Formula:Quadratic Formula

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

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5. 5.

   A wave has frequency 791 Hz and wavelength 0.56 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   Find the momentum of a 51 kg object moving at 10 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   Find the force needed to accelerate a 35 kg mass at 1.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   An object with initial velocity 5 m/s accelerates at 2.5 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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9. 9.

   CHF 700 is invested at 4% 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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10. 10.

    Find the sum of the first 5 terms of a geometric series with first term a = 2 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 body starts at 8 m/s and accelerates at 1.9 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    A force of 26 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.

    Find the gravitational potential energy of a 13 kg object raised 13 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    CHF 2,100 is invested at 4% 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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15. 15.

    A force of 432 N acts on an area of 1.3 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    An object with initial velocity 6 m/s accelerates at 4.9 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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17. 17.

    Find the sum of the first 11 terms of an arithmetic series with first term a = 11 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

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

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18. 18.

    A wave has frequency 320 Hz and wavelength 4.33 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    Two masses 6,300 kg and 740 kg are 11 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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20. 20.

    A cone has base radius 3 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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