Switzerland · Grade 10 · Practice Sheet 34

1. 1.

   A cylinder has radius 6 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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2. 2.

   Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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3. 3.

   A wave has frequency 583 Hz and wavelength 1.83 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   CHF 1,200 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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5. 5.

   A cone has base radius 2 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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6. 6.

   A force of 150 N acts on an area of 7.9 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   A cylinder has radius 14 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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8. 8.

   An object with initial velocity 3 m/s accelerates at 2.9 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.

   A device runs at 40 V drawing 9.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    An object has mass 121.6 g and volume 32 cm³. Find its density.

    Formula:Density

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

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11. 11.

    Solve for x: 4x + 14 = 46.

    Formula:Solving a Linear Equation

    $x = \dfrac{c - b}{a}$

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12. 12.

    A bag has 25 equally likely marbles, of which 9 are red. Find the probability of drawing a red marble (to 3 d.p.).

    Formula:Simple Probability

    $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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13. 13.

    Solve using the quadratic formula: x² + 0x − 16 = 0.

    Formula:Quadratic Formula

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

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14. 14.

    Find the gravitational potential energy of a 15 kg object raised 28 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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16. 16.

    Solve for x: 3x + 1 = 10.

    Formula:Solving a Linear Equation

    $x = \dfrac{c - b}{a}$

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17. 17.

    A cylinder has radius 3 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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18. 18.

    A wave has frequency 667 Hz and wavelength 3.16 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    Find the momentum of a 37 kg object moving at 6 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    A device runs at 74 V drawing 4.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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