Switzerland · Grade 10 · Practice Sheet 9

1. 1.

   An object has mass 56.4 g and volume 12 cm³. Find its density.

   Formula:Density

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

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2. 2.

   A cylinder has radius 4 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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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.

   Find the force needed to accelerate a 41 kg mass at 8.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   Find the sum of the first 13 terms of an arithmetic series with first term a = 3 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

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

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6. 6.

   A value changes from 75 to 203. Find the percentage change (to 2 d.p.).

   Formula:Percentage Change

   $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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7. 7.

   Find the momentum of a 23 kg object moving at 18 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A right-angled triangle has legs of 13 cm and 12 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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9. 9.

   Solve for x: 3x + 19 = 43.

   Formula:Solving a Linear Equation

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

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10. 10.

    Solve using the quadratic formula: x² + 3x − 10 = 0.

    Formula:Quadratic Formula

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

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11. 11.

    A current of 4.7 A flows through a 21 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    A force of 195 N acts on an area of 3.3 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A triangle has sides a = 10 cm and b = 11 cm with an included angle C = 120°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

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14. 14.

    A current of 5.4 A flows through a 28 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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15. 15.

    A triangle has sides a = 14 cm and b = 8 cm with an included angle C = 120°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

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16. 16.

    A force of 317 N acts on an area of 9.5 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    A force of 76 N moves an object 16 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    A wave has frequency 710 Hz and wavelength 4.14 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    A triangle has sides a = 12 cm and b = 13 cm with an included angle C = 45°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

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20. 20.

    A device runs at 40 V drawing 2.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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