Austria · Klasse 10 · Practice Sheet 29

1. 1.

   A current of 7 A flows through a 43 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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2. 2.

   In a triangle, a = 10, b = 6 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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3. 3.

   A right-angled triangle has legs of 10 cm and 11 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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4. 4.

   A value changes from 44 to 40. 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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5. 5.

   In a triangle, a = 18, b = 17 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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6. 6.

   Find the force needed to accelerate a 2 kg mass at 1.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   A body starts at 13 m/s and accelerates at 5.2 m/s² for 2 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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8. 8.

   A force of 387 N acts on an area of 7.9 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   A wave has frequency 823 Hz and wavelength 0.24 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    A body starts at 19 m/s and accelerates at 3.7 m/s² for 12 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    A cone has base radius 9 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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12. 12.

    Find the momentum of a 45 kg object moving at 26 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    A force of 64 N moves an object 4 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    An object has mass 156.2 g and volume 22 cm³. Find its density.

    Formula:Density

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

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15. 15.

    Solve using the quadratic formula: x² + 0x − 36 = 0.

    Formula:Quadratic Formula

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

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16. 16.

    A wave has frequency 122 Hz and wavelength 4.37 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    Find the sum of the first 12 terms of an arithmetic series with first term a = 7 and common difference d = 8.

    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 volume of a sphere of radius 10 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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19. 19.

    A value changes from 85 to 24. 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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20. 20.

    An object has mass 59 g and volume 10 cm³. Find its density.

    Formula:Density

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

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