France · Classe 10 · Practice Sheet 12

1. 1.

   A force of 87 N moves an object 34 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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2. 2.

   A device runs at 74 V drawing 0.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   Find the sum of the first 18 terms of an arithmetic series with first term a = 1 and common difference d = 2.

   Formula:Sum of an Arithmetic Series

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

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4. 4.

   A force of 118 N moves an object 6 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

   A right-angled triangle has legs of 4 cm and 11 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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6. 6.

   Solve for x: 5x + 14 = 54.

   Formula:Solving a Linear Equation

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

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7. 7.

   Find the force needed to accelerate a 15 kg mass at 0.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A wave has frequency 95 Hz and wavelength 0.27 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   Find the sum of the first 19 terms of an arithmetic series with first term a = 10 and common difference d = 3.

   Formula:Sum of an Arithmetic Series

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

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10. 10.

    Solve using the quadratic formula: x² + 3x − 18 = 0.

    Formula:Quadratic Formula

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

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11. 11.

    A right-angled triangle has legs of 7 cm and 8 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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12. 12.

    Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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13. 13.

    A cone has base radius 2 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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14. 14.

    A bag has 29 equally likely marbles, of which 25 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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15. 15.

    Find the gravitational potential energy of a 8 kg object raised 38 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    Solve for x: 3x + 16 = 43.

    Formula:Solving a Linear Equation

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

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17. 17.

    A current of 1.4 A flows through a 13 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    A cone has base radius 6 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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19. 19.

    Find the force needed to accelerate a 41 kg mass at 3.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A force of 176 N acts on an area of 6 m². Find the pressure.

    Formula:Pressure

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

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