France · Classe 10 · Practice Sheet 26

1. 1.

   In a triangle, a = 7, b = 10 and the included angle C = 100°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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2. 2.

   A current of 6.2 A flows through a 31 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   A triangle has sides a = 13 cm and b = 19 cm with an included angle C = 30°. 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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4. 4.

   A cone has base radius 9 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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5. 5.

   €2,900 is invested at 6% simple interest per year for 4 years. Find the interest earned.

   Formula:Simple Interest

   $I = \dfrac{P \times r \times t}{100}$

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6. 6.

   A force of 412 N acts on an area of 2.4 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   A wave has frequency 321 Hz and wavelength 1.41 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   Find the gravitational potential energy of a 45 kg object raised 5 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   A device runs at 190 V drawing 2.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    Find the momentum of a 5 kg object moving at 23 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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12. 12.

    Find the force needed to accelerate a 3 kg mass at 8.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    A body starts at 7 m/s and accelerates at 2.3 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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14. 14.

    A force of 63 N acts on an area of 5 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    €4,500 is invested at 3% simple interest per year for 5 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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16. 16.

    An object has mass 58 g and volume 20 cm³. Find its density.

    Formula:Density

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

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17. 17.

    Solve for x: 6x + 13 = 61.

    Formula:Solving a Linear Equation

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

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18. 18.

    Solve using the quadratic formula: x² + 9x + 20 = 0.

    Formula:Quadratic Formula

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

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19. 19.

    Solve for x: 8x + 3 = 35.

    Formula:Solving a Linear Equation

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

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20. 20.

    A wave has frequency 73 Hz and wavelength 3.84 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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