France · Classe 10 · Practice Sheet 49

1. 1.

   A bag has 24 equally likely marbles, of which 13 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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2. 2.

   Find the sum of the first 13 terms of an arithmetic series with first term a = 7 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

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3. 3.

   Solve for x: 2x + 10 = 26.

   Formula:Solving a Linear Equation

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

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4. 4.

   A population of 4,300 grows 10% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

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5. 5.

   Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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6. 6.

   A device runs at 73 V drawing 9.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   An object has mass 52.8 g and volume 24 cm³. Find its density.

   Formula:Density

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

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8. 8.

   A 23 kg object moves at 9 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2} m v^2$

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9. 9.

   A force of 9 N moves an object 3 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    Find the gravitational potential energy of a 24 kg object raised 33 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    A cylinder has radius 13 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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12. 12.

    A wave has frequency 166 Hz and wavelength 2.5 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    A right-angled triangle has legs of 7 cm and 17 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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14. 14.

    Find the sum of the first 13 terms of an arithmetic series with first term a = 1 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

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

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15. 15.

    Solve for x: 9x + 16 = 34.

    Formula:Solving a Linear Equation

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

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16. 16.

    In a triangle, a = 11, b = 16 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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17. 17.

    A wave has frequency 670 Hz and wavelength 3.08 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    A cylinder has radius 4 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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19. 19.

    Solve for x: 7x + 12 = 47.

    Formula:Solving a Linear Equation

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

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20. 20.

    Find the momentum of a 30 kg object moving at 26 m/s.

    Formula:Momentum

    $p = mv$

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