Mexico · Grado 10 · Practice Sheet 30

1. 1.

   Find the momentum of a 2 kg object moving at 30 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   $4,000 is invested at 5% simple interest per year for 3 years. Find the interest earned.

   Formula:Simple Interest

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

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3. 3.

   A population of 3,100 grows 5% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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4. 4.

   $2,500 is invested at 5% simple interest per year for 6 years. Find the interest earned.

   Formula:Simple Interest

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

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5. 5.

   A wave has frequency 58 Hz and wavelength 2.76 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   Solve using the quadratic formula: x² − 10x + 24 = 0.

   Formula:Quadratic Formula

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

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7. 7.

   A triangle has sides a = 20 cm and b = 6 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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8. 8.

   A device runs at 230 V drawing 8.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   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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10. 10.

    A body starts at 19 m/s and accelerates at 2.7 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    A 6 kg object moves at 3 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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12. 12.

    Solve for x: 7x + 3 = 31.

    Formula:Solving a Linear Equation

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

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13. 13.

    A wave has frequency 385 Hz and wavelength 1.53 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    A bag has 13 equally likely marbles, of which 4 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.

    A wave has frequency 86 Hz and wavelength 1.45 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    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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17. 17.

    A device runs at 24 V drawing 8.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    A wave has frequency 285 Hz and wavelength 1.41 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    Solve for x: 3x + 13 = 19.

    Formula:Solving a Linear Equation

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

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20. 20.

    A force of 378 N acts on an area of 4.6 m². Find the pressure.

    Formula:Pressure

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

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