France · Classe 10 · Practice Sheet 29

1. 1.

   Find the momentum of a 28 kg object moving at 21 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   €2,100 is invested at 3% compound interest per annum for 5 years. Find the final amount (to 2 d.p.).

   Formula:Compound Interest

   $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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3. 3.

   A force of 33 N moves an object 32 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   A 31 kg object moves at 17 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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5. 5.

   Find the momentum of a 50 kg object moving at 8 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A force of 30 N moves an object 13 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   Find the sum of the first 6 terms of an arithmetic series with first term a = 1 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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8. 8.

   Find the force needed to accelerate a 19 kg mass at 5.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A cone has base radius 5 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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10. 10.

    Find the force needed to accelerate a 53 kg mass at 1.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    Solve using the quadratic formula: x² − 2x − 15 = 0.

    Formula:Quadratic Formula

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

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12. 12.

    A triangle has sides a = 5 cm and b = 6 cm with an included angle C = 60°. 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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13. 13.

    €4,000 is invested at 6% compound interest per annum for 4 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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14. 14.

    A bag has 10 equally likely marbles, of which 7 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 325 Hz and wavelength 2.96 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    €800 is invested at 8% 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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17. 17.

    A body starts at 15 m/s and accelerates at 1.2 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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18. 18.

    Find the gravitational potential energy of a 49 kg object raised 25 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    A triangle has sides a = 16 cm and b = 13 cm with an included angle C = 90°. 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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20. 20.

    A cone has base radius 2 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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