Ireland · Year 10 · Practice Sheet 34

1. 1.

   A force of 100 N moves an object 4 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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2. 2.

   A 15 kg object moves at 8 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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3. 3.

   A triangle has sides a = 19 cm and b = 15 cm with an included angle C = 45°. 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.

   €2,900 is invested at 6% compound interest per annum for 2 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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5. 5.

   Find the momentum of a 45 kg object moving at 13 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   Solve for x: 9x + 4 = 40.

   Formula:Solving a Linear Equation

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

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7. 7.

   Find the force needed to accelerate a 31 kg mass at 8.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A force of 101 N moves an object 2 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   €1,500 is invested at 3% 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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10. 10.

    A body starts at 15 m/s and accelerates at 2.3 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    A cone has base radius 8 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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12. 12.

    €3,000 is invested at 4% 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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13. 13.

    A cylinder has radius 14 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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14. 14.

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

    Formula:Quadratic Formula

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

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15. 15.

    An object with initial velocity 12 m/s accelerates at 1.6 m/s² for 2 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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16. 16.

    Find the force needed to accelerate a 53 kg mass at 6.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    €600 is invested at 3% compound interest per annum for 3 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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18. 18.

    Find the gravitational potential energy of a 11 kg object raised 34 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    A bag has 30 equally likely marbles, of which 3 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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20. 20.

    A cone has base radius 5 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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