Belgium · Year 10 · Practice Sheet 48

1. 1.

   An object with initial velocity 6 m/s accelerates at 2.9 m/s² for 10 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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2. 2.

   Find the sum of the first 14 terms of an arithmetic series with first term a = 5 and common difference d = 1.

   Formula:Sum of an Arithmetic Series

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

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3. 3.

   A cylinder has radius 14 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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4. 4.

   A triangle has sides a = 18 cm and b = 10 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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5. 5.

   Solve using the quadratic formula: x² − 3x + 2 = 0.

   Formula:Quadratic Formula

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

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6. 6.

   Find the sum of the first 16 terms of an arithmetic series with first term a = 8 and common difference d = 3.

   Formula:Sum of an Arithmetic Series

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

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7. 7.

   A device runs at 93 V drawing 5.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   Find the gravitational potential energy of a 12 kg object raised 5 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   Solve for x: 5x + 6 = 61.

   Formula:Solving a Linear Equation

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

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10. 10.

    A force of 168 N acts on an area of 0.5 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    A 4 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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12. 12.

    Find the gravitational potential energy of a 49 kg object raised 26 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    A wave has frequency 740 Hz and wavelength 3.53 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    A body starts at 10 m/s and accelerates at 2.9 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    A current of 2.3 A flows through a 11 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    Find the momentum of a 49 kg object moving at 3 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

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

    Formula:Quadratic Formula

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

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18. 18.

    An object with initial velocity 2 m/s accelerates at 1 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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19. 19.

    €2,400 is invested at 8% 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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20. 20.

    A triangle has sides a = 12 cm and b = 5 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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