Belgium · Year 12 · Practice Sheet 28

1. 1.

   Solve using the quadratic formula: x² − 8x + 15 = 0.

   Formula:Quadratic Formula

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

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2. 2.

   A current of 3.1 A flows through a 53 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   Find the gravitational potential energy of a 34 kg object raised 38 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   A wave has frequency 830 Hz and wavelength 3.53 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   Find the gravitational potential energy of a 6 kg object raised 22 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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7. 7.

   Find the force needed to accelerate a 15 kg mass at 3.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A force of 49 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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9. 9.

   Find the sum of the first 13 terms of an arithmetic series with first term a = 5 and common difference d = 2.

   Formula:Sum of an Arithmetic Series

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

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10. 10.

    Find the force needed to accelerate a 48 kg mass at 6.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    €3,100 is invested at 6% 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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12. 12.

    A wave has frequency 511 Hz and wavelength 2.04 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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14. 14.

    Find the sum of the first 9 terms of an arithmetic series with first term a = 2 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

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

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15. 15.

    €1,100 is invested at 4% 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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16. 16.

    A triangle has sides a = 12 cm and b = 8 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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17. 17.

    Find the momentum of a 33 kg object moving at 25 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    An object with initial velocity 12 m/s accelerates at 4.7 m/s² for 4 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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19. 19.

    A wave has frequency 495 Hz and wavelength 3.19 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    Two masses 4,500 kg and 590 kg are 16 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

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