Ireland · Year 12 · Practice Sheet 11

1. 1.

   A population of 7,300 grows 10% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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2. 2.

   A wave has frequency 23 Hz and wavelength 1.49 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   A device runs at 180 V drawing 0.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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5. 5.

   An object with initial velocity 12 m/s accelerates at 3.4 m/s² for 9 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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6. 6.

   Find the force needed to accelerate a 54 kg mass at 4.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   A force of 23 N moves an object 12 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   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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9. 9.

   Find the gravitational potential energy of a 22 kg object raised 25 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    A wave has frequency 762 Hz and wavelength 3.01 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    Find the gravitational potential energy of a 11 kg object raised 15 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    Find the force needed to accelerate a 56 kg mass at 7.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    A population of 2,100 grows 3% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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14. 14.

    A triangle has sides a = 15 cm and b = 13 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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15. 15.

    Solve using the quadratic formula: x² + 0x − 36 = 0.

    Formula:Quadratic Formula

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

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16. 16.

    Find the force needed to accelerate a 43 kg mass at 7.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    €1,100 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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18. 18.

    A wave has frequency 444 Hz and wavelength 3.05 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    A force of 9 N moves an object 10 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    Find the force needed to accelerate a 9 kg mass at 2.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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