Netherlands · Year 12 · Practice Sheet 50

1. 1.

   Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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2. 2.

   A population of 6,500 grows 10% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   A triangle has sides a = 15 cm and b = 17 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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4. 4.

   Find the force needed to accelerate a 4 kg mass at 1.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   A device runs at 86 V drawing 8.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   A 40 kg object moves at 24 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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7. 7.

   Find the sum of the first 3 terms of a geometric series with first term a = 2 and common ratio r = 4.

   Formula:Sum of a Geometric Series

   $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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8. 8.

   An object with initial velocity 15 m/s accelerates at 3.7 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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9. 9.

   A device runs at 17 V drawing 0.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    An object with initial velocity 11 m/s accelerates at 4.2 m/s² for 6 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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11. 11.

    Find the momentum of a 31 kg object moving at 22 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    A population of 1,300 grows 3% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    €2,000 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.

    An object with initial velocity 8 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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15. 15.

    A device runs at 43 V drawing 8.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    A wave has frequency 568 Hz and wavelength 1.96 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    A current of 5 A flows through a 33 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    Find the force needed to accelerate a 2 kg mass at 6.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A force of 67 N moves an object 21 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 10 kg mass at 7.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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