Australia · Year 12 · Practice Sheet 33

1. 1.

   Find the sum of the first 3 terms of a geometric series with first term a = 7 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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2. 2.

   $2,500 is invested at 6% compound interest per annum for 5 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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3. 3.

   A body starts at 19 m/s and accelerates at 5.9 m/s² for 11 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   Find the gravitational potential energy of a 33 kg object raised 31 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   Find the force needed to accelerate a 14 kg mass at 8.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   Find the sum of the first 8 terms of a geometric series with first term a = 1 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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7. 7.

   Find the gravitational potential energy of a 31 kg object raised 4 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   A wave has frequency 714 Hz and wavelength 3.99 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   Two masses 6,600 kg and 190 kg are 9 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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10. 10.

    In a triangle, a = 8, b = 6 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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11. 11.

    Find the population standard deviation of: 12, 9, 11, 19, 18 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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12. 12.

    An object with initial velocity 7 m/s accelerates at 1 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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13. 13.

    A device runs at 96 V drawing 1.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    Find the sum of the first 17 terms of an arithmetic series with first term a = 4 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.

    A 35 kg object moves at 11 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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16. 16.

    A force of 94 N moves an object 16 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    Find the force needed to accelerate a 2 kg mass at 8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A force of 90 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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19. 19.

    Find the momentum of a 10 kg object moving at 18 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    A cone has base radius 7 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

    $V = \tfrac{1}{3} \pi r^2 h$

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