Brazil · Ano 12 · Practice Sheet 45

1. 1.

   A cone has base radius 12 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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2. 2.

   A population of 8,600 grows 2% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   Solve using the quadratic formula: x² − 6x + 5 = 0.

   Formula:Quadratic Formula

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

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4. 4.

   A force of 90 N moves an object 31 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

   A population of 2,900 grows 10% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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6. 6.

   A wave has frequency 802 Hz and wavelength 0.57 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   Find the momentum of a 20 kg object moving at 28 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A wave has frequency 144 Hz and wavelength 3.19 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   A force of 108 N moves an object 25 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    A wave has frequency 268 Hz and wavelength 3.03 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    Find the population standard deviation of: 8, 16, 9, 16, 11 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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12. 12.

    R$ 2,700 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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13. 13.

    A triangle has sides a = 10 cm and b = 11 cm with an included angle C = 60°. 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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14. 14.

    Find the force needed to accelerate a 34 kg mass at 8.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A current of 4.1 A flows through a 37 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    A force of 91 N moves an object 11 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 sum of the first 6 terms of a geometric series with first term a = 8 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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18. 18.

    Find the sum of the first 18 terms of an arithmetic series with first term a = 4 and common difference d = 8.

    Formula:Sum of an Arithmetic Series

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

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19. 19.

    An object with initial velocity 0 m/s accelerates at 2.8 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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20. 20.

    Find the force needed to accelerate a 4 kg mass at 1.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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