Indonesia · Grade 12 · Practice Sheet 24

1. 1.

   Find the population standard deviation of: 4, 16, 19, 18, 16 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   In a triangle, a = 6, b = 17 and the included angle C = 110°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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3. 3.

   A wave has frequency 672 Hz and wavelength 1.66 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   An object with initial velocity 0 m/s accelerates at 4.5 m/s² for 5 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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5. 5.

   Find the sum of the first 7 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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6. 6.

   A cone has base radius 7 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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7. 7.

   Find the force needed to accelerate a 12 kg mass at 2.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A wave has frequency 436 Hz and wavelength 3.63 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   Find the gravitational potential energy of a 32 kg object raised 18 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    A body starts at 14 m/s and accelerates at 1.2 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    Find the population standard deviation of: 12, 18, 12, 18, 17 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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12. 12.

    A device runs at 211 V drawing 1.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    Rp 2,000 is invested at 3% 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.

    A current of 4.8 A flows through a 41 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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15. 15.

    A wave has frequency 480 Hz and wavelength 2.01 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    A device runs at 204 V drawing 5.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    Find the sum of the first 5 terms of a geometric series with first term a = 6 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.

    A force of 254 N acts on an area of 10 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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19. 19.

    Find the force needed to accelerate a 25 kg mass at 0.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A force of 243 N acts on an area of 1 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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