China · Grade 12 · Practice Sheet 37

1. 1.

   In a triangle, a = 11, b = 14 and the included angle C = 50°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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2. 2.

   A body starts at 9 m/s and accelerates at 4.1 m/s² for 10 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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3. 3.

   An object with initial velocity 7 m/s accelerates at 2.2 m/s² for 7 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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4. 4.

   Find the population standard deviation of: 17, 15, 5, 6, 18 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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5. 5.

   A population of 3,700 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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6. 6.

   Find the sum of the first 3 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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7. 7.

   In a triangle, a = 17, b = 14 and the included angle C = 70°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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8. 8.

   Find the force needed to accelerate a 19 kg mass at 4.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A wave has frequency 853 Hz and wavelength 0.44 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    A current of 4.2 A flows through a 14 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    Find the sum of the first 4 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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12. 12.

    A wave has frequency 854 Hz and wavelength 3.32 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    An object with initial velocity 2 m/s accelerates at 1.9 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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14. 14.

    A device runs at 73 V drawing 8.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    A force of 458 N acts on an area of 7.4 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    A current of 5.3 A flows through a 55 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    A wave has frequency 86 Hz and wavelength 0.35 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    Find the gravitational potential energy of a 11 kg object raised 20 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    ¥2,500 is invested at 8% 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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20. 20.

    A current of 1.6 A flows through a 13 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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