Peru · Grado 12 · Practice Sheet 38

1. 1.

   In a triangle, a = 13, b = 9 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.

   Find the population standard deviation of: 2, 8, 17, 2, 17 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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3. 3.

   An object with initial velocity 3 m/s accelerates at 1.8 m/s² for 3 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 sum of the first 6 terms of a geometric series with first term a = 6 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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5. 5.

   Find the force needed to accelerate a 31 kg mass at 3.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   Find the gravitational potential energy of a 29 kg object raised 13 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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8. 8.

   A triangle has sides a = 18 cm and b = 13 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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9. 9.

   A 40 kg object moves at 16 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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10. 10.

    Find the population standard deviation of: 7, 11, 2, 15, 9 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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11. 11.

    A wave has frequency 486 Hz and wavelength 0.54 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    S/ 1,000 is invested at 4% compound interest per annum for 2 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 current of 4.4 A flows through a 8 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    A device runs at 102 V drawing 1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    Find the momentum of a 40 kg object moving at 27 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    Find the gravitational potential energy of a 19 kg object raised 38 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    A population of 3,300 grows 5% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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18. 18.

    Find the momentum of a 28 kg object moving at 18 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    Find the force needed to accelerate a 24 kg mass at 6.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A force of 59 N moves an object 4 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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