Chile · Grado 12 · Practice Sheet 14

1. 1.

   A body starts at 19 m/s and accelerates at 2.3 m/s² for 10 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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2. 2.

   A force of 20 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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3. 3.

   Find the population standard deviation of: 14, 15, 6, 19, 20 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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4. 4.

   Find the gravitational potential energy of a 17 kg object raised 16 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   Find the sum of the first 4 terms of a geometric series with first term a = 5 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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6. 6.

   A population of 4,400 grows 5% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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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 wave has frequency 442 Hz and wavelength 4.86 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   Find the sum of the first 6 terms of an arithmetic series with first term a = 1 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

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10. 10.

    Find the sum of the first 4 terms of a geometric series with first term a = 8 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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11. 11.

    $3,000 is invested at 3% 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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12. 12.

    A triangle has sides a = 17 cm and b = 19 cm with an included angle C = 30°. 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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13. 13.

    A force of 103 N moves an object 28 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    Find the force needed to accelerate a 3 kg mass at 3.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A force of 40 N acts on an area of 5.2 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    A device runs at 50 V drawing 2.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    A force of 103 N moves an object 28 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    A wave has frequency 180 Hz and wavelength 4.62 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    A force of 448 N acts on an area of 6.8 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    An object with initial velocity 15 m/s accelerates at 2.3 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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