Peru · Grado 12 · Practice Sheet 37

1. 1.

   An object with initial velocity 0 m/s accelerates at 4.2 m/s² for 8 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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2. 2.

   A force of 25 N moves an object 38 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   In a triangle, a = 17, b = 9 and the included angle C = 60°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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4. 4.

   An object with initial velocity 14 m/s accelerates at 1.9 m/s² for 4 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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5. 5.

   A population of 5,300 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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6. 6.

   An object with initial velocity 6 m/s accelerates at 3.4 m/s² for 6 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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7. 7.

   A 33 kg object moves at 12 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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8. 8.

   A wave has frequency 562 Hz and wavelength 3.79 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   Find the population standard deviation of: 7, 15, 9, 6, 14 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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10. 10.

    A population of 3,000 grows 3% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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11. 11.

    A wave has frequency 534 Hz and wavelength 4.61 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

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

    Formula:Sum of a Geometric Series

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

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13. 13.

    A 27 kg object moves at 25 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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14. 14.

    A force of 357 N acts on an area of 2.6 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    A body starts at 6 m/s and accelerates at 1.1 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    Find the gravitational potential energy of a 6 kg object raised 36 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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18. 18.

    A wave has frequency 274 Hz and wavelength 1.61 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    Find the population standard deviation of: 11, 15, 16, 16, 5 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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20. 20.

    S/ 2,400 is invested at 8% compound interest per annum for 5 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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