United Arab Emirates · Grade 12 · Practice Sheet 35

1. 1.

   Find the gravitational potential energy of a 33 kg object raised 37 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   A cone has base radius 9 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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3. 3.

   A device runs at 44 V drawing 2.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   A body starts at 18 m/s and accelerates at 4.7 m/s² for 10 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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5. 5.

   A wave has frequency 184 Hz and wavelength 4.2 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   Find the population standard deviation of: 19, 14, 19, 18, 12 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   Solve using the quadratic formula: x² − 7x + 10 = 0.

   Formula:Quadratic Formula

   $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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8. 8.

   A population of 8,300 grows 2% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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9. 9.

   Find the gravitational potential energy of a 31 kg object raised 26 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    Find the sum of the first 5 terms of a geometric series with first term a = 1 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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11. 11.

    Find the force needed to accelerate a 29 kg mass at 3.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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13. 13.

    A force of 99 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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14. 14.

    A triangle has sides a = 15 cm and b = 14 cm with an included angle C = 120°. 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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15. 15.

    A force of 57 N moves an object 5 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    AED 3,300 is invested at 5% 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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17. 17.

    An object with initial velocity 10 m/s accelerates at 3.3 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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18. 18.

    Find the gravitational potential energy of a 6 kg object raised 7 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    Find the momentum of a 32 kg object moving at 18 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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