Israel · Grade 11 · Practice Sheet 39

1. 1.

   Find the gravitational potential energy of a 30 kg object raised 33 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   A right-angled triangle has legs of 19 cm and 20 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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3. 3.

   Find the sum of the first 5 terms of a geometric series with first term a = 3 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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4. 4.

   A force of 292 N acts on an area of 4.3 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   A body starts at 6 m/s and accelerates at 1.5 m/s² for 7 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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6. 6.

   A force of 29 N acts on an area of 1.2 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   A force of 111 N moves an object 16 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   Find the gravitational potential energy of a 45 kg object raised 31 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   A device runs at 81 V drawing 3.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    A current of 7.2 A flows through a 48 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    An object with initial velocity 4 m/s accelerates at 3.6 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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12. 12.

    A triangle has sides a = 6 cm and b = 12 cm with an included angle C = 45°. 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.

    Find the sum of the first 13 terms of an arithmetic series with first term a = 2 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

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

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14. 14.

    Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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15. 15.

    A device runs at 204 V drawing 0.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    A wave has frequency 512 Hz and wavelength 4.62 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    An object with initial velocity 7 m/s accelerates at 1.4 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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18. 18.

    Find the population standard deviation of: 18, 16, 5, 19, 15 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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19. 19.

    A device runs at 213 V drawing 1.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    Find the force needed to accelerate a 4 kg mass at 5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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