Lebanon · Grade 12 · Practice Sheet 34

1. 1.

   Solve using the quadratic formula: x² + 3x − 4 = 0.

   Formula:Quadratic Formula

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

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2. 2.

   A force of 205 N acts on an area of 5.8 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   A 25 kg object moves at 5 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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4. 4.

   A current of 4.6 A flows through a 16 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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5. 5.

   A 11 kg object moves at 20 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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6. 6.

   LL 1,800 is invested at 5% 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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7. 7.

   Find the momentum of a 42 kg object moving at 13 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A force of 115 N moves an object 13 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   A force of 348 N acts on an area of 7.8 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    A cone has base radius 8 cm and height 4 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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11. 11.

    Find the population standard deviation of: 20, 8, 11, 12, 5 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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12. 12.

    A wave has frequency 341 Hz and wavelength 4.52 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    An object with initial velocity 1 m/s accelerates at 3.2 m/s² for 2 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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14. 14.

    A force of 82 N moves an object 10 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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15. 15.

    Find the sum of the first 3 terms of a geometric series with first term a = 7 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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16. 16.

    A device runs at 6 V drawing 4.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    Find the force needed to accelerate a 31 kg mass at 7.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    Find the sum of the first 11 terms of an arithmetic series with first term a = 3 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

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

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19. 19.

    A 14 kg object moves at 19 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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20. 20.

    A triangle has sides a = 19 cm and b = 14 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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