Ukraine · Grade 12 · Practice Sheet 25

1. 1.

   ₴1,400 is invested at 4% compound interest per annum for 4 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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2. 2.

   Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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3. 3.

   Find the momentum of a 26 kg object moving at 26 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   A 35 kg object moves at 9 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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5. 5.

   ₴1,500 is invested at 6% 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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6. 6.

   Find the force needed to accelerate a 50 kg mass at 8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   Solve using the quadratic formula: x² − 5x + 4 = 0.

   Formula:Quadratic Formula

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

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8. 8.

   A current of 3.3 A flows through a 9 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   A device runs at 143 V drawing 1.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    Find the population standard deviation of: 18, 2, 2, 20, 14 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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11. 11.

    A device runs at 100 V drawing 7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    A wave has frequency 714 Hz and wavelength 2.98 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    Find the population standard deviation of: 11, 18, 9, 7, 11 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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14. 14.

    Find the momentum of a 1 kg object moving at 22 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    A force of 103 N moves an object 25 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    A triangle has sides a = 12 cm and b = 12 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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17. 17.

    In a triangle, a = 5, b = 9 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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18. 18.

    An object with initial velocity 2 m/s accelerates at 2.7 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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19. 19.

    A force of 80 N moves an object 29 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    Find the population standard deviation of: 14, 7, 17, 7, 6 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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