Russia · Grade 12 · Practice Sheet 17

1. 1.

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

   Formula:Quadratic Formula

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

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2. 2.

   A 16 kg object moves at 8 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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3. 3.

   Find the population standard deviation of: 8, 16, 12, 3, 12 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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4. 4.

   Find the gravitational potential energy of a 32 kg object raised 6 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   A device runs at 229 V drawing 8.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   A force of 119 N moves an object 28 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   A triangle has sides a = 6 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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8. 8.

   An object with initial velocity 6 m/s accelerates at 2.8 m/s² for 9 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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9. 9.

   Find the momentum of a 12 kg object moving at 22 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    An object with initial velocity 14 m/s accelerates at 4.2 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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11. 11.

    A cone has base radius 2 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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12. 12.

    Two masses 1,700 kg and 170 kg are 19 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

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13. 13.

    A triangle has sides a = 7 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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14. 14.

    Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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15. 15.

    An object with initial velocity 2 m/s accelerates at 4.2 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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16. 16.

    Find the force needed to accelerate a 9 kg mass at 8.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    ₽2,700 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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18. 18.

    A device runs at 102 V drawing 5.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    In a triangle, a = 9, b = 5 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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20. 20.

    A 15 kg object moves at 2 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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