Ethiopia · Grade 12 · Practice Sheet 13

1. 1.

   Solve using the quadratic formula: x² + 0x − 9 = 0.

   Formula:Quadratic Formula

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

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2. 2.

   In a triangle, a = 12, b = 6 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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3. 3.

   Find the force needed to accelerate a 57 kg mass at 1.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   A force of 37 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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5. 5.

   Two masses 6,900 kg and 590 kg are 3 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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6. 6.

   A cone has base radius 2 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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7. 7.

   A body starts at 8 m/s and accelerates at 2.9 m/s² for 12 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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8. 8.

   An object with initial velocity 12 m/s accelerates at 4.4 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 force needed to accelerate a 33 kg mass at 7.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A force of 163 N acts on an area of 1.4 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    Find the force needed to accelerate a 51 kg mass at 3.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A wave has frequency 346 Hz and wavelength 2.4 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    A current of 1.1 A flows through a 44 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    A body starts at 10 m/s and accelerates at 5.2 m/s² for 12 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    Br 3,400 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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16. 16.

    A force of 14 N moves an object 36 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    Find the gravitational potential energy of a 44 kg object raised 18 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    A 2 kg object moves at 4 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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19. 19.

    A body starts at 10 m/s and accelerates at 3.3 m/s² for 7 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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