Ethiopia · Grade 11 · Practice Sheet 33

1. 1.

   Two masses 1,700 kg and 280 kg are 17 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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2. 2.

   Solve using the quadratic formula: x² − 11x + 30 = 0.

   Formula:Quadratic Formula

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

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3. 3.

   A triangle has sides a = 11 cm and b = 19 cm with an included angle C = 90°. 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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4. 4.

   A right-angled triangle has legs of 9 cm and 17 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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5. 5.

   A cylinder has radius 10 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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6. 6.

   Find the sum of the first 15 terms of an arithmetic series with first term a = 6 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

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

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7. 7.

   Find the population standard deviation of: 10, 5, 12, 3, 13 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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8. 8.

   Find the momentum of a 14 kg object moving at 9 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   A current of 6.3 A flows through a 33 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    Find the momentum of a 4 kg object moving at 13 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    A 11 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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12. 12.

    A population of 2,100 grows 3% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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13. 13.

    A 37 kg object moves at 12 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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14. 14.

    Find the momentum of a 26 kg object moving at 11 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    A force of 120 N moves an object 30 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    An object with initial velocity 6 m/s accelerates at 2.9 m/s² for 4 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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17. 17.

    Br 1,000 is invested at 8% compound interest per annum for 5 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.

    In a triangle, a = 18, b = 12 and the included angle C = 40°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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19. 19.

    Find the gravitational potential energy of a 36 kg object raised 19 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    An object with initial velocity 5 m/s accelerates at 2.7 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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