Tanzania · Grade 11 · Practice Sheet 33

1. 1.

   Two masses 7,200 kg and 370 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.

   In a triangle, a = 8, b = 10 and the included angle C = 110°. 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.

   Solve using the quadratic formula: x² − 9x + 18 = 0.

   Formula:Quadratic Formula

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

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4. 4.

   Two masses 8,200 kg and 180 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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5. 5.

   Find the force needed to accelerate a 38 kg mass at 1.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   TSh 1,900 is invested at 3% 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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7. 7.

   Find the gravitational potential energy of a 34 kg object raised 17 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   Two masses 1,700 kg and 560 kg are 5 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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9. 9.

   A current of 3.9 A flows through a 51 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    In a triangle, a = 8, b = 11 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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11. 11.

    Solve using the quadratic formula: x² − 4x − 12 = 0.

    Formula:Quadratic Formula

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

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12. 12.

    A force of 133 N acts on an area of 8.8 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A current of 2 A flows through a 29 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    Find the momentum of a 35 kg object moving at 23 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    Find the gravitational potential energy of a 41 kg object raised 16 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    A right-angled triangle has legs of 13 cm and 17 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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17. 17.

    A wave has frequency 552 Hz and wavelength 2.67 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    Find the force needed to accelerate a 2 kg mass at 2.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A cylinder has radius 5 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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20. 20.

    Find the force needed to accelerate a 25 kg mass at 6.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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