Egypt · Grade 11 · Practice Sheet 14

1. 1.

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

   Formula:Volume of a Cone

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

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2. 2.

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

   Formula:Quadratic Formula

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

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3. 3.

   Find the gravitational potential energy of a 7 kg object raised 7 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   A 10 kg object moves at 13 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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5. 5.

   A right-angled triangle has legs of 6 cm and 15 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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6. 6.

   Solve using the quadratic formula: x² + 2x − 15 = 0.

   Formula:Quadratic Formula

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

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7. 7.

   A wave has frequency 126 Hz and wavelength 0.21 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   A cone has base radius 11 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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9. 9.

   In a triangle, a = 12, b = 12 and the included angle C = 100°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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10. 10.

    A wave has frequency 872 Hz and wavelength 0.63 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    Two masses 3,300 kg and 390 kg are 10 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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12. 12.

    A device runs at 87 V drawing 8.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    A wave has frequency 704 Hz and wavelength 3.6 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    Find the sum of the first 5 terms of a geometric series with first term a = 5 and common ratio r = 4.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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15. 15.

    An object has mass 126.4 g and volume 16 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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16. 16.

    A current of 0.7 A flows through a 14 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    A cone has base radius 11 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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18. 18.

    E£ 1,700 is invested at 8% 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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19. 19.

    Two masses 6,600 kg and 330 kg are 20 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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20. 20.

    Find the population standard deviation of: 5, 15, 3, 20, 12 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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