Ecuador · Grado 12 · Practice Sheet 50

1. 1.

   A cone has base radius 4 cm and height 4 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.

   A wave has frequency 28 Hz and wavelength 1.19 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   A cone has base radius 6 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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4. 4.

   Find the population standard deviation of: 17, 14, 8, 15, 7 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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5. 5.

   A current of 0.8 A flows through a 53 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   Find the momentum of a 43 kg object moving at 4 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   Two masses 1,700 kg and 320 kg are 2 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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8. 8.

   $700 is invested at 6% 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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9. 9.

   A 3 kg object moves at 3 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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10. 10.

    A current of 3.6 A flows through a 45 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    Find the population standard deviation of: 10, 3, 15, 18, 4 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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12. 12.

    A population of 8,600 grows 3% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    In a triangle, a = 8, b = 5 and the included angle C = 70°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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14. 14.

    Solve using the quadratic formula: x² + 1x − 12 = 0.

    Formula:Quadratic Formula

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

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15. 15.

    A force of 34 N acts on an area of 1.8 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    A body starts at 9 m/s and accelerates at 1.5 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    A force of 35 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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18. 18.

    A current of 5.9 A flows through a 59 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    A body starts at 10 m/s and accelerates at 2.8 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    Find the momentum of a 52 kg object moving at 11 m/s.

    Formula:Momentum

    $p = mv$

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