Portugal · Ano 11 · Practice Sheet 13

1. 1.

   A body starts at 4 m/s and accelerates at 2.4 m/s² for 12 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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2. 2.

   A cylinder has radius 4 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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3. 3.

   A population of 4,800 grows 2% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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4. 4.

   A right-angled triangle has legs of 14 cm and 14 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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5. 5.

   In a triangle, a = 14, b = 7 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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6. 6.

   Find the sum of the first 7 terms of a geometric series with first term a = 1 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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7. 7.

   Two masses 3,700 kg and 590 kg are 6 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.

   A current of 5.3 A flows through a 42 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   A force of 236 N acts on an area of 0.9 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    Find the gravitational potential energy of a 18 kg object raised 30 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    A population of 4,700 grows 5% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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12. 12.

    A current of 0.5 A flows through a 52 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    A device runs at 230 V drawing 5.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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15. 15.

    A cone has base radius 10 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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16. 16.

    A wave has frequency 619 Hz and wavelength 2.34 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    Find the force needed to accelerate a 43 kg mass at 4.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    Find the sum of the first 5 terms of an arithmetic series with first term a = 7 and common difference d = 5.

    Formula:Sum of an Arithmetic Series

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

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19. 19.

    A force of 83 N moves an object 7 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    A current of 5.4 A flows through a 42 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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