Austria · Klasse 12 · Practice Sheet 11

1. 1.

   A cone has base radius 6 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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2. 2.

   In a triangle, a = 9, 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.

   Two masses 8,000 kg and 700 kg are 8 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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4. 4.

   A current of 7.8 A flows through a 15 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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5. 5.

   Solve using the quadratic formula: x² + 1x − 30 = 0.

   Formula:Quadratic Formula

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

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6. 6.

   A triangle has sides a = 11 cm and b = 11 cm with an included angle C = 60°. 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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7. 7.

   Find the sum of the first 8 terms of a geometric series with first term a = 3 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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8. 8.

   Find the sum of the first 7 terms of an arithmetic series with first term a = 5 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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9. 9.

   A body starts at 11 m/s and accelerates at 2.4 m/s² for 2 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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10. 10.

    A wave has frequency 647 Hz and wavelength 3.47 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    A body starts at 14 m/s and accelerates at 4.1 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    A force of 11 N moves an object 5 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    A force of 211 N acts on an area of 3.5 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    A device runs at 182 V drawing 2.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    A force of 111 N acts on an area of 6.3 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Find the sum of the first 7 terms of a geometric series with first term a = 8 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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17. 17.

    A body starts at 8 m/s and accelerates at 6 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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18. 18.

    Find the force needed to accelerate a 41 kg mass at 2.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    Solve using the quadratic formula: x² + 1x − 2 = 0.

    Formula:Quadratic Formula

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

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20. 20.

    A force of 87 N acts on an area of 6.9 m². Find the pressure.

    Formula:Pressure

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

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