Austria · Klasse 11 · Practice Sheet 31

1. 1.

   €3,000 is invested at 5% 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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2. 2.

   Find the force needed to accelerate a 16 kg mass at 4.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   Solve using the quadratic formula: x² + 3x − 18 = 0.

   Formula:Quadratic Formula

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

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4. 4.

   A current of 4 A flows through a 57 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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5. 5.

   A right-angled triangle has legs of 16 cm and 7 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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6. 6.

   A triangle has sides a = 9 cm and b = 17 cm with an included angle C = 90°. 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.

   Solve using the quadratic formula: x² + 10x + 24 = 0.

   Formula:Quadratic Formula

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

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8. 8.

   A force of 60 N acts on an area of 9.6 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   In a triangle, a = 14, b = 10 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.

    Find the gravitational potential energy of a 19 kg object raised 16 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    Find the force needed to accelerate a 55 kg mass at 1.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A wave has frequency 306 Hz and wavelength 1.49 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    A force of 14 N moves an object 4 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    Find the force needed to accelerate a 37 kg mass at 0.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A current of 7 A flows through a 32 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    Find the sum of the first 15 terms of an arithmetic series with first term a = 6 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

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

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17. 17.

    An object has mass 33 g and volume 10 cm³. Find its density.

    Formula:Density

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

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18. 18.

    Find the momentum of a 47 kg object moving at 11 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A cylinder has radius 7 cm and height 12 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 momentum of a 31 kg object moving at 17 m/s.

    Formula:Momentum

    $p = mv$

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