Germany · Klasse 10 · Practice Sheet 22

1. 1.

   A body starts at 19 m/s and accelerates at 1.4 m/s² for 11 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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2. 2.

   A current of 7.8 A flows through a 26 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   A 27 kg object moves at 22 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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4. 4.

   A right-angled triangle has legs of 18 cm and 7 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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5. 5.

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

   Formula:Quadratic Formula

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

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6. 6.

   In a triangle, a = 13, b = 6 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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7. 7.

   A 32 kg object moves at 23 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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8. 8.

   A population of 2,700 grows 10% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

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

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9. 9.

   A device runs at 162 V drawing 9.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    Find the gravitational potential energy of a 2 kg object raised 33 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    An object has mass 218.3 g and volume 37 cm³. Find its density.

    Formula:Density

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

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12. 12.

    A triangle has sides a = 14 cm and b = 19 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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13. 13.

    A device runs at 169 V drawing 3.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    Find the sum of the first 13 terms of an arithmetic series with first term a = 11 and common difference d = 6.

    Formula:Sum of an Arithmetic Series

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

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15. 15.

    A 24 kg object moves at 2 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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16. 16.

    Find the force needed to accelerate a 60 kg mass at 4.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A force of 113 N moves an object 34 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    A cylinder has radius 3 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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19. 19.

    €2,400 is invested at 8% compound interest per annum for 5 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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20. 20.

    A device runs at 114 V drawing 6.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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