Germany · Klasse 10 · Practice Sheet 29

1. 1.

   A bag has 14 equally likely marbles, of which 13 are red. Find the probability of drawing a red marble (to 3 d.p.).

   Formula:Simple Probability

   $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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2. 2.

   An object with initial velocity 15 m/s accelerates at 4.2 m/s² for 7 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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3. 3.

   A bag has 21 equally likely marbles, of which 4 are red. Find the probability of drawing a red marble (to 3 d.p.).

   Formula:Simple Probability

   $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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4. 4.

   €3,300 is invested at 5% simple interest per year for 4 years. Find the interest earned.

   Formula:Simple Interest

   $I = \dfrac{P \times r \times t}{100}$

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5. 5.

   Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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6. 6.

   €4,100 is invested at 5% simple interest per year for 2 years. Find the interest earned.

   Formula:Simple Interest

   $I = \dfrac{P \times r \times t}{100}$

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7. 7.

   A force of 31 N moves an object 30 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   €800 is invested at 8% simple interest per year for 3 years. Find the interest earned.

   Formula:Simple Interest

   $I = \dfrac{P \times r \times t}{100}$

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9. 9.

   Find the force needed to accelerate a 25 kg mass at 5.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    An object has mass 27.6 g and volume 6 cm³. Find its density.

    Formula:Density

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

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11. 11.

    A current of 0.6 A flows through a 16 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    A cylinder has radius 8 cm and height 25 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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13. 13.

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

    An object has mass 200.9 g and volume 41 cm³. Find its density.

    Formula:Density

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

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15. 15.

    A force of 451 N acts on an area of 8.7 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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17. 17.

    A cone has base radius 8 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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18. 18.

    €1,600 is invested at 5% compound interest per annum for 3 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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19. 19.

    A wave has frequency 706 Hz and wavelength 0.7 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    An object with initial velocity 14 m/s accelerates at 3 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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