Germany · Klasse 10 · Practice Sheet 14

1. 1.

   A bag has 27 equally likely marbles, of which 16 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.

   A current of 0.8 A flows through a 41 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   A body starts at 6 m/s and accelerates at 5.3 m/s² for 7 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   €2,200 is invested at 6% compound interest per annum for 2 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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5. 5.

   Solve for x: 5x + 1 = 26.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

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6. 6.

   A device runs at 28 V drawing 5.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   A 29 kg object moves at 24 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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8. 8.

   Solve for x: 5x + 2 = 17.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

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9. 9.

   Solve using the quadratic formula: x² − 6x + 5 = 0.

   Formula:Quadratic Formula

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

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10. 10.

    In a triangle, a = 17, b = 14 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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11. 11.

    A force of 158 N acts on an area of 5.7 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    A force of 27 N moves an object 2 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    A bag has 17 equally likely marbles, of which 6 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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14. 14.

    A current of 6.8 A flows through a 54 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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15. 15.

    €1,400 is invested at 5% compound interest per annum for 2 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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16. 16.

    A cone has base radius 6 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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17. 17.

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

    Formula:Quadratic Formula

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

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18. 18.

    A cylinder has radius 13 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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19. 19.

    A force of 51 N acts on an area of 4.4 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    A 28 kg object moves at 20 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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