Mexico · Grado 9 · Practice Sheet 7

1. 1.

   A right-angled triangle has legs of 19 cm and 9 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   Find the gravitational potential energy of a 18 kg object raised 24 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   A current of 6.6 A flows through a 48 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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4. 4.

   Find the momentum of a 22 kg object moving at 2 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   Solve for x: 7x + 14 = 49.

   Formula:Solving a Linear Equation

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

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6. 6.

   Find the force needed to accelerate a 5 kg mass at 8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   A cone has base radius 2 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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8. 8.

   A value changes from 153 to 103. Find the percentage change (to 2 d.p.).

   Formula:Percentage Change

   $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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9. 9.

   Solve for x: 8x + 16 = 40.

   Formula:Solving a Linear Equation

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

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10. 10.

    A device runs at 83 V drawing 7.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    A value changes from 56 to 163. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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12. 12.

    A bag has 20 equally likely marbles, of which 8 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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13. 13.

    A 14 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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14. 14.

    An object has mass 82.5 g and volume 15 cm³. Find its density.

    Formula:Density

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

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15. 15.

    Find the momentum of a 51 kg object moving at 19 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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17. 17.

    A value changes from 40 to 23. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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18. 18.

    Find the momentum of a 53 kg object moving at 11 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A bag has 27 equally likely marbles, of which 23 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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20. 20.

    An object has mass 64 g and volume 16 cm³. Find its density.

    Formula:Density

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

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