Chile · Grado 9 · Practice Sheet 49

1. 1.

   Find the gravitational potential energy of a 35 kg object raised 39 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   A 14 kg object moves at 11 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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3. 3.

   A current of 0.5 A flows through a 38 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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4. 4.

   A car travels 480 km in 6 hours. Find its average speed.

   Formula:Speed

   $v = \dfrac{d}{t}$

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5. 5.

   Solve for x: 5x + 16 = 36.

   Formula:Solving a Linear Equation

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

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6. 6.

   A wave has frequency 647 Hz and wavelength 4.34 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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8. 8.

   Find the circumference of a circle whose radius is 6 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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9. 9.

   A cone has base radius 10 cm and height 18 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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10. 10.

    A right-angled triangle has legs of 11 cm and 5 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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11. 11.

    A car travels 609 km in 7 hours. Find its average speed.

    Formula:Speed

    $v = \dfrac{d}{t}$

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12. 12.

    A force of 29 N moves an object 13 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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14. 14.

    Find the force needed to accelerate a 42 kg mass at 7.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A wave has frequency 271 Hz and wavelength 4.35 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    Find the force needed to accelerate a 9 kg mass at 7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A value changes from 27 to 184. 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.

    A bag has 20 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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19. 19.

    A car travels 475 km in 5 hours. Find its average speed.

    Formula:Speed

    $v = \dfrac{d}{t}$

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20. 20.

    $2,100 is invested at 8% 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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