Ecuador · Grado 9 · Practice Sheet 29

1. 1.

   A cone has base radius 2 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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2. 2.

   Solve for x: 4x + 11 = 59.

   Formula:Solving a Linear Equation

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

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3. 3.

   A train moves at 49 km/h for 4.4 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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4. 4.

   $4,900 is invested at 4% simple interest per year for 5 years. Find the interest earned.

   Formula:Simple Interest

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

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5. 5.

   $4,000 is invested at 4% 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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6. 6.

   A cylinder has radius 11 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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7. 7.

   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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8. 8.

   An object has mass 77 g and volume 22 cm³. Find its density.

   Formula:Density

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

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9. 9.

   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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10. 10.

    A force of 105 N moves an object 12 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    A force of 42 N acts on an area of 7.7 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    $4,000 is invested at 8% 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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13. 13.

    A cylinder has radius 12 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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14. 14.

    A wave has frequency 742 Hz and wavelength 1.61 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    A car travels 240 km in 5 hours. Find its average speed.

    Formula:Speed

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

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16. 16.

    Find the circumference of a circle whose radius is 10 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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17. 17.

    A device runs at 14 V drawing 0.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    A cone has base radius 11 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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19. 19.

    A 23 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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20. 20.

    A bag has 15 equally likely marbles, of which 3 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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