Mongolia · Grade 9 · Practice Sheet 39

1. 1.

   A value changes from 155 to 60. 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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2. 2.

   A bag has 23 equally likely marbles, of which 20 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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3. 3.

   An object has mass 39 g and volume 5 cm³. Find its density.

   Formula:Density

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

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4. 4.

   ₮248 is shared in the ratio 4 : 4. Find each share.

   Formula:Dividing in a Ratio

   $\text{share} = \dfrac{\text{part}}{\text{total parts}} \times T$

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5. 5.

   A circle has a radius of 12 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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6. 6.

   A wave has frequency 40 Hz and wavelength 1.84 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   Find the gravitational potential energy of a 23 kg object raised 6 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   ₮3,100 is invested at 10% 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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9. 9.

   A car travels 168 km in 2 hours. Find its average speed.

   Formula:Speed

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

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10. 10.

    A 9 kg object moves at 13 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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11. 11.

    Find the force needed to accelerate a 46 kg mass at 4.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A 23 kg object moves at 2 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

    A force of 490 N acts on an area of 7.2 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    A right-angled triangle has legs of 18 cm and 16 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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15. 15.

    Find the circumference of a circle whose radius is 7 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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16. 16.

    A bag has 29 equally likely marbles, of which 27 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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17. 17.

    A value changes from 34 to 32. 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.

    An object has mass 59.4 g and volume 9 cm³. Find its density.

    Formula:Density

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

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19. 19.

    A bag has 26 equally likely marbles, of which 5 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.

    A cylinder has radius 2 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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