Mongolia · Grade 9 · Practice Sheet 49

1. 1.

   Find the circumference of a circle whose radius is 12 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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2. 2.

   A right-angled triangle has legs of 6 cm and 17 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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3. 3.

   A current of 2.5 A flows through a 17 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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4. 4.

   Solve for x: 9x + 18 = 108.

   Formula:Solving a Linear Equation

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

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5. 5.

   Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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6. 6.

   ₮600 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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7. 7.

   An object has mass 48 g and volume 6 cm³. Find its density.

   Formula:Density

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

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8. 8.

   Solve for x: 4x + 3 = 19.

   Formula:Solving a Linear Equation

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

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9. 9.

   A car travels 327 km in 3 hours. Find its average speed.

   Formula:Speed

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

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10. 10.

    A train moves at 74 km/h for 2.8 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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11. 11.

    A bag has 18 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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12. 12.

    An object has mass 166.6 g and volume 49 cm³. Find its density.

    Formula:Density

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

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13. 13.

    Find the momentum of a 12 kg object moving at 17 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    A wave has frequency 26 Hz and wavelength 1.26 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    ₮2,200 is invested at 5% compound interest per annum for 3 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 value changes from 27 to 69. 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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17. 17.

    A 30 kg object moves at 3 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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18. 18.

    ₮2,000 is invested at 5% 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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19. 19.

    Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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20. 20.

    Find the force needed to accelerate a 32 kg mass at 7.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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