Denmark · Grade 9 · Practice Sheet 23

1. 1.

   A cone has base radius 4 cm and height 6 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.

   Find the momentum of a 31 kg object moving at 3 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   A force of 16 N moves an object 4 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   A wave has frequency 86 Hz and wavelength 0.65 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   An object has mass 340 g and volume 50 cm³. Find its density.

   Formula:Density

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

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6. 6.

   kr 2,700 is invested at 7.5% simple interest per year for 3 years. Find the interest earned.

   Formula:Simple Interest

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

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7. 7.

   A car travels 328 km in 4 hours. Find its average speed.

   Formula:Speed

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

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8. 8.

   A force of 90 N moves an object 34 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   A bag has 9 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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10. 10.

    kr 144 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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11. 11.

    A bag has 21 equally likely marbles, of which 18 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.

    Find the force needed to accelerate a 60 kg mass at 2.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    A train moves at 36 km/h for 3.9 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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14. 14.

    kr 3,600 is invested at 6% compound interest per annum for 5 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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15. 15.

    A right-angled triangle has legs of 11 cm and 4 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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16. 16.

    A value changes from 96 to 87. 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 wave has frequency 39 Hz and wavelength 3.44 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    A train moves at 51 km/h for 4.5 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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19. 19.

    Find the circumference of a circle whose radius is 21 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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20. 20.

    kr 2,900 is invested at 4% 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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