Spain · Grado 9 · Practice Sheet 17

1. 1.

   A right-angled triangle has legs of 16 cm and 13 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A cone has base radius 11 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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3. 3.

   €76 is shared in the ratio 3 : 1. Find each share.

   Formula:Dividing in a Ratio

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

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4. 4.

   An object has mass 187.2 g and volume 39 cm³. Find its density.

   Formula:Density

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

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5. 5.

   €3,100 is invested at 4% 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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6. 6.

   Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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7. 7.

   €4,000 is invested at 5% compound interest per annum for 4 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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8. 8.

   Find the momentum of a 7 kg object moving at 30 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   Find the force needed to accelerate a 43 kg mass at 4.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A cone has base radius 12 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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11. 11.

    A car travels 126 km in 2 hours. Find its average speed.

    Formula:Speed

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

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12. 12.

    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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13. 13.

    A wave has frequency 871 Hz and wavelength 3.27 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    A value changes from 177 to 182. 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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15. 15.

    €3,700 is invested at 10% 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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16. 16.

    €42 is shared in the ratio 1 : 1. Find each share.

    Formula:Dividing in a Ratio

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

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17. 17.

    A train moves at 62 km/h for 4.3 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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18. 18.

    €3,400 is invested at 8% 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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19. 19.

    Find the momentum of a 22 kg object moving at 10 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    A force of 500 N acts on an area of 3.3 m². Find the pressure.

    Formula:Pressure

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

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