Greece · Grade 10 · Practice Sheet 36

1. 1.

   An object has mass 25.2 g and volume 9 cm³. Find its density.

   Formula:Density

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

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2. 2.

   €500 is invested at 4% simple interest per year for 6 years. Find the interest earned.

   Formula:Simple Interest

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

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3. 3.

   An object has mass 212.8 g and volume 38 cm³. Find its density.

   Formula:Density

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

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4. 4.

   Find the force needed to accelerate a 54 kg mass at 7.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   €1,800 is invested at 3% 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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6. 6.

   Find the momentum of a 5 kg object moving at 15 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A triangle has sides a = 11 cm and b = 12 cm with an included angle C = 30°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

   $A = \tfrac{1}{2} ab\sin C$

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8. 8.

   A population of 8,700 grows 8% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

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9. 9.

   A cone has base radius 7 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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10. 10.

    A right-angled triangle has legs of 5 cm and 15 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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11. 11.

    A value changes from 22 to 97. 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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12. 12.

    €3,200 is invested at 5% simple interest per year for 6 years. Find the interest earned.

    Formula:Simple Interest

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

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13. 13.

    A wave has frequency 823 Hz and wavelength 4.15 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    An object with initial velocity 1 m/s accelerates at 1.7 m/s² for 7 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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15. 15.

    Find the force needed to accelerate a 8 kg mass at 5.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    A wave has frequency 340 Hz and wavelength 0.2 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    Find the momentum of a 6 kg object moving at 23 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    Find the force needed to accelerate a 56 kg mass at 8.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    €2,600 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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20. 20.

    A right-angled triangle has legs of 6 cm and 4 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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