Ireland · Year 10 · Practice Sheet 1

1. 1.

   Find the force needed to accelerate a 27 kg mass at 5.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   A triangle has sides a = 16 cm and b = 16 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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3. 3.

   A current of 4.9 A flows through a 4 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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4. 4.

   A right-angled triangle has legs of 11 cm and 19 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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5. 5.

   Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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6. 6.

   A value changes from 148 to 190. 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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7. 7.

   An object with initial velocity 13 m/s accelerates at 3.9 m/s² for 3 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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8. 8.

   An object has mass 108.3 g and volume 19 cm³. Find its density.

   Formula:Density

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

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9. 9.

   A right-angled triangle has legs of 14 cm and 16 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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10. 10.

    A wave has frequency 489 Hz and wavelength 1.64 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    An object with initial velocity 7 m/s accelerates at 1.9 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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12. 12.

    €2,500 is invested at 6% 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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13. 13.

    Find the momentum of a 55 kg object moving at 29 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    A value changes from 101 to 197. 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.

    €2,500 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 66 to 172. 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 cone has base radius 7 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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18. 18.

    A right-angled triangle has legs of 14 cm and 16 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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19. 19.

    A device runs at 139 V drawing 6.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    Find the force needed to accelerate a 14 kg mass at 1.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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