Ireland · Year 10 · Practice Sheet 28

1. 1.

   A right-angled triangle has legs of 10 cm and 4 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   Solve for x: 4x + 15 = 39.

   Formula:Solving a Linear Equation

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

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3. 3.

   A 40 kg object moves at 12 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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4. 4.

   A body starts at 1 m/s and accelerates at 2.6 m/s² for 10 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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5. 5.

   €1,200 is invested at 8% 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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6. 6.

   €2,400 is invested at 3% 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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7. 7.

   A device runs at 15 V drawing 4.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   An object with initial velocity 1 m/s accelerates at 4.2 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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9. 9.

   Solve for x: 7x + 15 = 64.

   Formula:Solving a Linear Equation

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

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10. 10.

    A current of 4.5 A flows through a 39 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    A force of 41 N moves an object 36 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    A 17 kg object moves at 7 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

    Find the momentum of a 25 kg object moving at 27 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    A body starts at 14 m/s and accelerates at 2.3 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    An object with initial velocity 12 m/s accelerates at 4.8 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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16. 16.

    Find the force needed to accelerate a 8 kg mass at 1.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A force of 77 N moves an object 20 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    A force of 390 N acts on an area of 8.8 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    A wave has frequency 185 Hz and wavelength 4.04 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    €4,000 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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