Ireland · Year 10 · Practice Sheet 5

1. 1.

   A device runs at 238 V drawing 8.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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2. 2.

   Find the force needed to accelerate a 29 kg mass at 6.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   A bag has 14 equally likely marbles, of which 1 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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4. 4.

   A population of 3,000 grows 3% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

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5. 5.

   A body starts at 10 m/s and accelerates at 1.2 m/s² for 12 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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6. 6.

   Solve for x: 4x + 14 = 22.

   Formula:Solving a Linear Equation

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

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7. 7.

   Find the momentum of a 29 kg object moving at 20 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A device runs at 14 V drawing 2.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   Find the sum of the first 15 terms of an arithmetic series with first term a = 8 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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10. 10.

    Find the momentum of a 42 kg object moving at 13 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    An object with initial velocity 6 m/s accelerates at 3.7 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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12. 12.

    A current of 5.8 A flows through a 56 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    A wave has frequency 352 Hz and wavelength 1.65 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    Find the force needed to accelerate a 21 kg mass at 6.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A force of 22 N moves an object 35 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    €2,800 is invested at 3% simple interest per year for 2 years. Find the interest earned.

    Formula:Simple Interest

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

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17. 17.

    An object with initial velocity 11 m/s accelerates at 4.8 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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18. 18.

    Solve for x: 6x + 14 = 86.

    Formula:Solving a Linear Equation

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

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19. 19.

    €3,400 is invested at 8% 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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20. 20.

    A wave has frequency 113 Hz and wavelength 2.51 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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