Ireland · Year 10 · Practice Sheet 13

1. 1.

   A current of 5.3 A flows through a 25 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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2. 2.

   A force of 87 N moves an object 3 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   Solve for x: 2x + 11 = 23.

   Formula:Solving a Linear Equation

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

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4. 4.

   A value changes from 163 to 141. 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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5. 5.

   €3,700 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.

   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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7. 7.

   A wave has frequency 339 Hz and wavelength 2.61 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   A bag has 10 equally likely marbles, of which 6 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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9. 9.

   A current of 1.9 A flows through a 5 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    Find the sum of the first 16 terms of an arithmetic series with first term a = 5 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

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

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11. 11.

    A device runs at 105 V drawing 4.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    Solve for x: 2x + 13 = 19.

    Formula:Solving a Linear Equation

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

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13. 13.

    A current of 6.6 A flows through a 29 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    A right-angled triangle has legs of 8 cm and 12 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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15. 15.

    A cylinder has radius 10 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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16. 16.

    A value changes from 27 to 110. 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.

    In a triangle, a = 5, b = 7 and the included angle C = 40°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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18. 18.

    A body starts at 20 m/s and accelerates at 4.7 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    A force of 78 N acts on an area of 8.2 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    Solve using the quadratic formula: x² + 2x + 0 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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