Ireland · Year 10 · Practice Sheet 12

1. 1.

   Find the force needed to accelerate a 7 kg mass at 6.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   In a triangle, a = 15, b = 8 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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3. 3.

   A current of 2.8 A flows through a 24 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 18 cm and 8 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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5. 5.

   €800 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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6. 6.

   A wave has frequency 471 Hz and wavelength 1.45 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   A right-angled triangle has legs of 11 cm and 18 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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8. 8.

   Solve for x: 3x + 20 = 47.

   Formula:Solving a Linear Equation

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

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9. 9.

   A current of 3 A flows through a 8 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    A bag has 8 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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11. 11.

    Solve for x: 7x + 11 = 74.

    Formula:Solving a Linear Equation

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

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12. 12.

    A force of 86 N moves an object 4 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    A device runs at 117 V drawing 4.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    A current of 7.8 A flows through a 35 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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15. 15.

    An object with initial velocity 6 m/s accelerates at 3.5 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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16. 16.

    A wave has frequency 581 Hz and wavelength 0.64 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    A 14 kg object moves at 24 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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18. 18.

    A right-angled triangle has legs of 18 cm and 9 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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19. 19.

    A triangle has sides a = 11 cm and b = 12 cm with an included angle C = 120°. 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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20. 20.

    Find the sum of the first 20 terms of an arithmetic series with first term a = 8 and common difference d = 6.

    Formula:Sum of an Arithmetic Series

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

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