Ireland · Year 9 · Practice Sheet 32

1. 1.

   €2,500 is invested at 3% compound interest per annum for 5 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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2. 2.

   A wave has frequency 565 Hz and wavelength 4.62 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   A car travels 410 km in 5 hours. Find its average speed.

   Formula:Speed

   $v = \dfrac{d}{t}$

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4. 4.

   A wave has frequency 507 Hz and wavelength 4.53 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   A car travels 303 km in 3 hours. Find its average speed.

   Formula:Speed

   $v = \dfrac{d}{t}$

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6. 6.

   Solve for x: 6x + 5 = 23.

   Formula:Solving a Linear Equation

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

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7. 7.

   Find the gravitational potential energy of a 28 kg object raised 31 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   Find the momentum of a 52 kg object moving at 21 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   A car travels 114 km in 2 hours. Find its average speed.

   Formula:Speed

   $v = \dfrac{d}{t}$

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10. 10.

    A bag has 21 equally likely marbles, of which 7 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.

    A value changes from 95 to 245. 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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12. 12.

    A force of 81 N moves an object 30 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    A train moves at 60 km/h for 5.2 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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14. 14.

    Solve for x: 9x + 8 = 53.

    Formula:Solving a Linear Equation

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

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15. 15.

    A right-angled triangle has legs of 3 cm and 16 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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16. 16.

    €4,300 is invested at 6% 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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17. 17.

    A circle has a radius of 4 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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18. 18.

    A train moves at 70 km/h for 5.4 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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19. 19.

    Find the gravitational potential energy of a 10 kg object raised 12 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    Solve for x: 4x + 3 = 31.

    Formula:Solving a Linear Equation

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

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