New Zealand · Year 9 · Practice Sheet 44

1. 1.

   $130 is shared in the ratio 2 : 3. Find each share.

   Formula:Dividing in a Ratio

   $\text{share} = \dfrac{\text{part}}{\text{total parts}} \times T$

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2. 2.

   Find the circumference of a circle whose radius is 13 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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3. 3.

   Find the momentum of a 18 kg object moving at 27 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   A force of 337 N acts on an area of 6.3 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   A bag has 29 equally likely marbles, of which 17 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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6. 6.

   A car travels 623 km in 7 hours. Find its average speed.

   Formula:Speed

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

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7. 7.

   A train moves at 87 km/h for 2.3 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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8. 8.

   $176 is shared in the ratio 3 : 5. Find each share.

   Formula:Dividing in a Ratio

   $\text{share} = \dfrac{\text{part}}{\text{total parts}} \times T$

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9. 9.

   A current of 2 A flows through a 24 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    A wave has frequency 532 Hz and wavelength 0.61 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    Solve for x: 8x + 10 = 66.

    Formula:Solving a Linear Equation

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

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12. 12.

    $3,400 is invested at 5% 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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13. 13.

    Find the circumference of a circle whose radius is 19 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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14. 14.

    A value changes from 198 to 250. 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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15. 15.

    A force of 91 N moves an object 29 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    $1,600 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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17. 17.

    $112 is shared in the ratio 5 : 2. Find each share.

    Formula:Dividing in a Ratio

    $\text{share} = \dfrac{\text{part}}{\text{total parts}} \times T$

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18. 18.

    $1,500 is invested at 6% simple interest per year for 5 years. Find the interest earned.

    Formula:Simple Interest

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

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19. 19.

    A car travels 180 km in 6 hours. Find its average speed.

    Formula:Speed

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

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20. 20.

    Find the momentum of a 1 kg object moving at 27 m/s.

    Formula:Momentum

    $p = mv$

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