New Zealand · Year 10 · Practice Sheet 11

1. 1.

   A population of 4,700 grows 5% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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2. 2.

   $4,900 is invested at 6% 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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3. 3.

   A force of 107 N moves an object 23 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   Find the momentum of a 56 kg object moving at 27 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   A triangle has sides a = 6 cm and b = 6 cm with an included angle C = 60°. 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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6. 6.

   A current of 6 A flows through a 18 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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7. 7.

   Find the momentum of a 1 kg object moving at 15 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A current of 0.5 A flows through a 51 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   Find the force needed to accelerate a 36 kg mass at 5.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A wave has frequency 718 Hz and wavelength 3.75 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    A cone has base radius 7 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

    $V = \tfrac{1}{3} \pi r^2 h$

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12. 12.

    A force of 240 N acts on an area of 2.1 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A force of 74 N moves an object 33 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    A value changes from 180 to 100. 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 40 N moves an object 23 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    A device runs at 138 V drawing 2.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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18. 18.

    A current of 1.5 A flows through a 24 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    $1,300 is invested at 5% 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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20. 20.

    $800 is invested at 7.5% 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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