Australia · Year 9 · Practice Sheet 26

1. 1.

   Solve for x: 6x + 17 = 65.

   Formula:Solving a Linear Equation

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

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2. 2.

   Find the force needed to accelerate a 6 kg mass at 6.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   A bag has 11 equally likely marbles, of which 3 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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4. 4.

   A car travels 183 km in 3 hours. Find its average speed.

   Formula:Speed

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

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5. 5.

   A cone has base radius 6 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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6. 6.

   A device runs at 163 V drawing 9.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   $2,200 is invested at 3% 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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8. 8.

   A device runs at 42 V drawing 3.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   A bag has 16 equally likely marbles, of which 9 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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10. 10.

    A wave has frequency 632 Hz and wavelength 1.43 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

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

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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12. 12.

    Find the gravitational potential energy of a 38 kg object raised 2 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    A current of 4.4 A flows through a 44 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    A cylinder has radius 13 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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15. 15.

    A wave has frequency 856 Hz and wavelength 1.29 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    Find the momentum of a 58 kg object moving at 6 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    A 6 kg object moves at 2 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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18. 18.

    Solve for x: 3x + 1 = 13.

    Formula:Solving a Linear Equation

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

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19. 19.

    $1,200 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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20. 20.

    A car travels 348 km in 4 hours. Find its average speed.

    Formula:Speed

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

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