New Zealand · Year 9 · Practice Sheet 21

1. 1.

   $1,000 is invested at 8% compound interest per annum for 3 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 3 kg object moves at 12 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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3. 3.

   Find the gravitational potential energy of a 12 kg object raised 31 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   A car travels 208 km in 2 hours. Find its average speed.

   Formula:Speed

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

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5. 5.

   A force of 92 N moves an object 25 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   A bag has 17 equally likely marbles, of which 12 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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7. 7.

   A cylinder has radius 10 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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8. 8.

   Solve for x: 9x + 7 = 97.

   Formula:Solving a Linear Equation

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

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9. 9.

   A force of 432 N acts on an area of 9.9 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    A wave has frequency 181 Hz and wavelength 2.5 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    A cone has base radius 8 cm and height 18 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 wave has frequency 722 Hz and wavelength 4.63 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    Find the circumference of a circle whose radius is 12 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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14. 14.

    Find the force needed to accelerate a 22 kg mass at 1.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A force of 40 N moves an object 24 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    A bag has 22 equally likely marbles, of which 18 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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17. 17.

    Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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18. 18.

    A bag has 26 equally likely marbles, of which 14 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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19. 19.

    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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20. 20.

    A 4 kg object moves at 9 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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