New Zealand · Year 9 · Practice Sheet 23

1. 1.

   A train moves at 48 km/h for 3.3 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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2. 2.

   A force of 444 N acts on an area of 8.6 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   $66 is shared in the ratio 4 : 2. Find each share.

   Formula:Dividing in a Ratio

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

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4. 4.

   Find the force needed to accelerate a 32 kg mass at 2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   A train moves at 34 km/h for 3 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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6. 6.

   Find the circumference of a circle whose radius is 4 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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7. 7.

   A force of 21 N acts on an area of 6.1 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   Find the gravitational potential energy of a 31 kg object raised 13 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   A force of 63 N moves an object 22 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    A circle has a radius of 10 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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11. 11.

    A right-angled triangle has legs of 15 cm and 18 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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12. 12.

    Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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13. 13.

    A cone has base radius 3 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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14. 14.

    $3,900 is invested at 6% 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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15. 15.

    A circle has a radius of 9 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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16. 16.

    $1,800 is invested at 6% 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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17. 17.

    $175 is shared in the ratio 4 : 1. Find each share.

    Formula:Dividing in a Ratio

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

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18. 18.

    A 18 kg object moves at 8 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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19. 19.

    A right-angled triangle has legs of 8 cm and 3 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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20. 20.

    An object has mass 39 g and volume 39 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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