Australia · Year 10 · Practice Sheet 32

1. 1.

   A right-angled triangle has legs of 20 cm and 5 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A cone has base radius 2 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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3. 3.

   A force of 57 N moves an object 10 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   A cylinder has radius 9 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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5. 5.

   In a triangle, a = 15, b = 14 and the included angle C = 50°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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6. 6.

   A bag has 26 equally likely marbles, of which 25 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 triangle has sides a = 13 cm and b = 11 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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8. 8.

   In a triangle, a = 18, b = 8 and the included angle C = 60°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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9. 9.

   A wave has frequency 731 Hz and wavelength 3.54 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    An object has mass 137.2 g and volume 49 cm³. Find its density.

    Formula:Density

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

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11. 11.

    Solve using the quadratic formula: x² − 1x + 0 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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12. 12.

    A cone has base radius 4 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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13. 13.

    $1,800 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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14. 14.

    An object has mass 35 g and volume 7 cm³. Find its density.

    Formula:Density

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

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15. 15.

    Find the force needed to accelerate a 27 kg mass at 1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    In a triangle, a = 9, b = 10 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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17. 17.

    A force of 292 N acts on an area of 9.8 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    Find the gravitational potential energy of a 39 kg object raised 19 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    A body starts at 17 m/s and accelerates at 3 m/s² for 7 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    Find the momentum of a 12 kg object moving at 26 m/s.

    Formula:Momentum

    $p = mv$

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