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Questions and Answers
Solve the quadratic equation $x^2 + 5x - 6 = 0$ using analytical techniques.
Solve the quadratic equation $x^2 + 5x - 6 = 0$ using analytical techniques.
Factorization: $x^2 + 5x - 6 = (x + 6)(x - 1) = 0$ , so $x = -6$ or $x = 1$.
A rectangular prism has a length of 6cm, a width of 4cm and a height of 3cm. Find its surface area.
A rectangular prism has a length of 6cm, a width of 4cm and a height of 3cm. Find its surface area.
Surface area = 2(lw + lh + wh) = 2(64 + 63 + 4*3) = 2(24 + 18 + 12) = 108 cm²
A sphere has a radius of 5cm. Find its volume.
A sphere has a radius of 5cm. Find its volume.
Volume = (4/3)πr³ = (4/3)π(5)³ = (500/3)π = 523.6 cm³
A car is travelling at a speed of 60 km/h. If the distance from the starting point to the finishing point is directly proportional to the time taken, determine the constant of proportionality.
A car is travelling at a speed of 60 km/h. If the distance from the starting point to the finishing point is directly proportional to the time taken, determine the constant of proportionality.
Draw a graph to illustrate the relationship between the distance an object travels and time, given that the object accelerates uniformly from rest.
Draw a graph to illustrate the relationship between the distance an object travels and time, given that the object accelerates uniformly from rest.
A ship is sailing due east at a speed of 20 km/h. If the bearing of a lighthouse from the ship is 060°, how far is the ship from the lighthouse?
A ship is sailing due east at a speed of 20 km/h. If the bearing of a lighthouse from the ship is 060°, how far is the ship from the lighthouse?
A triangular prism has a base area of 20 cm² and a height of 8cm. Find its volume.
A triangular prism has a base area of 20 cm² and a height of 8cm. Find its volume.
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Study Notes
Equations and Inequalities
- Solves linear and simple quadratic equations using analytical and graphical techniques
- Solves complex linear, quadratic, simple cubic and simultaneous equations
- Rearranges literal equations
Geometry
- Calculates the areas of composite shapes
- Calculates the surface areas of rectangular and triangular prisms
- Calculates the surface areas of right prisms, cylinders and related composite solids
- Calculates the volumes of composite solids composed of right prisms and cylinders
- Calculates the volumes of right pyramids, right cones, spheres and related composite solids
Proportion
- Recognises direct and indirect proportion
- Solves problems involving direct proportion
Graphs
- Draws, interprets and analyses graphs of physical phenomena
Trigonometry
- Applies trigonometry to solve problems involving angles of elevation and depression
- Applies trigonometry to solve problems involving bearings
- Uses Pythagoras' theorem, trigonometric relationships, the sine rule, the cosine rule and the area rule to solve problems
- Solves problems involving three dimensions
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