7 Questions
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.
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.
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.
Distance = speed * time, so k = 60 km/h.
Draw a graph to illustrate the relationship between the distance an object travels and time, given that the object accelerates uniformly from rest.
A graph with a positive curvature, passing through the origin, representing the equation d = 0.5at².
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?
Use the cosine rule: c² = 20² + l² - 2(20)(l)cos(60°), where l is the distance from the ship to the lighthouse.
A triangular prism has a base area of 20 cm² and a height of 8cm. Find its volume.
Volume = base area * height = 20 * 8 = 160 cm³
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
This quiz covers solving linear and quadratic equations, linear inequalities, and linear simultaneous equations. It also covers calculating areas and volumes of various shapes including composite solids.
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