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Study guides
76 short guides, one for each kind of question at Levels 6–10: the idea, the steps, worked examples, what to watch out for, and a few to try. The same guides are in the app.
Level 6 · Master
- Age puzzles
- Chance (probability) from a bag
- Circles: area and the distance around
- Distance between two points
- Factoring x² + bx + c
- Adding and multiplying fractions
- Friendly numbers: × 25, × 50 and × 125
- Working out f(x)
- Patterns that multiply (geometric sequences)
- Growth that builds on itself (compound growth)
- Handshakes (counting pairs)
- Multiplying numbers near a round number
- Percent change
- A rectangle from its area and perimeter
- Solving quadratics by factoring
- Squaring numbers that end in 5
- Adding a long list of numbers in a row
- The chance of two things both happening
Level 7 · Geometry
- Arc length and pizza slices (sectors)
- Areas of triangles, trapezoids and parallelograms
- The equation of a circle
- Counting diagonals
- Can these sides make a triangle
- Angles in a circle
- Ladders and Pythagoras
- The midpoint of two points
- Flips and turns on a grid
- Angles and parallel lines
- Angles inside a polygon
- Right triangles: the Pythagorean theorem
- Regular polygons: each angle
- Scale: what happens to area and volume
- Shadows and similar triangles
- Similar triangles
- Special right triangles
- Angles in a triangle
- Volumes: cylinders, cones and balls
Level 8 · Algebra 2
- Absolute value equations
- Combining functions: f(g(x))
- The last digit of a big power
- How many times does a parabola cross the x-axis
- Negative and fraction powers
- Equations with x in the power
- Doubling and halving over time
- Adding a doubling list
- The number i
- Inverse functions
- More workers, fewer days (inverse variation)
- Logarithms (logs)
- Equations with logs
- Remainders without long division
- The vertex of a parabola
Level 9 · Trigonometry
- The angle between clock hands
- The law of cosines
- Heights and distances with angles
- Exact values of sin, cos and tan
- Amplitude and period of a sine wave
- Finding cos from sin (and back)
- Quadrants and reference angles
- Degrees and radians
- Finding a side with sin, cos or tan
- SOH-CAH-TOA: sin, cos and tan in a right triangle
- Solving simple trig equations
- Turning: wheels and clock hands