Free preview · Senior 6 Mathematics · Practical activities
Senior 6 practical activities
9 units · 18 activities. In every unit, activity 1 is improvised (simple local materials) and activity 2 is conventional (mathematical instruments): two different activities. Below are 5 free pages; then get the whole level in one PDF.
- Title and aim of every activity
- Required materials and safety notes
- A clear, diagram or diagram
- Step-by-step procedure and a results table to fill in
- Observation and conclusion
- Three questions per activity, with sample results and answers at the end of the unit
See all 18 activities of this level and what each one is about
- Unit 1: Complex Numbers
- 1.1 Improvised · Multiplying by i: turning on a floor grid. To show that multiplying a complex number by i rotates it through 90° about the origin.
- 1.2 Conventional · The Argand diagram and roots of unity. To check the rules for the modulus and argument of a product and to construct the sixth roots of unity.
- Unit 2: Logarithmic and Exponential Functions
- 2.1 Improvised · Cooling hot water. To show that the excess temperature of cooling water decreases exponentially, using logarithms.
- 2.2 Conventional · eˣ and ln x: inverse functions and gradients. To draw y = eˣ and y = ln x, show they are inverses, and verify that the gradient of eˣ equals eˣ.
- Unit 3: Series
- 3.1 Improvised · Book overhang and the harmonic series. To stack books so the top one overhangs the table as far as possible and relate the overhang to a series.
- 3.2 Conventional · Summing series on the calculator. To approximate e and sin x with partial sums of series and measure the error.
- Unit 4: Integration
- 4.1 Improvised · Area under a curve by weighing paper. To find the area under y = x² by weighing a card cut-out and compare with integration.
- 4.2 Conventional · The trapezium rule. To estimate a definite integral with the trapezium rule and compare with the exact value.
- Unit 5: Differential Equations
- 5.1 Improvised · Draining a bottle. To show that the water level in a draining bottle obeys dh/dt = −k√h.
- 5.2 Conventional · Slope fields and Euler’s method. To draw a slope field, sketch a solution curve, and compare Euler’s method with the exact solution.
- Unit 6: Intersection and Sum of Subspaces
- 6.1 Improvised · Two slotted cards: planes through the origin. To model two planes through the origin and see that they meet in a line.
- 6.2 Conventional · Calculating intersections and sums. To find U ∩ V and U + V for two subspaces of ℝ³ algebraically and check the dimension formula.
- Unit 7: Transformation of Matrices
- 7.1 Improvised · Two villages: a migration model with beans. To model movement between two villages with beans and find the steady state (an eigenvector).
- 7.2 Conventional · Finding eigenvectors by drawing. To find the directions that a matrix does not rotate, and compare with eigenvalues and eigenvectors found algebraically.
- Unit 8: Conics
- 8.1 Improvised · Conic sections from a torch beam. To produce the four conic sections by shining a torch at a wall at different angles.
- 8.2 Conventional · The ellipse by the auxiliary-circle method. To construct an ellipse with compasses and ruler and verify the focal property PF₁ + PF₂ = 2a.
- Unit 9: Random Variables
- 9.1 Improvised · The total of two dice. To find the probability distribution, expected value and variance of the sum of two dice by experiment and theory.
- 9.2 Conventional · The binomial distribution. To compare experimental results of coin tossing with the binomial distribution B(10, ½).
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