Contents Charlie’s Examples, from the presentation Audience Suggestions Colourful blank Venn diagrams
Charlie’s Examples
Numbers Smaller than 100 Prime Odd
Numbers Multiples of 5 3n + 1 Triangle Numbers
More than 1 line of symmetry Polygons Quadrilaterals Even number of sides More than 1 line of symmetry
Symmetrical about the y axis y = ax2 + bx + c Turning point at (2,5) a < 0 Symmetrical about the y axis
Audience Suggestions Number Sequences (i.e. terms that fit the given sequences) More Sequences (Sequences that have the given properties) Straight Line Graphs Quadratics Mean, Median, Mode KS5 Functions Others (Fractions, 3D Shapes, Simultaneous Equations, Modulus equations, Matrices) Problem Solving
Number
2 is a factor Multiple of 3 Multiple of 5
Multiple of 9 Even Multiple of 7
Factor of 24 Prime Multiple of 3
Multiple of 4 Factor of 36 Square
Multiple of 3 Less than 200 Square
Prime Square Cube
Square Triangular Fibonacci
Sequences The numbers in these are those that would be found in the sequence
2n 3n+1 5n-1
2n+2 3n-1 n+4
5n-3 3n+1 n2
3n+1 5n-2 n2+1
More Sequences The objects placed in the Venn diagrams are sequences
[n2 is, n2+1 isn’t from the sheet] Special Sequences [n2 is, n2+1 isn’t from the sheet] Quadratic Sequences Linear Sequences
Contains 4 Linear Sequence Quadratic Sequence
Fibonacci Style Sixth term is 2 First term negative
Converging Oscillating Increasing
Shapes
Triangles and Quadrilaterals only Has an obtuse angle Has a right angle Has an acute angle
Has at least one right angle Regular Has at least one right angle Triangle
Rotational Symmetry Reflective Symmetry Regular Polygon
Straight Line Graphs
Positive gradient Negative y-intercept -1 < gradient < 1
Positive Gradient Negative y-intercept Passes through (1,2)
y-intercept = 2 Positive Gradient Gradient < 2
(2,3) on the line Even y-intercept Positive gradient
Passes through (2,8) m=3 c=3
Gradient of 3 Goes through (3,6) y-intercept at (0,2)
Quadratic Equations
Integer Solutions Crosses x-axis x=0 is a line of symmetry
(x+2) a factor (x-3) a factor (x+5) a factor
Handling Data
Mode = 5 Mean = 5 Median = 5
Median = 5 Mean = 6 Range = 7
Give (grouped/ungrouped) frequency tables Mode = 1 Mean and Median estimated Mean > Median (or estimates thereof)
KS5 Functions
Quadratic Range y ≤0 Domain x≥0
Odd function Infinite domain Infinite range
f(3)=2 f’(1)=0 f(-1)=0
Others Fractions 3D shapes Simultaneous equations Modulus equations Matrices
Fractions Equivalent to 1/3 In simplest form Prime denominator
a,b,d,e not multiples of each other Simultaneous Equations ax+by=c dx+ey=f x and y are negative OR: x=-2, y=-3 a,b,d,e not multiples of each other b and e negative
Modulus Equations Equations of the form |ax+b|=|cx+d| (or ≥,≤,<,>,=) b=0 Only one solution Solutions include x=0
Matrices Orthogonal Singular Diagonal
Problem Solving This Venn diagram admits questions into the regions, with techniques for solving them around the outside. (These were intended as needing both, but a different interpretation would be questions that admit different methods of solution)
“Baby” trigonometry (In a right-angled triangle) Sine Rule Pythagoras’ Theorem
Colourful Blank Venn Diagrams