Contents Charlie’s Examples, from the presentation Audience Suggestions Colourful blank Venn diagrams

Charlie’s Examples

Numbers Prime Smaller than 100 Odd

Numbers Multiples of 5 3n + 1 Triangle Numbers

Polygons Quadrilaterals Even number of sides More than 1 line of symmetry

y = ax 2 + 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, Coordinate Geometry, Modulus equations, Matrices) Problem Solving

Number

2 is a factorMultiple of 3 Multiple of 5

Multiple of 9Even Multiple of 7

Factor of 24Prime Multiple of 3

Multiple of 4Factor of 36 Square

Multiple of 3Less than 200 Square

PrimeSquare Cube

SquareTriangular Fibonacci

Sequences The numbers in these are those that would be found in the sequence

2n3n+1 5n-1

2n+23n-1 n+4

5n-33n+1 n2n2

5n-2 n 2 +1

More Sequences The objects placed in the Venn diagrams are sequences

Quadratic Sequences Special Sequences [n 2 is, n 2 +1 isn’t from the sheet] Linear Sequences

Contains 4Linear Sequence Quadratic Sequence

Fibonacci Style Sixth term is 2 First term negative

ConvergingOscillating Increasing

Shapes

Has an obtuse angle Has a right angle Has an acute angle Triangles and Quadrilaterals only

RegularHas 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

m=3 Passes through (2,8) c=3

Gradient of 3Goes 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 = 5Mean = 5 Median = 5

Mean = 6 Range = 7

Mode = 1Mean and Median estimated Mean > Median (or estimates thereof) Give (grouped/ungrouped) frequency tables

KS5 Functions

QuadraticRange y ≤0 Domain x ≥0

Odd functionInfinite domain Infinite range

f(3)=2f’(1)=0 f(-1)=0

Others Fractions 3D shapes Simultaneous equations Coordinate Geometry Modulus equations Matrices

Equivalent to 1/3 In simplest form Prime denominator Fractions

a,b,d,e not multiples of each other x and y are negative b and e negative Simultaneous Equations ax+by=c dx+ey=f OR: x=-2, y=-3

Lies on the line y=x+1 Lies on the circle x 2 +(y-1) 2 =25 Distance 5 from the origin Coordinate Geometry

Lies on the line y=x Lies on the parabola y=x Lies on the circle x 2 +y 2 =32 Coordinate Geometry

b=0Only one solution Solutions include x=0 Equations of the form |ax+b|=|cx+d| (or ≥,≤,,=) Modulus Equations

OrthogonalSingular Diagonal Matrices

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