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