## Mathematics

### Foundation

Foundation: Unit 1 Inequalities and Functions

A22 Solve linear inequalities in one variable; represent the solution set on a number line

A7 Where appropriate, interpret simple expressions as functions with inputs and outputs
Clip 288 https://hegartymaths.com/function-notation-1
https://app.mymaths.co.uk/1779-lesson/functions-1

A12 Recognise, plot, sketch and interpret graphs of simple cubic functions
Clip 299 https://hegartymaths.com/cubic-graphs-recognising
Clip 298 https://hegartymaths.com/cubic-graphs-from-a-table-of-values
https://app.mymaths.co.uk/222-lesson/plotting-graphs-4-non-linear
A12 Recognise, plot, sketch and interpret graphs of the reciprocal function, y = with x ≠ 0.
Clip 300 https://hegartymaths.com/reciprocal-graphs-1
Clip 301 https://hegartymaths.com/reciprocal-graphs-2
https://app.mymaths.co.uk/222-lesson/plotting-graphs-4-non-linear
https://app.mymaths.co.uk/223-lesson/reciprocals

A14 Speed-distance-time graphs: Plot and interpret graphs of non-standard functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration
Clip 874 https://hegartymaths.com/distance-time-graphs-1
Clip 875 https://hegartymaths.com/distance-time-graphs-2
Clip 880 https://hegartymaths.com/speed-time-graphs-1
https://app.mymaths.co.uk/217-lesson/distance-time-graphs
https://corbettmaths.com/2013/05/25/travel-graphs/

G11 Solve geometrical problems on coordinate axes
Clip 199 https://hegartymaths.com/cartesian-axes-coordinates
https://corbettmaths.com/2013/04/15/coordinates-and-shapes/

Foundation: Unit 2 Probability

Using systematic listing strategies
Clip 670 https://hegartymaths.com/systematic-listing

Apply systematic listing strategies including use of the product rule for counting
Clip 671 https://hegartymaths.com/product-rule-for-counting-1
Video Sheet

Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments
Clip 349 https://hegartymaths.com/express-a-probability-in-words
Clip 350 https://hegartymaths.com/express-a-probability-in-numbers
Clip 351 https://hegartymaths.com/probability-of-single-events-1
Clip 352 https://hegartymaths.com/probability-of-single-events-2
Video Sheet
Mymaths -> Probability -> Relative frequency

Finding the expected number of outcomes
Clip 355 https://hegartymaths.com/expectation

Relative expected frequencies to theoretical probability, using appropriate language and the 0 to 1 probability scale
Clip 350 https://hegartymaths.com/express-a-probability-in-numbers
Clip 356 https://hegartymaths.com/experimental-probability-relative-frequency
Mymaths -> Probability -> experimental probability

Using probability of all possible outcomes adds up to 1, finding the probability of an event not happening.
Clip 353 https://hegartymaths.com/probability-of-an-event-not-happening
Video Sheet

Understanding and finding probabilities for mutually exclusive events.
Clip 354 https://hegartymaths.com/mutually-exclusive-events

Find probabilities for single events, including where outcomes are equally likely
Clip 352 https://hegartymaths.com/probability-of-single-events-2
Video Sheet

Sample Space diagrams: Construct and use (possibility spaces) to find probabilities for more than one event.
Clip 358 https://hegartymaths.com/probability-of-more-than-one-event-1
Clip 359 https://hegartymaths.com/probability-of-more-than-one-event-2

Venn diagrams: Filling in Venn diagrams for events happening, including where events are mutually exclusive.
Clip 372 https://hegartymaths.com/displaying-sets-in-venn-diagrams-1
Clip 373 https://hegartymaths.com/displaying-sets-in-venn-diagrams-2

Venn diagrams: Shading in areas in Venn diagrams and listing possible outcomes.
Clip 377 https://hegartymaths.com/listing-elements-from-sets-in-venn-diagrams
Video Sheet

Venn diagrams: Completing Venn Diagrams and using it to the amount in set groups.
Clip 379 https://hegartymaths.com/counting-sets-using-venn-diagrams-2

Calculate the probability of independent and dependent combined events
Clip 360 https://hegartymaths.com/independent-events
Video Sheet
Video Sheet

Display outcomes and calculate probability using tree diagrams
Tree diagrams: Find outcomes and calculate probability using tree diagrams for independent events
Clip 361 https://hegartymaths.com/independent-events-probability-trees-1
Clip 363 https://hegartymaths.com/independent-events-simplified-probability-trees
Video Sheet

Frequency Trees: Recording, describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees
Clip 368 https://hegartymaths.com/frequency-trees-1
Clip 369 https://hegartymaths.com/frequency-trees-2
Video Sheet

Two-way tables: Calculate and interpret conditional probabilities
Clip 421 https://hegartymaths.com/two-way-tables-1
Video Sheet

Foundation: Unit 3 Similarity

G15 Measure angles in geometric figures
Clip 458 https://hegartymaths.com/measuring-angles-1
Clip 459 https://hegartymaths.com/measuring-angles-2
Clip 460 https://hegartymaths.com/measuring-angles-3
https://app.mymaths.co.uk/254-lesson/measuring-angles

G15 Interpreting maps and scale drawings
Clip 864 https://hegartymaths.com/scale-diagrams-1
Clip 865 https://hegartymaths.com/scale-diagrams-2
Clip 866 https://hegartymaths.com/scale-diagrams-3
Clip 867 https://hegartymaths.com/scale-diagrams-4
https://app.mymaths.co.uk/303-lesson/scale-drawing

R2 Use scale factors, scale diagrams and maps
Clip 868 https://hegartymaths.com/scale-diagrams-5
Clip 869 https://hegartymaths.com/scale-diagrams-with-bearings
https://corbettmaths.com/2013/11/13/maps-scales/

G5 Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)
Clip 680 https://hegartymaths.com/congruence-1
Clip 681 https://hegartymaths.com/congruence-2
Clip 682 https://hegartymaths.com/congruent-triangles
https://app.mymaths.co.uk/247-lesson/congruent-triangles
https://corbettmaths.com/2013/04/15/congruent-triangles/
G19 Apply the concepts of congruence

Clip 608 https://hegartymaths.com/similar-polygons-1
Clip 609 https://hegartymaths.com/similar-polygons-2
Clip 610 https://hegartymaths.com/similar-polygons-3
Clip 611 https://hegartymaths.com/similar-triangles-1
https://corbettmaths.com/2012/08/10/congruent-and-similar-shapes/
https://corbettmaths.com/2013/11/16/similarshapes/
https://app.mymaths.co.uk/306-lesson/similar-triangles
G19 Apply the concepts of similarity, including the relationships between lengths in similar figures

R12 Compare lengths, areas and volumes using ratio notation; make links to similarity (including trigonometric ratios) and scale factors
Clip 615 https://hegartymaths.com/area-of-similar-shapes-1
Clip 618 https://hegartymaths.com/volume-of-similar-shapes-1
https://app.mymaths.co.uk/307-lesson/area-scale-factor
https://app.mymaths.co.uk/308-lesson/volume-scale-factor
G2 Use the standard ruler and compass constructions to construct given figures

G2 Construct a perpendicular bisector of a line segment using a ruler and compass
Clip 660 https://hegartymaths.com/construct-a-perpendicular-bisector
https://corbettmaths.com/2012/08/24/perpendicular-bisector/

G2 Construct a perpendicular to a given line from a given point using a ruler and compass: know that the perpendicular distance from a point to a line is the shortest distance to the line
Clip 662 https://hegartymaths.com/construct-a-perpendicular-from-a-point-to-a-line
https://corbettmaths.com/2013/03/25/perpendicular-from-a-line-to-a-point/
https://app.mymaths.co.uk/278-lesson/drawing-loci

G2 Construct a perpendicular to a given line at a given point using a ruler and compass
Clip 663 https://hegartymaths.com/construct-a-perpendicular-from-a-point-on-a-line
https://corbettmaths.com/2013/03/29/perpendicular-through-a-point-on-a-line/

G2 Construct an angle bisector using a ruler and compass
Clip 661 https://hegartymaths.com/construct-an-angle-bisector
https://corbettmaths.com/2013/03/26/angle-bisector/
G2 Use the standard ruler and compass constructions to solve loci problems
Clip 674 https://hegartymaths.com/loci-1
Clip 675 https://hegartymaths.com/loci-2
Clip 676 https://hegartymaths.com/loci-3
https://app.mymaths.co.uk/278-lesson/drawing-loci

### Higher

Unit 1: Inequalities and Functions

A22 Solve linear inequalities and represent the solution set on a number line

A22 Solve linear inequalities with one variable; represent the solution set on a graph

A22 Solve linear inequalities in two or more variables; represent the solution set on a number line, using set notation and on a graph

A22 Solve linear inequalities in two variables where one is a quadratic; represent the solution set on a number line, using set notation and on a graph

A7 Where appropriate, interpret simple expressions as functions with inputs and outputs

A7 Interpret the reverse process as the ‘inverse function’

A7 Interpret the succession of two functions as a ‘composite function’

A12 Recognise, plot, sketch and interpret graphs of simple cubic functions

A12 Recognise, plot, sketch and interpret graphs of the reciprocal function, y = with x ≠ 0.
Clip 300 https://hegartymaths.com/reciprocal-graphs-1
Clip 301 https://hegartymaths.com/reciprocal-graphs-2
https://app.mymaths.co.uk/222-lesson/plotting-graphs-4-non-linear
https://app.mymaths.co.uk/223-lesson/reciprocals

A12 Recognise, plot, sketch and interpret graphs of the exponential functionsy = k x for positive values ofk

A14 Speed-distance-time graphs: Plot and interpret graphs of non-standard functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration
Clip 874 https://hegartymaths.com/distance-time-graphs-1
Clip 875 https://hegartymaths.com/distance-time-graphs-2
Clip 880 https://hegartymaths.com/speed-time-graphs-1
https://app.mymaths.co.uk/217-lesson/distance-time-graphs
https://corbettmaths.com/2013/05/25/travel-graphs/

non-linear graphs), and interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts
Clip 876 https://hegartymaths.com/distance-time-graphs-3
Clip 877 https://hegartymaths.com/distance-time-graphs-4
Clip 878 https://hegartymaths.com/distance-time-graphs-5
Clip 879 https://hegartymaths.com/distance-time-graphs-6
Clip 881 https://hegartymaths.com/speed-time-graphs-2
Clip 882 https://hegartymaths.com/speed-time-graphs-3
Clip 883 https://hegartymaths.com/speed-time-graphs-4

A15 Area: Calculate or estimate areas under graphs (including quadratic and other
non-linear graphs), and interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts
Clip 884 https://hegartymaths.com/speed-time-graphs-5
Clip 885 https://hegartymaths.com/speed-time-graphs-6
Clip 886 https://hegartymaths.com/speed-time-graphs-7
https://corbettmaths.com/2018/01/31/area-under-a-graph/
https://app.mymaths.co.uk/1783-lesson/area-under-a-curve

A13 Sketch translations of a given function
Clip 307 https://hegartymaths.com/graph-transformations-1-fxa
Clip 308 https://hegartymaths.com/graph-transformations-2-fxa
https://app.mymaths.co.uk/3265-lesson/transforming-graphs-1

A13 Sketch translations and reflections of a given function
Clip 311 https://hegartymaths.com/graph-transformations-5-fx
Clip 312 https://hegartymaths.com/graph-transformations-6-f-x
https://app.mymaths.co.uk/3265-lesson/transforming-graphs-1

G11 Solve geometrical problems on coordinate axes
Clip 199 https://hegartymaths.com/cartesian-axes-coordinates
https://corbettmaths.com/2013/04/15/coordinates-and-shapes/

R16 Work with general iterative processes
Clip 322 https://hegartymaths.com/iteration
https://corbettmaths.com/2017/06/13/iteration-video/

A20 Find approximate solutions to equations numerically using iteration
Clip 322 https://hegartymaths.com/iteration
https://app.mymaths.co.uk/3268-lesson/iterative-methods

Unit 2: Probability

Using systematic listing strategies
Clip 670 https://hegartymaths.com/systematic-listing

Using the product rule for counting, as a systematic listing strategy
Clip 671 https://hegartymaths.com/product-rule-for-counting-1
Clip 672 https://hegartymaths.com/product-rule-for-counting-2
Clip 673 https://hegartymaths.com/product-rule-for-counting-3
Video Sheet

Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments
Clip 350 https://hegartymaths.com/express-a-probability-in-numbers
Clip 351 https://hegartymaths.com/probability-of-single-events-1
Clip 352 https://hegartymaths.com/probability-of-single-events-2
Video Sheet

Mymaths -> Probability -> Relative frequency
Finding the expected number of outcomes
Clip 355 https://hegartymaths.com/expectation

Relative expected frequencies to theoretical probability, using appropriate language and the 0 to 1 probability scale
Clip 350 https://hegartymaths.com/express-a-probability-in-numbers
Clip 356 https://hegartymaths.com/experimental-probability-relative-frequency
Clip 357 https://hegartymaths.com/relative-frequency-testing-for-bias

Mymaths -> Probability -> experimental probability
Using probability of all possible outcomes adds up to 1, finding the probability of an event not happening.
Clip 353 https://hegartymaths.com/probability-of-an-event-not-happening

Understanding and finding probabilities for mutually exclusive events.
Clip 354 https://hegartymaths.com/mutually-exclusive-events
Video Sheet

Find probabilities for single events, including where outcomes are equally likely
Clip 352 https://hegartymaths.com/probability-of-single-events-2
Video Sheet

Sample Space diagrams: Construct and use (possibility spaces) to find probabilities for more than one event.
Clip 358 https://hegartymaths.com/probability-of-more-than-one-event-1
Clip 359 https://hegartymaths.com/probability-of-more-than-one-event-2

Venn diagrams: Completing and using to find probabilities for more than one event happening, including where events are mutually exclusive.
Clip 383 https://hegartymaths.com/venn-diagrams-for-probability-1
Clip 384 https://hegartymaths.com/venn-diagrams-for-probability-2
Clip 385 https://hegartymaths.com/venn-diagrams-for-probability-3
Clip 386 https://hegartymaths.com/venn-diagrams-for-probability-4
Video Sheet

Venn diagrams: Using the union and intersection to find probabilities.
Clip 387 https://hegartymaths.com/venn-diagrams-for-probability-5
Clip 388 https://hegartymaths.com/venn-diagrams-for-probability-6
Calculate the probability of independent and dependent combined events
Clip 360 https://hegartymaths.com/independent-events
Video Sheet
Video Sheet

Tree diagrams: Find outcomes and calculate probability using tree diagrams for independent events
Clip 361 https://hegartymaths.com/independent-events-probability-trees-1
Clip 362 https://hegartymaths.com/independent-events-probability-trees-2
Clip 363 https://hegartymaths.com/independent-events-simplified-probability-trees
Video Sheet

Two-way tables: Calculate and interpret conditional probabilities
Clip 423 https://hegartymaths.com/two-way-tables-2
Clip 424 https://hegartymaths.com/two-way-tables-3
Video Sheet

See above for and Venn diagrams.
Tree diagrams: Calculate and interpret conditional (dependant) probabilities
Clip 364 https://hegartymaths.com/conditional-probability-1
Clip 365 https://hegartymaths.com/conditional-probability-2
Clip 366 https://hegartymaths.com/conditional-probability-3
Clip 367 https://hegartymaths.com/conditional-probability-4

Venn Diagrams: Calculate and interpret conditional (dependant) probabilities
Clip 391 https://hegartymaths.com/venn-diagrams-conditional-probability-combined

Frequency Trees: Recording, describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees
Clip 368 https://hegartymaths.com/frequency-trees-1
Clip 369 https://hegartymaths.com/frequency-trees-2
Video Sheet

Unit 3: Similarity

G15 Interpreting maps and scale drawings
Clip 864 https://hegartymaths.com/scale-diagrams-1
Clip 865 https://hegartymaths.com/scale-diagrams-2
Clip 866 https://hegartymaths.com/scale-diagrams-3
Clip 867 https://hegartymaths.com/scale-diagrams-4
https://app.mymaths.co.uk/303-lesson/scale-drawing

R2 Use scale factors, scale diagrams and maps
Clip 868 https://hegartymaths.com/scale-diagrams-5
Clip 869 https://hegartymaths.com/scale-diagrams-with-bearings
Clip 870 https://hegartymaths.com/scale-diagrams-problem-solving-1
Clip 871 https://hegartymaths.com/scale-diagrams-problem-solving-2
https://corbettmaths.com/2013/11/13/maps-scales/

G5 Congruency: Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)
Clip 680 https://hegartymaths.com/congruence-1
Clip 681 https://hegartymaths.com/congruence-2
Clip 682 https://hegartymaths.com/congruent-triangles
https://app.mymaths.co.uk/247-lesson/congruent-triangles
https://corbettmaths.com/2013/04/15/congruent-triangles/

G19 Apply the concepts of congruence including the relationships between lengths, areas and volumes
Clip 684 https://hegartymaths.com/congruent-triangles-problem-solving-1
Clip 685 https://hegartymaths.com/congruent-triangles-problem-solving-2
Clip 686 https://hegartymaths.com/congruent-triangles-problem-solving-3
Clip 687 https://hegartymaths.com/congruent-triangles-problem-solving-4
Clip 689 https://hegartymaths.com/congruent-triangles-problem-solving-6
https://corbettmaths.com/2012/08/10/congruent-and-similar-shapes/

G19 Apply the concepts of similarity, including the relationships between lengths in similar figures
Clip 608 https://hegartymaths.com/similar-polygons-1
Clip 609 https://hegartymaths.com/similar-polygons-2
Clip 610 https://hegartymaths.com/similar-polygons-3
Clip 611 https://hegartymaths.com/similar-triangles-1
Clip 612 https://hegartymaths.com/similar-triangles-2
Clip 613 https://hegartymaths.com/similar-triangles-3
Clip 614 https://hegartymaths.com/similar-shapes-problem-solving
https://corbettmaths.com/2012/08/10/congruent-and-similar-shapes/
https://corbettmaths.com/2013/11/16/similarshapes/
https://app.mymaths.co.uk/306-lesson/similar-triangles

G19 Apply the concepts of congruence and similarity, including the relationships between areas in similar figures
Clip 615 https://hegartymaths.com/area-of-similar-shapes-1
Clip 616 https://hegartymaths.com/area-of-similar-shapes-2
Clip 617 https://hegartymaths.com/area-of-similar-shapes-3
https://corbettmaths.com/2013/11/16/similar-shapes-areas/

G19 Apply the concepts of congruence and similarity, including the relationships between volumes in similar figures
Clip 618 https://hegartymaths.com/volume-of-similar-shapes-1
Clip 619 https://hegartymaths.com/volume-of-similar-shapes-2
Clip 620 https://hegartymaths.com/volume-of-similar-shapes-3
Clip 621 https://hegartymaths.com/volume-of-similar-shapes-4
https://corbettmaths.com/2013/11/17/similar-shape-volumes/

R12 Compare lengths, areas and volumes using ratio notation; make links to similarity (including trigonometric ratios) and scale factors
Clip 615 https://hegartymaths.com/area-of-similar-shapes-1
Clip 618 https://hegartymaths.com/volume-of-similar-shapes-1
https://app.mymaths.co.uk/307-lesson/area-scale-factor
https://app.mymaths.co.uk/308-lesson/volume-scale-factor

G2 Use the standard ruler and compass constructions to construct given figures
Clip 659 https://hegartymaths.com/construct-a-circle
Clip 664 https://hegartymaths.com/construct-a-90deg-or-45deg-angle
Clip 665 https://hegartymaths.com/construct-a-60deg-30deg-or-120deg-angle
Clip 666 https://hegartymaths.com/construct-an-equilateral-triangle
Clip 667 https://hegartymaths.com/construct-a-regular-hexagon
Clip 683 https://hegartymaths.com/constructing-triangles
https://app.mymaths.co.uk/276-lesson/constructing-triangles
https://app.mymaths.co.uk/277-lesson/constructing-shapes

G2 Construct a perpendicular bisector of a line segment using a ruler and compass
Clip 660 https://hegartymaths.com/construct-a-perpendicular-bisector
https://corbettmaths.com/2012/08/24/perpendicular-bisector/

G2 Construct a perpendicular to a given line from a given point using a ruler and compass: know that the perpendicular distance from a point to a line is the shortest distance to the line
Clip 662 https://hegartymaths.com/construct-a-perpendicular-from-a-point-to-a-line
https://corbettmaths.com/2013/03/25/perpendicular-from-a-line-to-a-point/

G2 Construct a perpendicular to a given line at a given point using a ruler and compass
Clip 663 https://hegartymaths.com/construct-a-perpendicular-from-a-point-on-a-line
https://corbettmaths.com/2013/03/29/perpendicular-through-a-point-on-a-line/

G2 Construct an angle bisector using a ruler and compass
Clip 661 https://hegartymaths.com/construct-an-angle-bisector
https://corbettmaths.com/2013/03/26/angle-bisector/

G2 Use the standard ruler and compass constructions to solve loci problems
Clip 674 https://hegartymaths.com/loci-1
Clip 675 https://hegartymaths.com/loci-2
Clip 676 https://hegartymaths.com/loci-3
Clip 677 https://hegartymaths.com/loci-4
Clip 678 https://hegartymaths.com/loci-5
Clip 679 https://hegartymaths.com/loci-problem-solving
https://app.mymaths.co.uk/278-lesson/drawing-loci