# Maths (Foundation) - Year 11

### Term 1: Pythagoras' Theorem and Trigonometry, Constructions and Loci, Vectors & Circles continued

Pythagoras' Theorem.

Trigonometry ratios: SOHCAHTOA

Exact trigonometric values of sin, cos and tan of 30, 45 and 60 degrees.

The area and perimeter of parts of a circle and of a sector.

Standard ruler and compass constructions

Solving problems using loci

Position vectors

The area and perimeter of parts of a circle and of a sector

1. Test on:

Constructions & loci, Circles 2, Pythagoras' Theorem and Trigonometry & Working in 3D.

###### Volume

The amount of space that a 3D object occupies

###### Surface Area

The total area of the surface of a 3D object

###### Sphere

A round 3D object with every point on its surface equidistant from its centre e.g. a ball

###### Prism

A 3D solid with a constant area of cross section

###### Pyramid

A solid with a base and sloping faces that meet in a point at the top

###### Trigonometry

The mathematics of triangles

Next to

###### Vector

A quantity that has direction and magnitude

A quadrilateral where all four vertices lie on the circumference of a circle

• Spiritual
• Moral
• Social
• Cultural
###### Develop the individual:

All mathematics has a rich history and a cultural context in which it was first discovered or used. The opportunity to consider the lives of specific mathematicians is promoted when studying Pythagoras’ Theorem. When solving mathematical problems students will develop their creative skills. Students are encouraged to question “why”; they compose proofs and arguments and make assumptions. Students learn geometrical reasoning through knowledge and application of angle rules.

###### Create a supportive community:

Students own social development is widened through paired work where students discuss mathematical concepts and solve unfamiliar problems.. .

### Term 2: Calculations 2 & Graphs 1 and Simultaneous Equations

Squares, cubes and roots.

The rules of indices.

Reciprocals.

Exact calculations.

Standard form.

Plotting straight line graphs and the equation of a straight line, y=mx+c.

The gradient of a straight line.

Solving simultaneous equations.

Distance-time graphs and velocity-time graphs.

Year 11 Mock GCSE Exams.

1. GCSE Mock 1 Exam on all topics

week beginning tbc.

1 non-calculator paper and 2 calculator papers

The slope of a line

###### Parallel

Lines that never meet

###### Perpendicular

At right-angles

A function that contains a squared term

###### The solutions of an equation

A number that when multiplied by itself an indicated number of times forms a product equal to a specified number

###### Inequality

The relation between two expressions that are greater or less than each other

###### Reciprocal

One of a pair of numbers whose product is 1

Power

###### Surd

An expression containing one or more irrational roots of numbers, such as 2√3, 3√2 + 6

###### Standard form

A number written in the form a × 〖10〗^b where a is a number between 1 and 10 (not including 10)

• Spiritual
• Moral
• Social
• Cultural
###### Develop the individual:

Mathematics provides opportunities for students to develop a sense of “awe and wonder”. Standard form promotes “awe and wonder” by providing a way for students to write extremely large and extremely small numbers.

###### Create a supportive community:

Students own social development is widened through paired work where students discuss mathematical concepts and solve unfamiliar problems.. .

### Term 3: Graphs 2, Inequalities, Probability and Venn Diagrams

Maximum and minimum points of a quadratic graph.

Solving equations by factorising.

Drawing reciprocal and cubic functions.

The inequality sign, drawing inequalities on a number line and solving inequalities.

Real life graphs and trends.

Venn diagrams and set notation.

Possibility space diagrams.

Probability tree diagrams.

1. Practice GCSE exam papers
###### Cubic Function

A function containing a term to the power 3

###### Venn Diagram

A diagram in which mathematical sets are represented by overlapping circles

###### Universal Set

The set of all elements in a Venn Diagram

###### Intersection

The intersection of two or more sets are the members common to all sets

###### Union

The union of two or more sets is the combination of all the individual members of both sets

###### Possibility space diagram

A list of all possible probability events

###### Conditional probabilty

The probability of an event (A), given that another (B) has already occurred

###### Mutually Exclusive Events

Two or more events are said to be mutually exclusive if they cannot occur at the same time

###### Independent Events

Two events are independent if the occurrence of one does not affect the occurrence of the other

• Spiritual
• Moral
• Social
• Cultural
###### Develop the individual:

The topic of probability provides opportunities for students to consider whether situations are fair or biased and discuss gambling, betting, lotteries, raffles and games of chance. A knowledge of probability will benefit students’ functioning in society as they will understand bias and the chance of an event happening.

###### Create a supportive community:

Students own social development is widened through paired work where students discuss mathematical concepts and solve unfamiliar problems.. .

### Term 4: Sequences, Units & Proportion

Sequence rules for finding the next term.

Finding the nth term of a sequence.

Arithmetic, geometric and Fibonacci sequences.

Compound units (speed, density and pressure).

Direct and inverse proportion.

Growth and decay problems.

Compound interest.

1. GCSE Mock 2 Exam on all topics

week beginning

tbc.

1 non-calculator paper and 2 calculator papers

###### Arithmetic Progression

A sequence in which each term is obtained by adding a constant number to the preceding term e.g. 1, 4, 7, 10, 13,…

###### Geometric Progression

A sequence in which each term after the first term a is obtained by multiplying the previous term by a constant r, called the common ratio e.g. 1, 2, 4, 8, 16, 32, ...

###### Direct Proportion

Two quantities are directly proportional when one quantity increases the other increases by the same amount. If y is directly proportional to x, this can be written as y ∝ x or y = kx

###### Inverse Proportion

Two quantities are inversely proportional when one quantity increases the other decreases. If y is inversely proportional to x, this can be written as y ∝ 1/x or y= k/x

• Spiritual
• Moral
• Social
• Cultural
###### Develop the individual:

All mathematics has a rich history and a cultural context in which it was first discovered or used. The opportunity to consider the lives of specific mathematicians is promoted when studying Fibonacci sequences. Numerical fluency and an understanding of proportion will benefit students’ functioning in society. For example to be able to convert between units, or state which is the better value for money? Students enjoy exploring patterns and sequences, making predictions and generalisations. Mathematics provides opportunities for students to develop a sense of “awe and wonder”. Mathematical investigations produce beautiful elegance in their surprising symmetries, patterns or results.

###### Create a supportive community:

Students own social development is widened through paired work where students discuss mathematical concepts and solve unfamiliar problems.. .

### Term 5: GCSE revision and preparation

GCSE revision and preparation

1. GCSE exam

Paper 1 (non-calculator)

• Spiritual
• Moral
• Social
• Cultural

### Term 6: GCSE revision and preparation

GCSE revision and preparation

1. GCSE exam

Paper 2 (calculator)

Paper 3 (calculator)

• Spiritual
• Moral
• Social
• Cultural