# Year 11 — Maths (Foundation)

### Term 1: Working in 3D, Pythagoras' Theorem and Trigonometry, Vectors

Names and properties of 3D shapes

Faces, edges and vertices

Nets

Plans and elevations

Volume & surface area of a cuboid, prism, cylinder,

sphere, pyramid, and cone

Pythagoras' theorem

Trigonometric ratios

SOHCANTOA

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

Position vectors

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

Plotting straight-line graphs

The gradient of a straight line

The equation of a straight line, y= mx + c

Distance-time graphs

Velocity-time graphs

Squares, cubes and roots

The rules of indices

Reciprocals

Exact calculations

Standard form

Year 11 Mock GCSE Exams

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, Probability and Venn Diagrams

Maximum and minimum points of a quadratic graph

Drawing reciprocal and cubic functions

Sketching functions

Real-life graphs and trends

Venn diagrams and set notation

Possibility space diagrams

Tree diagrams

Practice examination papers set by the class teacher

### 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 probability

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, Constructions & Loci

Sequence rules for finding the next term

Finding the nth term

Arithmetic, geometric, quadratic and Fibonacci sequences

Compound units (speed, density & pressure)

Direct proportion

Inverse proportion

Growth and decay problems

Compound interest

Standard constructions

Loci

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 sequence

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 & Preparation

GCSE Revision & Preparation.

GCSE

Paper 1(Non-Calculator paper)

• Spiritual
• Moral
• Social
• Cultural

#### Create a supportive community:

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

### Term 6: GCSE Revision & Preparation

GCSE Revision & Preparation.

GCSE

Paper 2

(Calculator paper)

&

Paper 3

(Calculator paper)

• Spiritual
• Moral
• Social
• Cultural

#### Create a supportive community:

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