# Maths (Higher) - Year 11

### Term 1: Surds, Pythagoras and Trigonometry, Constructions and Loci, Vectors, Circle Theorems

Simplifying surds and rationalising the denominator.

Pythagoras' Theorem in 2D and 3D.

Trigonometric ratios: SOHCAHTOA.

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

The Sine and Cosine rules.

Area of a triangle = 1/2ab SinC.

Using Pythagoras' Theorem and trigonometry to solve 2D and 3D problems.

Ruler and compass constructions.

Solving problems involving loci.

Vectors and vector proofs.

Circle theorems.

1. Test on: Circle theorems, constructions & loci, Working in 3D. Pythagoras' Theorem, trigonometry and vectors
###### Volume

The amount of space that a 3D object occupies

###### Surface area

The total area of the surface of a 3D object

###### Spere

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 (reciprocals, rules of indices & standard form) & Graphs 1

The gradient of a straight line.

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

Parallel and perpendicular lines.

Plotting quadratic functions, including roots and turning points.

Completing the square.

Solving simultaneous equations.

Solving quadratic inequalities and representing inequalities as regions.

Distance-time graphs.

Velocity-time graphs.

Reciprocals.

Rules of indices.

Fractional and negative indices.

Exact calculations.

Standard form.

1. GCSE Mock 1 Exam on all topics

weeks beginning tbc.

Paper 1(non-calculator)

Paper 2(Calculator)

Paper 3(Calculator)

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 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

Cubic and reciprocal functions.

Exponential and trigonometric functions.

Distance-time graphs.

Distance-velocity graphs.

Gradients and area under a curve (Trapezium rule).

Equation of a circle centre the origin.

Transformations and reflections of a given function.

Venn diagrams and set notation.

Possibility space diagrams.

Probability tree diagrams and conditional probability.

###### 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: Gradients and the area under a curve, Sequences, Iterative Methods, Units & Proportionality

Gradients and the area under a curve.

Interpreting the gradient and area under a curve.

Arithmetic and geometric sequences.

Special sequences.

Approximate solutions and iterative methods.

Compound units (speed, density and pressure).

Converting between units.

Direct and inverse proportion.

Rates of change.

Growth and decay problems.

Compound interest.

1. GCSE Mock 2 Exam on all topics

week beginning

tbc.

Paper 1(Non-calculator)

Paper 2(Calculator)

Paper 3(Calculator)

###### 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