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.
Standard ruler and compass constructions
Solving problems using loci
Position vectors
The area and perimeter of parts of a circle and of a sector.
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
Adjacent
Next to
Vector
A quantity that has direction and magnitude
Cyclic quadrilateral
A quadrilateral where all four vertices lie on the circumference of a circle
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.
GCSE Mock 1 Exam on all topics
week beginning tbc.
1 non-calculator paper and 2 calculator papers
Gradient
The slope of a line
Parallel
Lines that never meet
Perpendicular
At right-angles
Quadratic function
A function that contains a squared term
Root
The solutions of an equation
Or
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 then each other
Reciprocal
One of a pair of numbers whose product is 1
Index
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)
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 and Inequalities, Probability and Venn Diagrams
Solving quadratic equations by factorising.
Plotting quadratic graphs.
Maximum and minimum points of a quadratic graph.
Drawing reciprocal and cubic functions.
Sketching functions.
Representing inequalities on a number line.
Solving inequalities.
Real life graphs and trends.
Venn diagrams and set notation.
Possibility space diagrams.
Probability tree diagrams.
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
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.
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
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)
Develop the individual:
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)
Develop the individual:
Create a supportive community:
Students own social development is widened through paired work where students discuss mathematical concepts and solve unfamiliar problems.. .