# Maths at Thrybergh Academy and Sports College

## Course description

This is a linear qualification with two exams at the end of the course. The two exams (one is 'non-calculator' and the other is 'calculator') each carry a 50% weighting of the overall grade.

The mathematics GCSE will include work in the areas of number and algebra, shape, space and measure and data handling. In addition to this students will be expected to demonstrate 'functional skills' in their work.

## Course content

**Number and algebra **

n add, subtract, multiply and divide any number;

n order rational numbers;

n use the concepts and vocabulary of factor (divisor), multiple, common factor, highest common factor, least common multiple, prime number and prime factor decomposition;

n use the terms square, positive and negative square root, cube and cube root;

n use index notation for squares, cubes and powers of ten;

n use index laws for multiplication and division of integer, fractional and negative powers;

n interpret, order and calculate with numbers written in standard index form;

n understand equivalent fractions, simplifying a fraction by cancelling all common factors;

n add and subtract fractions;

n use decimal notation and recognise that each terminating decimal is a fraction;

n recognise that recurring decimals are exact fractions, and that some exact fractions are recurring decimals;

n understand that ‘percentage’ means ‘number of parts per 100’ and use this to compare proportions;

n use percentage, repeated proportional change;

n understand and use direct and indirect proportion;

n interpret fractions, decimals and percentages as operators;

n use ratio notation, including reduction to its simplest form and its various links to fraction notation;

n understand and use number operations and the relationships between them, including inverse operations and hierarchy of operations;

n use surds and π in exact calculations;

n calculate upper and lower bounds;

n divide a quantity in a given ratio;

n approximate to specified or appropriate degrees of accuracy including a given power of ten, number of decimal places and significant figures;

n use calculators effectively and efficiently, including statistical and trigonometrical functions;

n distinguish the different roles played by letter symbols in algebra, using the correct notation;

n distinguish in meaning between the words equation, formula, identity and expression;

n manipulate algebraic expressions by collecting like terms, by multiplying a single term over a bracket, and by taking out common factors, multiplying two linear expressions, factorising quadratic expressions including the difference of two squares, and simplifying rational expressions;

n set up and solve simple equations including simultaneous equations in two unknowns;

n solve quadratic equations;

n derive a formula, substitute numbers into a formula and change the subject of a formula;

n solve linear inequalities in one or two variables, and represent the solution set on a number line or suitable diagram;

n use systematic trial and improvement to find approximate solutions of equations where there is no simple analytical method of solving them;

n generate terms of a sequence using term-to-term and position-to-term definitions of the sequence;

n use linear expressions to describe the *n*th term of an arithmetic sequence;

n use the conventions for coordinates in the plane and plot points in all four quadrants, including using geometric information;

n recognise and plot equations that correspond to straight-line graphs in the coordinate plane, including finding gradients;

n understand that the form *y = mx + c *represents a straight line and that
*m *is the gradient of the line and *c *is the value of the *y-*intercept;

n understand the gradients of parallel lines;

n find the intersection points of the graphs of a linear and quadratic function, knowing that these are the approximate solutions of the corresponding simultaneous equations representing the linear and quadratic functions;

n draw, sketch, recognise graphs of simple cubic functions, the reciprocal function
*y = **x*1 with *x*0, the function *y = k*≠ *x *
for integer values of *x *and simple positive values of *k*, the trigonometric functions
*y *= sin *x *and *y *= cos *x; *

n construct the graphs of simple loci;

n construct linear, quadratic and other functions from real-life problems and plot their corresponding graphs;

n discuss, plot and interpret graphs (which may be non-linear) modelling real situations;

n generate points and plot graphs of simple quadratic functions, and use these to find approximate solutions.

**Geometry and measures **

n recall and use properties of angles at a point, angles at a point on a straight line (including right angles), perpendicular lines and opposite angles at a vertex;

n understand and use the angle properties of parallel and intersecting lines, triangles and quadrilaterals;

n calculate and use the sums of the interior and exterior angles of polygons;

n recall the properties and definitions of special types of quadrilateral, including square, rectangle, parallelogram, trapezium, kite and rhombus;

n recognise reflection and rotation symmetry of 2D shapes;

n understand congruence and similarity;

n use Pythagoras’ theorem in 2D and 3D;

n use the trigonometrical ratios and the sine and cosine rules to solve 2D and 3D problems;

n distinguish between centre, radius, chord, diameter, circumference, tangent, arc, sector and segment;

n understand and construct geometrical proofs using circle theorems;

n use 2D representations of 3D shapes;

n describe and transform 2D shapes using single or combined rotations, reflections, translations, or enlargements by a positive scale factor then use positive fractional and negative scale factors and distinguish properties that are preserved under particular transformations;

n use and interpret maps and scale drawings;

n understand and use the effect of enlargement for perimeter, area and volume of shapes and solids;

n interpret scales on a range of measuring instruments and recognise the inaccuracy of measurements;

n convert measurements from one unit to another;

n make sensible estimates of a range of measures;

n understand and use bearings;

n understand and use compound measures;

n measure and draw lines and angles;

n draw triangles and other 2D shapes using a ruler and protractor;

n use straight edge and a pair of compasses to do constructions;

n construct loci;

n calculate perimeters and areas of shapes made from triangles and rectangles and other shapes;

n calculate the area of a triangle using ½ *ab *sin *C; *

n find circumferences and areas of circles;

n calculate volumes of right prisms and of shapes made from cubes and cuboids;

n solve mensuration problems involving more complex shapes and solids.

**Statistics and probability **

n understand and use statistical problem solving process/handling data cycle;

n identify possible sources of bias;

n design an experiment or survey;

n design data-collection sheets, distinguishing between different types of data;

n extract data from printed tables and lists;

n design and use two-way tables for discrete and grouped data;

n produce charts and diagrams for various data types;

n calculate median, mean, range, quartiles and inter-quartile range, mode and modal class;

n interpret a wide range of graphs and diagrams and draw conclusions;

n look at data to find patterns and exceptions;

n recognise correlation and draw and/or use lines of best fit by eye, understanding what these represent;

n compare distributions and make inferences;

n compare distributions and make inferences;

n understand and use the vocabulary of probability and the probability scale;

n understand and use estimates or measures of probability from theoretical models (including equally likely outcomes), or from relative frequency;

n list all outcomes for single events, and for two successive events, in a systematic way and derive related probabilities;

n identify different mutually exclusive outcomes and know that the sum of the probabilities of all these outcomes is 1;

n know when to add or multiply two probabilities: if A and B are mutually exclusive, then the probability of A or B occurring is P(A) + P(B), whereas if A and B are independent events, the probability of A and B occurring is P(A) × P(B);

n use tree diagrams to represent outcomes of compound events, recognising when events are independent;

n compare experimental data and theoretical probabilities;

n understand that if they repeat an experiment, they may – and usually will – get different outcomes, and that increasing sample size generally leads to better estimates of probability and population characteristics.

## Entry requirements

There are no entry requirements for this course.

## Assessment

Two final written ‘linear’ exams which are worth 50% of the course each.

## Future opportunities

You could take this course to prepare for advanced level courses such as an A/AS Level in Mathematics or Statistics or you may need to strengthen your grades by completing a foundation or intermediate vocational qualification. With further training, you could go into a job related to mathematics such as an Accountant, Finance Clerk, Teacher or Payroll Officer. You could also go straight into employment and do further training or part time study with the support of your employer.

## Further information

To find out more about this qualification, contact us, ask your Connexions Personal Adviser or school/college careers staff.

## How to apply

You can apply for this course through UCAS Progress. Add this course to your favourites so you can start making an application.