GCSE Mathematics (Foundation) OCR

This subject is broken down into 62 topics in 5 modules:

  1. Algebra 4 topics
  2. Graphs 11 topics
  3. Ratio, Proportion and Rates of Change 9 topics
  4. Angles and Geometry 23 topics
  5. Probability and Statistics 15 topics
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This page was last modified on 28 September 2024.

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Mathematics (Foundation)

Algebra

Inequalities

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Inequalities

Understanding Inequalities

  • An inequality shows the relationship between two expressions that may not be equal.

  • The symbols used in inequalities are > (greater than), < (less than), ≥ (greater than or equal to), ≤ (less than or equal to), ≠ (not equal to).

  • A number line can be used to visualise an inequality.

Solving Inequalities

  • You can solve inequalities in the same way you solve equations.

  • When solving inequalities, remember to flip the inequality sign if you multiply or divide by a negative number.

Graphical Representation of Inequalities

  • Inequalities can be represented graphically on number lines or coordinate grids.

  • An open circle on a number line represents a 'less than' or 'greater than' inequality.

  • A closed circle on a number line represents a 'less than or equal to' or 'greater than or equal to' inequality.

  • To represent an inequality on a coordinate grid, use a dashed line for 'less than' or 'greater than', and a solid line for 'less than or equal to' or 'greater than or equal to'.

Inequalities with More Than One Variable

  • When dealing with inequalities with more than one variable, use similar techniques as with equations.

  • Remember to make one variable the subject first if the inequality does not involve a straight-line equation.

Solving Inequalities Involving Absolute Values

  • The absolute value of a number is its distance from zero.

  • Solving inequalities involving absolute values consists of two steps: solving the equation where the absolute value is greater, then where it is less.

  • Simplification methods are used to split the inequality into two separate inequalities based on the absolute value.

Inequalities and Real-Life Situations

  • Inequalities are widely used to represent real-life situations. For example, they can be used to describe the minimum or maximum limits on things like speed, weight, costs, etc.

Course material for Mathematics (Foundation), module Algebra, topic Inequalities

Mathematics (Foundation)

Angles and Geometry

3D Shapes- Surface Area

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3D Shapes- Surface Area

3D Shapes - Surface Area

Understanding 3D Shapes

  • 3D shapes are shapes which are not flat, but have depth.
  • They include cubes, cuboids, prisms, pyramids, cones, spheres, and cylinders.
  • They have faces, edges, and vertices, which are all essential in calculating surface area.

Surface Area

  • The surface area of a 3D shape is the total area of all its faces.
  • The units for surface area are always square units (such as cm² or m²).

Calculating Surface Area

  • The surface area of a cube is calculated by finding the area of one face then multiplying it by six, as a cube has six equal faces. Area of One Face (s²) x 6 = Surface Area. (s being the length of a side of the cube)
  • The surface area of a cuboid is calculated by finding the area of three faces then multiplying each by two, and adding the results. 2lw + 2lh + 2wh = Surface Area. (l: length, w: width, h: height)
  • The surface area of a cylinder is found by calculating the area of the two circles (bases), and the surface area of the curved side (a rectangle when unrolled). 2πrh + 2πr² = Surface Area. (r: radius, h: height)
  • For prisms, find the area of each individual face, and add them up. Be careful to count pairs of equal faces.
  • For other complex shapes, break them down into simpler 3D shapes, calculate the surface area for each, and add them up.

Problems Involving Surface Area

  • Surface area concepts are often used in real-life situations, from wrapping a present to painting a room.
  • It's also frequently encountered in word problems which involve dimensions and measurements, requiring an understanding of units and conversions (such as converting between square cm and square metres).

Tips for Success

  • Understanding formulae for individual shapes is crucial.
  • Use appropriate units and always give your answer with square units.
  • Be aware of how shapes can be made up of other shapes - for example, a house might be a cuboid with a triangular prism roof. Use these relationships to break down complex shapes.
  • In exams, diagrams and sketches help visualize the problem. Always write down added dimensions on your diagram.
  • Practice a variety of problems to build confidence.

Course material for Mathematics (Foundation), module Angles and Geometry, topic 3D Shapes- Surface Area

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