iGCSE Mathematics OxfordAQA

This subject is broken down into 59 topics in 5 modules:

  1. Number 13 topics
  2. Algebra 11 topics
  3. Geometry 14 topics
  4. Measures 5 topics
  5. Statistics 16 topics
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This page was last modified on 28 September 2024.

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Mathematics

Number

Number notation and place value

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Number notation and place value

Number Notation

  • Standard form notation: used to express very large or very small numbers. A number in standard form is written as a x 10^n where 1 ≤ a < 10 and n is an integer.
  • Decimal notation: most common number notation. Includes both integer part and fractional part separated by a decimal point.
  • Fractions: used to represent a part of a whole. It comprises of a numerator (top number) and a denominator (bottom number). Numerator indicates the number of parts, while denominator indicates the total number of equal parts in a whole.
  • Percentage notation: used to represent a number as a fraction of 100. It's symbolized by the '%' sign.

Place Value

  • Units place: the rightmost place in a number.
  • Tens place: to the left of the units place. Each move to the left multiplies the place value by 10.
  • Hundreds place: to the left of the tens. Continuing the pattern, each move to the left multiplies the place value by 10.
  • Decimal place values: includes tenths (one place after the decimal), hundredths (two places after the decimal) and so on.
  • Naming large numbers: Beyond hundreds, we use names such as thousands, millions, billions and so on according to the place value. For example, in number 1,000,000, the 1 is in the "millions" place.

Important Points

  • Understand how to convert between different number notations (standard form, decimals, fractions, and percentages).
  • Rounding numbers according to different place value is crucial. For example, if rounding to the nearest tens, the value in the units place will decide the result.
  • Comparing and ordering numbers will require a solid understanding of both number notation and place value. For example, you need to be able to determine which is larger: 0.25 or 25%.
  • Be aware of common misconceptions such as the belief that 0.5 is bigger than 0.45 because 5 is larger than 45. Always consider place value when comparing numbers.
  • Practice converting between different forms and being precise with place value to build speed and confidence.

Course material for Mathematics, module Number, topic Number notation and place value

Mathematics

Geometry

Perimeter, area, and volume

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Perimeter, area, and volume

Perimeter

  • The perimeter is the total distance around the outside of a shape.
  • To calculate the perimeter of a rectangle or square, add the lengths of all the sides together.
  • The perimeter of a triangle is the sum of the lengths of its three sides.
  • The perimeter of a circle, also known as the circumference, can be calculated using the formula 2πr where r is the radius of the circle.

Area

  • Area is the amount of space inside a shape.
  • The area of a rectangle is calculated by multiplying its width by its height (width × height).
  • For a square, you simply square the length of one side (side²).
  • The area of a triangle is given by 1/2 base × height.
  • The area of a circle is given by the formula πr², where r is the radius.
  • For a parallelogram, the area is given by the formula base x height.
  • The area of a trapezium is given by the formula 1/2 (a + b) x h where a and b are the lengths of the parallel sides and h is the height.

Volume

  • Volume is the amount of space that a three-dimensional object takes up.
  • For a solid cube or a cuboid, volume is calculated by multiplying length, width, and height together (length × width × height).
  • The volume of a cylinder is calculated by multiplying the area of the base (which is a circle) by the height: πr²h.
  • The volume of a cone is given by 1/3πr²h where r is the radius of the base and h is the height.
  • The volume of a sphere is given by 4/3πr³ where r is the radius.
  • A prism has the same cross section throughout its length. The volume of a prism is the cross-sectional area multiplied by its length.

Remember that understanding these fundamental concepts about perimeters, areas and volumes will be essential for handling a wide variety of geometry problems. Always keep these formulas at your fingertips.

Course material for Mathematics, module Geometry, topic Perimeter, area, and volume

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