Mental Maths (Without Calculators) - Chapter 1

The order of operations in mathematics, acronym stands for Brackets, Orders (powers and square roots), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).

The result of multiplying a number by itself. For example, the square of 5 is 5 x 5 = 25.

The inverse operation of squaring. The square root of a number is the value that when multiplied by itself equals the original number. For example, the square root of 25 is 5, because 5 x 5 = 25.

Numbers that can be expressed as the product of two equal integers. For example, 9 is a square number because 3 x 3 = 9.

The process of multiplying a number by itself three times. For example, the cube of 2 is 2 x 2 x 2 = 8.

The inverse operation of cubing. The cube root of a number is the value that when multiplied by itself three times equals the original number. For example, the cube root of 8 is 2, because 2 x 2 x 2 = 8.

Numbers that can be expressed as the product of three equal integers. For example, 27 is a cube number because 3 x 3 x 3 = 27.

A number that can be divided evenly by another number, leaving no remainder. For example, 12 is divisible by 3, because 12 ÷ 3 = 4.

A ratio is a comparison of two quantities, often expressed as a fraction.

Proportion is a statement that two ratios are equal. It means that the two quantities are in the same relationship.

A rate is a ratio that compares two quantities with different units.

When given a ratio and the value of one of the terms, you can calculate the total quantity by setting up a proportion and solving for the unknown value.

If you know the ratio between two quantities, you can find the value of each quantity if you know the total amount. Set up a proportion and solve for the unknown values.

A fraction can be converted into a decimal by dividing the numerator by the denominator.

A terminating decimal can be converted into a fraction by writing it as a fraction with a denominator of 10, 100, 1000, etc., depending on the number of decimal places and then simplifying it.

To multiply a decimal number by a power of 10, move the decimal point to the right by the number of zeros in the power of 10.

A method to estimate an unknown value within a range of known data points. It uses the relationship between existing data points to predict the value of an unknown point.

A theorem stating that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

The study of relationships between angles and sides of triangles, particularly right-angled triangles. Key ratios are sine (SOH), cosine (CAH), and tangent (TOA).

The trigonometric ratio that represents the ratio of the adjacent side to the hypotenuse in a right-angled triangle.

The trigonometric ratio that represents the ratio of the opposite side to the hypotenuse in a right-angled triangle.

A percentage is a fraction out of 100. It is represented by the symbol '%'.

Interpreting graphs involves understanding the relationship between the different data points and their respective coordinates. This includes recognizing trends and patterns.

Data handling involves organizing, analyzing, and interpreting data. It includes understanding different units of measurement for various quantities.

A year that has 366 days instead of 365 days. It occurs every four years, except for years divisible by 100 but not by 400.

The number of seconds in a minute is 60. The number of minutes in an hour is 60. The number of hours in a day is 24. The number of days in a week is 7. The number of weeks in a month is roughly 4. The number of months in a year is 12. The number of days in a year is 365 (or 366 in a leap year).

Converting between different units of time, like seconds to minutes, minutes to hours, etc.

Adding or subtracting values representing time, expressed in terms of seconds, minutes, hours, days, months, and years.

The line segment that joins the center of the circle to any point on the circle.

The distance around a circle.

The amount of space enclosed within a circle.

A closed plane figure formed by three or more straight line segments.

The amount of space a two-dimensional shape occupies. It's measured in square units like square centimeters or square inches.

The space enclosed within a three-dimensional shape. It's measured in cubic units like cubic meters or cubic feet.

The steepness of a line. It tells us how much the line rises or falls for every unit it moves horizontally.

A function that has a graph shaped like a parabola. It has a highest or lowest point called the vertex.

A function that grows or decays at an exponential rate. It has a consistent multiplier.

A four-sided figure with two parallel sides. You find its area by multiplying the base by the height.

A special type of parallelogram with four right angles. You find its area by multiplying the length and width.

A four-sided figure with one pair of parallel sides. You find its area by averaging the lengths of the parallel sides and multiplying by the height.