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IGCSE Mathematics

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Section 1

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Adding/subtracting vectors

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Math

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Mar 1, 2020

Cards (30)

Section 1

(30 cards)

Adding/subtracting vectors

Front

You simply place the start of a vector onto the end of another vector, and the line that connects the two is the result. If you want to subtract a minus b then it means you use the negative vector (opposite direction) of b.

Back

Column Vector

Front

Another way of representing a vector quantity

Back

log(a/b)

Front

log(a) - log(b)

Back

Strength of Correlation

Front

If the points are close together and follow a linear path, then they have strong correlation. If they are scattered they have a weak/no correlation.

Back

a^(m+n)

Front

a^m x a^n

Back

(a^m)^n

Front

a^(m x n)

Back

Front

Back

Vector

Front

A quantity that has magnitude and direction - can be visualised using an arrow (the length is the magnitude and where it is pointing is the direction) - they are parallel if they have the same direction and magnitude - a negative of a vector means it has the same length but points in a different direction

Back

y=b^x

Front

logb(y) = x

Back

Inverse Function

Front

To find out the inverse of a function flip the y and the x and isolate the y. - the domain of the original function will be the range of the inverse function - the range of the original function will be the domain of the inverse function - an inverse function is a reflection of the original function in y=x, meaning they are symmetrical about the line y = x

Back

Relative Frequency

Front

Frequency / Number of Trials

Back

Perimeter

Front

For any shape, add the length of all sides together.

Back

Distance Formula

Front

d = √[( x₂ - x₁)² + (y₂ - y₁)²] Formula used to find the distance between two points on the cartesian plane

Back

How to Find Quadratic Functions

Front

y= a(x - h)2 + k : the vertex form of a quadratic equation - a is the constant - (h,k) is the coordinates of the vertex - If a<0, we have a function that goes down - If a>0, we have a function that goes up - When the vertex form is y = a(x + h)2 + k, the coordinate of the vertex will be (-h, k) - When the vertex form is y = a(x - h)2 - k, the coordinate of the vertex will be (h, -k)

Back

SOHCAHTOA

Front

Sin θ = Opposite/Hypotenuse Cos θ = Adjacent/Hypotenuse Tan θ = Opposite/Adjacent

Back

Midpoint Formula

Front

Formula for calculating the midpoint between two lines on the cartesian plane, also known as the average of the x's and the average of the y's (x₁+x₂)/2, (y₁+y₂)/2

Back

log(ab)

Front

log(ab) = log(a) + log(b)

Back

Function

Front

When no value of x has two values of y, and when every element in x is directly related to a y element.

Back

Direct Variation

Front

a linear function defined by an equation of the form y=kx, where k does not equal 0

Back

Cubic Equation

Front

ax^3 + bx^2 + cx + d If a > 0, the graph will look like this: Positive Cubic If a < 0, the graph will look like this: Negative Cubic ax^3 + bx^2 + cx + d can also be arranged into the form a(x-h)^3 + k, and hence helps you to determine the translations: If h > 0, the curve moves h units to the left If h < 0, the curve moves h units to the right If k > 0, the curve moves k units up If k < 0, the curve moves k units down

Back

Inverse Variation

Front

Mathematical relationship between two variables which can be expressed by an equation in which the product of two variables is equal to a constant: y=k/x

Back

Interpolation and Extrapolation

Front

The highest and lowest values of x in a line. Values that are between these two numbers are interpolates and values that are outside are called extrapolation (unreliable because it assumes that the line continues beyond the poles)

Back

Scalar

Front

A physical quantity that has magnitude only.

Back

log(a)^b

Front

b . log(a) or log(a)

Back

Range

Front

all the y values in a function

Back

Domain

Front

all the x values in a function

Back

a^(m-n)

Front

(a^m)/(a^n)

Back

Gradient Rules

Front

The gradient is the rise over the run - parallel lines have equal gradients - perpendicular lines have negative reciprocal gradients

Back

Correlation

Front

A relationship between data points. Positive means it goes up/gets bigger and negative means it goes down/gets less.

Back

Area

Front

For a square/rectangle multiply one side by another For a triangle multiply the base by the height and divide it by two

Back