# Flash Cards

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- Created by: Charlottemh11
- Created on: 06-09-18 10:18

What is Factorising?

Factorising is the reverse of expanding brackets, so it is, for example, putting 2x² + x - 3 into the form (2x + 3)(x - 1). This is an important way of solving quadratic equations.

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What is the First Step to factorising?

The first step of factorising an expression is to 'take out' any common factors which the terms have. So if you were asked to factorise x² + x, since x goes into both terms, you would write x(x + 1) .

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What is trial and improvement?

Any equation can be solved by trial and improvement. Start by estimating the solution. Then substitute this into the equation.

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Example of trial and improvement

Solve t³ + t = 17 by trial and improvement. Firstly, select a value of t to try in the equation. I have selected t = 2. Put this value into the equation. We are trying to get the answer of 17. If t = 2, then t³ + t = 2³ + 2 = 10 .

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Iteration

This is a way of solving equations. It involves rearranging the equation you are trying to solve to give an iteration formula. This is then used repeatedly (using an estimate to start with) to get closer and closer to the answer.

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What a Iteration equation looks like

xn+1 = 2 + 1 (this is for the equation x2 = 2x + 1)

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Travel Graphs

This section covers travel graphs, speed, distance, time, trapezium rule and velocity.

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Formula for when speed stays consistant

Speed = distance / time

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What is the formula if the speed is not consistant and changes?

Average Speed = total distance travelled / total like taken

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Velocity and Acceleration

Velocity is the speed of a particle and its direction of motion (therefore velocity is a vector quantity, whereas speed is a scalar quantity).

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Velocity and Acceleration

When the velocity (speed) of a moving object is increasing we say that the object is accelerating. If the velocity decreases it is said to be decelerating. Acceleration is therefore the rate of change of velocity (change in velocity / time)

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What are the three main type of Average?

Mean, Median, Mode

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What is the mean?

It is found by adding up all of the numbers you have to find the mean of, and dividing by the number of numbers

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What is the median?

The median of a group of numbers is the number in the middle, when the numbers are in order

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What is the Mode?

The mode is the number in a set of numbers which occurs the most

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What is Range?

Highest Value - Lowest Value

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What is Probability?

Probability is the likelihood or chance of an event occurring.

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The equation for probability

Probability = the number of ways of achieving success / the total number of possible outcomes

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There are 6 beads in a bag, 3 are red, 2 are yellow and 1 is blue. What is the probability of picking a yellow?

The probability is the number of yellows in the bag divided by the total number of balls, i.e. 2/6 = 1/3.

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Lowest Common Multiple

The least or lowest common multiple (LCM) of two or more numbers is the smallest number into which they evenly divide.

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Highest Common Factor

The highest common factor (HCF) or Greatest Common Divisor of two or more numbers is the highest number which will divide into them both.

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LCM Example

The LCM of 2, 3, 4, 6 and 9 is 36.

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HCF Example

The HCF of 8 and 12 is 4

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Type of Number - Integers

Integers are whole numbers (both positive and negative, including zero).

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Type of Number - Rational

A rational number is a number which can be written as a fraction where numerator and denominator are integers (where the top and bottom of the fraction are whole numbers).

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Type of Number - Irrational

Irrational numbers are numbers which cannot be written as fractions, such as pi

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Type of Number - Square Numbers

Square numbers are numbers which can be obtained by multiplying another number by itself. E.g. 16 is a square number because it is 4 x 4 .

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Type of Number - Prime Numbers

Prime numbers are numbers above 1 which cannot be divided by anything (other than 1 and itself) to give an integer. The first prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19.

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Type of Number - A Factor

A factor (or divisor) of a number is a number which will divide into your number exactly. So you can divide a number by one of its factors and you won't be left with a remainder

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What is standard form?

Standard form is a way of writing down very large or very small numbers easily.

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Example of Standard form

10 cubed = 1000

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## Other cards in this set

### Card 2

#### Front

What is the First Step to factorising?

#### Back

The first step of factorising an expression is to 'take out' any common factors which the terms have. So if you were asked to factorise x² + x, since x goes into both terms, you would write x(x + 1) .

### Card 3

#### Front

What is trial and improvement?

#### Back

### Card 4

#### Front

Example of trial and improvement

#### Back

### Card 5

#### Front

Iteration

#### Back

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