Part 2: Algebra

• Letters are used to represent either a constant, which is fixed, or a variable which can change
• Constants are fixed
• Variables can change
• Coefficient = the number in front of an algebraic letter
• To simplify an algebraic expression, a good starting point is to collect like terms.
• One way of ensuring that you multiply everything in the first bracket with everything in the second bracket is by using the FOIL method

  • First
  • Outside
  • Inside
  • Last

  
• The general form of a quadratic is $ax^2+$$bx+$$c$
• Anything to the power of 1 is itself
• Anything to the power of 0 is 1
• When multiplying numbers with the same base, you add the powers.
• When raising one power to another, the powers are multiplied together.
• Lots of functions have inverse functions. These do the opposite of what a function does to a number. They are often written like this $f^{-1}\left(x\right)$
• When we extend the 𝑥 and 𝑦 axes beyond the origin, we obtain negative axes in addition to the positive axes. The four areas divide by the axes are called quadrants.

  
• When two lines meet at a right-angle, they are perpendicular
• Parallel lines are lines which are always the same distance apart, meaning parallel lines never meet.
• A root is a solution to a quadratic equation when it is set equal to zero
• The intercept is the place where the curve crosses the y-axis.
• A turning point is the place on a curve where it changes direction
• Cubic graphs can have more than one turning point and have equations of the form:

  $y\ =$$\ ax^3+$$bx^2+$$cx+$$d$

  
• Reciprocal graphs are of the form $y=$$\frac{1}{x}$ where x is not 0

  
• The trigonometric functions are functions that take angles as their inputs and relate them to the ratio of the sides of a right-angled triangle.
• Sin, cosine and tan are trigonometric functions.
• Sin curve

  
• Cosine curve

  
• Translation = a type of transformation of a function in which the curve or line moves in the vertical or horizontal direction
• Graphs can be used to show the relationships in real life between two variables.
• A displacement-time graph is a type of graph that shows how far an object is from its starting place

  
• A velocity time graph has velocity on the y-axis and time on the x-axis

  
• Equation of a circle centred at origin (0,0): $x^2+$$y^2=$$r^2$
• Quadratic formula: $x=$$\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
• To solve two linear simultaneous equations, we use elimination. One of the variables is eliminated by subtracting one equation from the other
• A sequence is a series of numbers that follow a particular rule or pattern