Flashcards in Algebra 1 Deck (14)
How do you simplify a linear algebraic expression?
Make it into its most compact form by collecting like terms, removing brackets, factorising and finding a common denominator
How do you solve linear equations?
You must do the same to both sides of the equation, and find the value of something by collecting like terms, removing brackets, tidying up, adding, subtracting, multiplying and dividing etc.
How do you set up an equation?
Define any variables you introduce, then write out the equation using the information from the question
How do you change the subject of an equation?
Divide, multiply, add, subtract etc. until you have changed the subject
What is a quadratic expression?
An expression in which the highest power of its terms is 2
How do you expand a quadratic expression?
You multiply out each part of the bracket until you have your expression without any brackets
How do you factorise a quadratic expression?
Inspection, completing the square, quadratic formula
How do you factorise a quadratic expression by inspection?
Find all the pairs of numbers that multiply to get the whole number (without any x's) and add to get the coefficient of the second number in the equation and put them in brackets with the appropriate x's
How do you factorise a quadratic equation by completing the square?
Subtract the constant term x² - 8x = -3
from both sides of the equation
Take the coefficient, -8
halve it -4
then square it 16
Add this to both sides of the x² - 8x + 16 = -3 + 16
equation and factorise it (x - 4)² = 13
Take the square root of both sides (x - 4) = ±√13
Add the number in the bracket to both sides x = 4 + √13
x = 4 - √13
Work out the answer x=7.6065... or x=0.3944...q
How do you factorise a quadratic equation by the quadratic formula?
The quadratic formula for ax² + bx + c = 0 is...
-b ±√ (b² - 4ac)
Then sub a, b and c in and work it out for both plus and minus on the top
(However if the answer can only be positive due to the units then only use a positive answer)
How can you solve simultaneous equations?
Drawing a graph, substitution and elimination
How do you solve simultaneous equations using graphs?
Rearrange the equations if you need to then draw them onto a graph and see where they intersect. Those coordinates will give you the values of x and y
How do you solve simultaneous equations using substitution?
Rearrange one of the equations so the subject is x or y
Substitute this equation into the other equation in place of the x or y
Solve the equation to find the value of x or y
Substitute this value back into one of the original equations to get the other value