Algebra 1

Question 1

How do you simplify a linear algebraic expression?

Answer 1

Make it into its most compact form by collecting like terms, removing brackets, factorising and finding a common denominator

Question 2

How do you solve linear equations?

Answer 2

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.

Question 3

How do you set up an equation?

Answer 3

Define any variables you introduce, then write out the equation using the information from the question

Question 4

How do you change the subject of an equation?

Answer 4

Divide, multiply, add, subtract etc. until you have changed the subject

Question 5

What is a quadratic expression?

Answer 5

An expression in which the highest power of its terms is 2

Question 6

How do you expand a quadratic expression?

Answer 6

You multiply out each part of the bracket until you have your expression without any brackets

Question 7

How do you factorise a quadratic expression?

Answer 7

Inspection, completing the square, quadratic formula

Question 8

How do you factorise a quadratic expression by inspection?

Answer 8

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

Question 9

How do you factorise a quadratic equation by completing the square?

Answer 9

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

Question 10

How do you factorise a quadratic equation by the quadratic formula?

Answer 10

The quadratic formula for ax² + bx + c = 0 is…

   -b ±√ (b² - 4ac) x= \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
             2a

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)

Question 11

How can you solve simultaneous equations?

Answer 11

Drawing a graph, substitution and elimination

Question 12

How do you solve simultaneous equations using graphs?

Answer 12

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

Question 13

How do you solve simultaneous equations using substitution?

Answer 13

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

Question 14

How do you solve simultaneous equations using elimination?

Answer 14

Multiply one or both of your equations so they both have the same value of either x or y

If the sign before the same value is +, the subtract one equation from the other to get one equation. If it is -, then add the equations to get one equation

Solve to find the value of x or y

Substitute this value into one of the original equations to find the other value