Algebra 1 Flashcards
What is an equation?
An expression that has an ‘=’ sign in it
True or False?
(2x + 3)2 = 4x2 + 9
False
(2x + 3)2
= (2x + 3)(2x + 3)
= 4x2 + 6x + 6x + 9
= 4x2 + 12x + 9
What is the first step to solve equations that involve brackets?
Expand the bracket
What is the first thing you would do to rearrange
x = 2y - 5
to make y the subject?
Add 5 to both sides
What is a term?
A single or group of numbers/letters together.
(not added or subtracted)
e.g. 5, y, 3x, 4ab2
What is the first step to make an expression from a worded problem?
Work out what the variable is
Expand 3(2x - 5)
6x - 15
What goes outside the bracket when factorising an expression?
The highest common factors of all the terms in the original expression.
A function machine takes a number,
divides it by 3,
then adds 4.
What is the output when 9 is put into the machine?
7
What is the first step to collect like terms?
Identify the terms that are the same type as each other
How do you expand a single bracket?
Multiply each term inside the bracket by the bit outside the bracket
What is
a x a x b x b
in its simplest form?
a2b2
Or
(ab)2
What is a formula?
A rule that helps you work something out
(has an ‘=’ sign)
Expand and simplify
(x + 3)(x - 1)
(x + 3)(x - 1)
= x2 - x + 3x - 3
= x2 + 2x - 3
Harry is three years older than Max.
Shelly is twice as old as Max.
Give an expression for the sum of their ages.
Let Max’s age be x
Then Harry is x + 3
and Shelly is 2x
Sum of their ages = x + x + 3 + 2x = 4x + 3
True of False?
When rearranging a formula,
you should do the opposite thing to each side.
False
You should do the same thing to both sides
How do you find the value put into a function machine, from the output?
Use the function machine in reverse.
Starting with the output value,
and doing the inverse operation at each stage
How could you check that a factorisation is correct?
Multiply it out again and check you get the original expression
Solve
x + 8 = 5
x = -3
What is the rule for factorising the difference between two squares?
Square root the first term and put this at the start of each bracket.
Square root the second term and put this at the back of each bracket.
One bracket has a plus, the other a minus
What is an expression?
A collection of terms without an ‘=’ sign
Simplify
2y + 9 - 6y - 4
-4y + 5
What is the first thing you should do to expand squared brackets?
Write them out as double brackets
1 km = 1.6m
What is 10 miles in kilometres?
16 km
What is the first thing you’d do to solve
5x - 9 = 6
Add 9 to both sides
How would you write 8 lots of a multiplied together?
a x a x a x a x a x a x a x a
a8
Expand and simplify
x(4x - 1) - 3x(2x + 3)
x(4x - 1) - 3x(2x + 3)
= 4x2 - x - 6x2 - 9x
= -2x2 - 10x
Make b the subject
a = ½( 5b - 3)
a = ½( 5b - 3)
(x2)
2a = 5b - 3
(+3)
2a + 3 = 5b
(÷5)
2a + 3 = b
5
Factorise
x2 - 49
Difference between two squares
(x + 7)(x-7)
A function machine takes a number,
multiplies it by 5,
then subtracts 3.
What is the input if the output is 17 ?
17 + 3 = 20
20 ÷ 5 = 4
4
Simplify
3 x p x p x q
3p2q
What is meant by factorising an expression?
Putting brackets into the expression
What is the first step to solve equations that have an x on both sides?
Get all the x terms on one side of the equation by getting rid of the lowest value of x from both sides.
Then get all the numbers on the other side of the equation
Factorise fully
4x2 + 6xy + 12xy2
2x(2x + 3y + 6y2)
Give the three rules for rearranging equations.
Do the same thing to both sides of the equation
Do the inverse operation to get rid of things you don’t want
Keep going until the letter you want is on its own
What is a function?
An expression that takes an input value,
processes it and produces an output value
How do you show
x ÷ y
using algebra notation?
x/y
Given the formula
m = 3n + 7
find m when n = 2
m = 3(2) + 7
m = 6 + 7
m = 13
Expand and simplify
(2x + 7)(3x - 4)
(2x + 7)(3x - 4)
= 6x2 - 8x + 21x - 28
= 6x2 + 13x - 28
A rectangle and a square have the same area.
The rectangle has sides 4 cm and x cm long.
The square has sides 6 cm long.
Find x.
Area of the rectangle = 4x
Area of the square = 36
4x = 36
x = 9
