Algebra And Equations Revision Flashcards
In what order should you write an equation? (Not too important)
With the letters in alphabetical order
4d+2d=
6d
n m
a x a =
n+m
a
n m
a / a =
n-m
a
0
Why does a equal 1?
Because it’s a/a and a/a = 1
-1
a = (as a fraction)
1
__
a
-2
a =
1
__
2
a
3w x 4w =
2
12w
because you multiply the 3 and 4 and the ws as well
2
4gh x 3gh =
2 3
12g h
because you multiply the 3 and the 4 and the gs and hs as well (separately)
5 3
8a x 7a =
8
56a
ADD THE POWERS!
6 3
7a / 2a =
3
3.5a
SUBTRACT THE POWERS!
7 4
14b / 3b =
3
4.6b
SUBTRACT THE POWERS!
How would you expand these brackets?
6(a+5)
Multiply what’s on the outside by what’s on the inside, giving me 6a+30
Expand these brackets:
9(2h+1)
18h+9
List the factors of 6x
1, 6x
2x, 3
3x, 2
x, 6
2
List the factors of 18x
2
x, 18
2
1, 18x
3x, 6
x, 18x
6x, 3x
2
6x , 3
2
2x, 9
9x, 2xWhat does factorise mean?
Putting something BACK into brackets
2
How would you factorise 18x + 6x ?
First I need to find the highest common
2
factor of 18x and 6x, which is 6x. We then put 6x outside the brackets and divide each term in the expression by 6x, giving me 6x(3x+1)
How would you solve 4x+5=27 ?
First take 5 from both sides, leaving me with 4x=22, then I divide both sides by 4, leaving me with x=5.5
How would you solve 5(7+2x)=65 ?
First, divide both sides by 5, leaving me with 7+2x=13, next, take 7 from both sides, leaving me with 2x=6 and finally, divide both sides by 2 leaving me with x=3
How would you solve p + 3 = 7 ?
__
2
First take 3 from both sides, leaving me with p = 4 and then multiply both
__ sides by, leaving me with
2 p=8
How do you find distance?
Speed x time
How do you find speed?
Distance
________
Time
How do you find time?
Distance
________
Speed
How would you rearrange hp=q so that p is the subject?
I would divide q by h, giving me p= q
__
h
How would you rearrange x+4=y so that x is the subject?
I take 4 from y, leaving me with y-4=x
How would you rearrange p-h=q so that p is the subject?
Add h to q, giving me p=q+h
Use the elimination method to solve
2x-y=1
3x+y=9
The signs are different, so I add them, giving me 5x=10 which means x=2. I then substitute x=2 into one of the equations, I’ll use 2x-y=1, giving me 4-y=1 so y must equal 3. This means that (2,3) would be where the lines cross.
With the elimination method, what do you do when the signs are different?
Add them
With the elimination method, what do you do when the signs are the same?
Subtract them
What should you do when solving simultaneous equations so that you don’t need to write an equation again when you refer to it?
Label the equations
How would you check your answers with the elimination method?
Substitute your answers into one of your equations
What would you do with the elimination method when the equations have all different values?
Multiply one by something to make at least one set of variables the same, then continue as you regularly would
What should you make sure of when using the elimination method?
That at least one set of variables are the same
How would you solve the equations
5x+y=9
y=4x
using the substitution method?
First I would substitute y=4x into the first equation, giving me 5x+4x=9 (REARRANGE IF NECESSARY! C: ) so x=1. We now know that y=4x1 when we substitute x=1 into y=4x so we know that y=4
How would you solve the equations
5x+y=9
y=4x
using the substitution method?
First, substitute y=4x into the first equation, giving me 5x+4x=9 (rearrange if necessary! c: ) so x=1. Now we know that y=4x1 because we can substitute x=1 into into y=4x so y=4
How do you find the mean?
Multiply the frequencies by the midpoints (or just the regular number of it’s not grouped data) then divide by the sum of the frequencies.
How do find the median?
Add the frequencies together and half the answer then count in through the frequencies until you get to that number and the data group that you end up in is the median.
How to you find the modal class?
Find the highest frequency and the data group it’s in is the modal class.
How do you find the range?
Find the difference between the lowest and highest frequencies
How would you factorise the expression:
2
5x +25x ?
First I would find the highest common
2
factor of 5x and 25x, which is 5x. I then put 5x outside of the brackets. Then I divide each term in the expression by 5x, leaving me with 5x(x+5)
