Algebra 2 Flashcards
What does the symbol ≥ mean?
Greater than or equal to
How should you check your answer when solving simultaneous equations?
Substitute your values for x and y into the other equation
When factorising a quadratic equation:
If the equation has a positive value for the last number,
what does it tell you about the signs for the factor pair chosen?
They will be the same
+ and +
OR
- and -
How do you find the next term in a Fibonacci type sequence?
Add the previous two terms together
True or False?
x ≤ 7 means x is greater than or equal to 7
False
It means
x is less than or equal to 7
What is the first thing you would do to solve the simultaneous equations?
3x - 4y = 2 and 2x + 5y = 9
Multiply both equations by numbers that will make the coefficients of x or y the same
e.g.
Multiply the first by 2
to give you 6x - 8y = 4
Then multiply the second by 3
to give you 6x + 15y = 27
If you multiply or divide both sides of an inequality by a negative number,
What happens to the inequality sign?
It is turned around
What is meant by the ‘common difference’ of a linear sequence?
The value you add or subtract to go from one term to the next
How can you prove that a statement is false?
Find an example that doesn’t work
Is 25 a term in the sequence
6n + 1 ?
Yes
6(4) + 1 = 25
It is the 4th term
What is the standard form of a quadratic?
x2 + bx + c = 0
b and c are numbers
What is a geometric sequence?
A sequence where you
multiply/divide
to go from one term to the next
True or False?
When n is an integer,
9n + 6
is always a multiple of 3
True
6 is a multiple of 3
9 x something will always be a multiple of 3
Which to symbols are represented by an open circle on a number line?
< and >
What is the rule for this sequence?
2, 6, 18, 54, …
Multiply by 3
It is a geometric sequence
How do you solve a factorised quadratic equation?
Find the values of x that will make each bracket equal zero
Prove this statement is false.
‘The product of two primes is always odd’
2 x 3 = 6
What is meant by the nth term of a linear sequence?
A rule that gives the terms in the sequence,
when you put in different values of n
Factorise
x2 - 6x + 8
(x - 4)(x - 2)
When solving simultaneous equations:
What do you do with the value of the first variable,
to find the value of the second variable?
Substitute it back into one of the original equations
What does the symbol ≡ mean?
It is the Identity symbol
The statement is always true for all values
How do you get from one term to the next in a linear sequence?
Add/Subtract the name number each time
How would you decide if a term is in a sequence?
Set the nth term equal to the number and then solve it.
If it is a whole number answer then it is in the sequence
What does the inequality
2 < x ≤ 7
mean?
x is greater than 2
and
less than or equal to 7
How do you get rid of a variable when solving simultaneous equations?
Match the coefficients of one of the variables,
then add/subtract the equations
How would you prove that two expressions ae the same?
Rearrange one to get the other
Solve
(x - 2)(x + 5) = 0
x = 2 and x = -5
On a number line what is used for these inequality symbols?
≤ and ≥
Closed circles
(coloured in circles)
Rearrange
x2 = 6 - 5x
so it can be factorised and solved.
x2 = 6 - 5x
add 5x both sides
x2 + 5x = 6
subtract 6 both sides
x2 + 5x - 6 = 0
What is the nth term of the sequence?
-1, 1, 3, 5, …
2n - 3
What is the difference between linear sequences and quadratic sequences?
For a quadratic sequence, the number you add/subtracts changes between each term.
For a linear, the number you add/subtract stays the same between each term.
Solve the inequality
x + 4 > 10
x + 4 > 10
Subtract 4 both sides
x > 6
What is meant by
‘factorising a quadratic equation’ ?
Putting it into two brackets
What type of sequence is
37, 26, 15, 4, …?
Linear sequence
What form should you rearrange simultaneous equations into before solving them?
ax + by = c
Where a, b, and c are numbers
List the integers that satisfy the inequality
-4 ≤ x < 1
-4, -3, -2, -1, 0
If the signs are different in a factorised quadratic equation,
will the value of the number at the end, when expanded,
be positive or negative?
Negative
How would the inequality x ≤ 5 on a number line?
With a closed circle over the 5,
and an arrow pointing toward the left (smaller numbers)
Prove this statement is false:
‘The sum of two square numbers is never a square number’
e.g.
32 + 42
= 9 + 16
=25
= 52
What is the common difference in the sequence:
11, 14, 17, 20, …?
3
