Algebra 2

Question 1

What does the symbol ≥ mean?

Answer 1

Greater than or equal to

Question 2

How should you check your answer when solving simultaneous equations?

Answer 2

Substitute your values for x and y into the other equation

Question 3

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?

Answer 3

They will be the same
+ and +
OR
- and -

Question 4

How do you find the next term in a Fibonacci type sequence?

Answer 4

Add the previous two terms together

Question 5

True or False?
x ≤ 7 means x is greater than or equal to 7

Answer 5

False
It means
x is less than or equal to 7

Question 6

What is the first thing you would do to solve the simultaneous equations?
3x - 4y = 2 and 2x + 5y = 9

Answer 6

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

Question 7

If you multiply or divide both sides of an inequality by a negative number,
What happens to the inequality sign?

Answer 7

It is turned around

Question 8

What is meant by the ‘common difference’ of a linear sequence?

Answer 8

The value you add or subtract to go from one term to the next

Question 9

How can you prove that a statement is false?

Answer 9

Find an example that doesn’t work

Question 10

Is 25 a term in the sequence
6n + 1 ?

Answer 10

Yes

6(4) + 1 = 25
It is the 4th term

Question 11

What is the standard form of a quadratic?

Answer 11

x² + bx + c = 0

b and c are numbers

Question 12

What is a geometric sequence?

Answer 12

A sequence where you
multiply/divide
to go from one term to the next

Question 13

True or False?
When n is an integer,
9n + 6
is always a multiple of 3

Answer 13

True

6 is a multiple of 3
9 x something will always be a multiple of 3

Question 14

Which to symbols are represented by an open circle on a number line?

Answer 14

< and >

Question 15

What is the rule for this sequence?
2, 6, 18, 54, …

Answer 15

Multiply by 3
It is a geometric sequence

Question 16

How do you solve a factorised quadratic equation?

Answer 16

Find the values of x that will make each bracket equal zero

Question 17

Prove this statement is false.
‘The product of two primes is always odd’

Answer 17

2 x 3 = 6

Question 18

What is meant by the nth term of a linear sequence?

Answer 18

A rule that gives the terms in the sequence,
when you put in different values of n

Question 19

Factorise
x² - 6x + 8

Answer 19

(x - 4)(x - 2)

Question 20

When solving simultaneous equations:

What do you do with the value of the first variable,
to find the value of the second variable?

Answer 20

Substitute it back into one of the original equations

Question 21

What does the symbol ≡ mean?

Answer 21

It is the Identity symbol
The statement is always true for all values

Question 22

How do you get from one term to the next in a linear sequence?

Answer 22

Add/Subtract the name number each time

Question 23

How would you decide if a term is in a sequence?

Answer 23

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

Question 24

What does the inequality
2 < x ≤ 7
mean?

Answer 24

x is greater than 2
and
less than or equal to 7

Question 25

How do you get rid of a variable when solving simultaneous equations?

Answer 25

Match the coefficients of one of the variables,
then add/subtract the equations

Question 26

How would you prove that two expressions ae the same?

Answer 26

Rearrange one to get the other

Question 27

Solve
(x - 2)(x + 5) = 0

Answer 27

x = 2 and x = -5

Question 28

On a number line what is used for these inequality symbols?
≤ and ≥

Answer 28

Closed circles
(coloured in circles)

Question 29

Rearrange
x² = 6 - 5x
so it can be factorised and solved.

Answer 29

x² = 6 - 5x
add 5x both sides
x² + 5x = 6
subtract 6 both sides
x² + 5x - 6 = 0

Question 30

What is the nth term of the sequence?
-1, 1, 3, 5, …

Answer 30

2n - 3

Question 31

What is the difference between linear sequences and quadratic sequences?

Answer 31

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.

Question 32

Solve the inequality
x + 4 > 10

Answer 32

x + 4 > 10
Subtract 4 both sides
x > 6

Question 33

What is meant by
‘factorising a quadratic equation’ ?

Answer 33

Putting it into two brackets

Question 34

What type of sequence is
37, 26, 15, 4, …?

Answer 34

Linear sequence

Question 35

What form should you rearrange simultaneous equations into before solving them?

Answer 35

ax + by = c

Where a, b, and c are numbers

Question 36

List the integers that satisfy the inequality
-4 ≤ x < 1

Answer 36

-4, -3, -2, -1, 0

Question 37

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?

Answer 37

Negative

Question 38

How would the inequality x ≤ 5 on a number line?

Answer 38

With a closed circle over the 5,
and an arrow pointing toward the left (smaller numbers)

Question 39

Prove this statement is false:
‘The sum of two square numbers is never a square number’

Answer 39

e.g.
3² + 4²
= 9 + 16
=25
= 5²

Question 40

What is the common difference in the sequence:
11, 14, 17, 20, …?

Answer 40

3