1.2 Algebra

Question 1

What is substitution in relation to algebra?

Answer 1

When you replace letters with values in a equation

Question 2

What is the process of transposition?

Answer 2

When you make a different letter the subject of the formula

Question 3

When doing transposition what is the must important thing to remember?

Answer 3

You must do it to both sides of the equation

Question 4

When simplifying algebraic equations what is important to remember?

Answer 4

You can only simplify if they have the same letter

Question 5

When using algebra what is the number in front of a symbol called?

Answer 5

A coefficient

Question 6

In relation to algebra what is cancelling down or lowest term?

Answer 6

When you can simplify the equation by expressing both sides (i.e a^2xb / a b^2 turns int a/b)

Question 7

What is meant by expanding brackets?

Answer 7

When you remove the brackets and each term within them is multiplied by the quantity outside the bracket

Question 8

What happens when you expand the brackets but a negative is outside he bracket?

Answer 8

You multiply them by the negative

Question 9

What is factorisation?

Answer 9

It is changing an equation by putting them into brackets

Question 10

What is the opposite of expanding a question?

Answer 10

Factorisation

Question 11

what is the opposite of factorisation?

Answer 11

Expanding

Question 12

How do you factorise an algebraic equation?

Answer 12

Find the highest common factor. Place it outside the brackets then divide each term inside by the highest common factor

Question 13

When two brackets are written next to each other what must you do?

Answer 13

Multiply both of them

Question 14

When expanding two sets of brackets what methods can you use?

Answer 14

FOIL or crab claw

Question 15

What does the method FOIL stand for?

Answer 15

First (F )x(F )
Outside (O )x( O)
Inside ( I)x(I )
Last ( L)x( L)

Question 16

When expanding a pair of brackets when can’t you use the method FOIL?

Answer 16

When one of the brackets contains more than two digits

Question 17

Why is the crab claw method better than FOIL when expanding brackets?

Answer 17

Because you can always use the crab claw method but FOIL can only be used when there is no more than two digits

Question 18

When multiplying or dividing algebraic fractions what should you do?

Answer 18

Express it into a single fraction i.e a/b x c/d is axc/bxd

Question 19

What is algebraic maths?

Answer 19

Maths with letters

Question 20

When simplifying algebraic fractions what can you do if the numerator and denominator have a common digit?

Answer 20

Cancel them out

Question 21

When cancelling out in an equation to get rid of something what must you do?

Answer 21

The opposite

Question 22

What are the two methods used in algebra to show two quantities are equivalent to each other?

Answer 22

Equation and identity

Question 23

In algebra what is meant by the equation method?

Answer 23

When there is only one value that will satisfy the question

Question 24

In algebra what is meant by the identity method?

Answer 24

Is when a question is true no matter what value is chosen to represent the letter

Question 25

In algebra what should the left hand side and right hand side be?

Answer 25

Equal

Question 26

When told to solve a linear equation what is it asking you to do?

Answer 26

To find what the letter equals

Question 27

When a number has a power or index or exponent what is the original number referred as? I.e 5^3

Answer 27

The base

Question 28

If a base number has a negative power what must you do? i.e 2^-3

Answer 28

Invert it into 1 over the base and power but its now positive. I.e 1/2^3 = 1/8

Question 29

What happens when you have a negative power against a fraction? i.e (3/2)^-3

Answer 29

You must flip it which turns it positive then solve

Question 30

What are the two key points with a negative power?

Answer 30

Its never a negative and you must have it in a fraction

Question 31

What do you get if your base number has a power number of 0?

Answer 31

It equals 1

Question 32

What happens when you get a number to the power of a fraction? I.e 4^½

Answer 32

You square root the number and The denominator indicates the root of the number. I.e 2^√4

Question 33

What happens when you have a base number that is being powered by a fraction with a numerator above one? i.e 8^⅔

Answer 33

Same as any fractional power but you give your number the numerator power to the digit before rooting. I.e 3^√8^2

Question 34

What happens when you have a base number being powered by a negative fraction?

Answer 34

Simply put your base number under 1 and being powered by your now positive fraction

Question 35

If a digit has a power of 1 what is the outcome?

Answer 35

It equals the base digit. I.e 8^1 = 8

Question 36

When multiplying two numbers with powers. If the bases are the same what can you do?

Answer 36

Add them together. I.e 2^5 x 2^3 = 2^8

Question 37

When dividing two numbers with powers. If the bases are the same what can you do?

Answer 37

Subtract the powers by each other 5^7 ÷ 5^3 = 5^4

Question 38

What happens when a digit has a power and then raised to another power?

Answer 38

The two powers are multiplied

Question 39

What two digits does binary use?

Answer 39

1 and 0

Question 40

What type of numbering system does a computer use when processing information?

Answer 40

Binary

Question 41

What digits does the octal number system use?

Answer 41

0-7

Question 42

What is the base value when using binary in an equation?

Answer 42

2

Question 43

What is the base value when using the octal numbering system?

Answer 43

8

Question 44

What numbering system does a computer use when sending information?

Answer 44

Octal

Question 45

What digits does hexadecimal use?

Answer 45

0-9 and A-F

Question 46

Why are letters used in the hexadecimal numbering system?

Answer 46

The tenth digits aren’t sufficient so letters are used to represent the numbers

Question 47

In the hexadecimal numbering system what do the letter A-F represent?

Answer 47

10-15

Question 48

What is the base value in the hexadecimal numbering system?

Answer 48

16

Question 49

What is a simultaneous equation?

Answer 49

When two or more equations can work together by having at least one variable that is the same

Question 50

How do you solve a simultaneous equation?

Answer 50

Multiply so that both coefficients are the same then add or subtract to find one value then simplify

Question 51

What is the standard format for quadratic equations?

Answer 51

Ax^2+bx+c=0

Question 52

How can you solve quadratic equations?

Answer 52

By factorisation (placing in brackets)

Question 53

When is a formula used instead of factorisation when solving a quadratic equation?

Answer 53

When factorisation is too difficult

Question 54

What is logarithm another word for?

Answer 54

Index or power

Question 55

If you had 3^2=9 and was told to write it into logarithm what would the answer be?

Answer 55

2=Log3^9

Question 56

What is the general rules for logarithms?

Answer 56

Log^y A+B then y^B=A

Question 57

What is the logarithmic scale that is used to measure sound?

Answer 57

Decibel scale

Question 58

If you had log x (1) what is the answer no matter what x is equal?

Answer 58

0

Question 59

If you had a logarithm with the same number after the log and in the brackets. What is the answer? I.e log x (x)

Answer 59

1

Question 60

If there is no given number after the log what is it being powered to?

Answer 60

10

Question 61

What would the answer to this question be? Log2 (16)

Answer 61

4 because 2x2x2x2= 16

Question 62

What would happen if you had this equation? 5log5(14)

Answer 62

You’d cancel out the 5s leaving you with log(14) which equals 14

Question 63

What would the answer be if you had 0.1, 0.01,0.001 after the log? I.e log(0.1),log(0.01),log(0.001)

Answer 63

Log(0.1)=-1 Log(0.01)=-2 Log(0.001)=-3

Question 64

What will the answer be if you have a fraction in the brackets after your log? I.e log3(1/9)

Answer 64

Negative i.e log3(1/9)=-2

Question 65

If the log number is bigger than the bracket number what will the answer be? I.e log9(3)

Answer 65

A fraction i.e log9(3)=1/2

Question 66

What happens if you have a log with a fraction in the bracket and a larger log number? I.e log9(1/3)

Answer 66

The answer will be a negative fraction i.e log9(1/3)=-½