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B1 1-Maths > 1.2 Algebra > Flashcards

1.2 Algebra Flashcards

1
Q

What is substitution in relation to algebra?

A

When you replace letters with values in a equation

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2
Q

What is the process of transposition?

A

When you make a different letter the subject of the formula

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3
Q

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

A

You must do it to both sides of the equation

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4
Q

When simplifying algebraic equations what is important to remember?

A

You can only simplify if they have the same letter

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5
Q

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

A

A coefficient

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6
Q

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

A

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

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7
Q

What is meant by expanding brackets?

A

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

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8
Q

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

A

You multiply them by the negative

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9
Q

What is factorisation?

A

It is changing an equation by putting them into brackets

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10
Q

What is the opposite of expanding a question?

A

Factorisation

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11
Q

what is the opposite of factorisation?

A

Expanding

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12
Q

How do you factorise an algebraic equation?

A

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

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13
Q

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

A

Multiply both of them

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14
Q

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

A

FOIL or crab claw

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15
Q

What does the method FOIL stand for?

A

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

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16
Q

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

A

When one of the brackets contains more than two digits

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17
Q

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

A

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

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18
Q

When multiplying or dividing algebraic fractions what should you do?

A

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

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19
Q

What is algebraic maths?

A

Maths with letters

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20
Q

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

A

Cancel them out

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21
Q

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

A

The opposite

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22
Q

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

A

Equation and identity

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23
Q

In algebra what is meant by the equation method?

A

When there is only one value that will satisfy the question

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24
Q

In algebra what is meant by the identity method?

A

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

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25
Q

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

A

Equal

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26
Q

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

A

To find what the letter equals

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27
Q

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

A

The base

28
Q

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

A

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

29
Q

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

A

You must flip it which turns it positive then solve

30
Q

What are the two key points with a negative power?

A

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

31
Q

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

A

It equals 1

32
Q

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

A

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

33
Q

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

A

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

34
Q

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

A

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

35
Q

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

A

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

36
Q

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

A

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

37
Q

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

A

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

38
Q

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

A

The two powers are multiplied

39
Q

What two digits does binary use?

A

1 and 0

40
Q

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

A

Binary

41
Q

What digits does the octal number system use?

A

0-7

42
Q

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

A

2

43
Q

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

A

8

44
Q

What numbering system does a computer use when sending information?

A

Octal

45
Q

What digits does hexadecimal use?

A

0-9 and A-F

46
Q

Why are letters used in the hexadecimal numbering system?

A

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

47
Q

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

A

10-15

48
Q

What is the base value in the hexadecimal numbering system?

A

16

49
Q

What is a simultaneous equation?

A

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

50
Q

How do you solve a simultaneous equation?

A

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

51
Q

What is the standard format for quadratic equations?

A

Ax^2+bx+c=0

52
Q

How can you solve quadratic equations?

A

By factorisation (placing in brackets)

53
Q

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

A

When factorisation is too difficult

54
Q

What is logarithm another word for?

A

Index or power

55
Q

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

A

2=Log3^9

56
Q

What is the general rules for logarithms?

A

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

57
Q

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

A

Decibel scale

58
Q

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

A

0

59
Q

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)

A

1

60
Q

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

A

10

61
Q

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

A

4 because 2x2x2x2= 16

62
Q

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

A

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

63
Q

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)

A

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

64
Q

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

A

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

65
Q

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

A

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

66
Q

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

A

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

B1 1-Maths (4 decks)

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