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2. Fundamentals of Maths (CSC 1026) > Algebra > Flashcards

Flashcards in Algebra Deck (20)
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1

What are the versions of these operators on vdmlab:
x, +, -, divide, ^x, root.

*, +, -, /, **, **(1/x).

2

What is a variable in maths?

A single letter which represents an unknown value. We use them when we are trying to figure out the value they represent or to say that something is true no matter what it's value is.

3

What does algebra do?

Deals with combining values using operators to create expressions. Sometimes these are known, sometimes we use variables to represent those we don't know.

4

What is a constant?

A value which we know.

5

What is a natural number?

A positive, whole number (0, 1, 5, 90)

6

What is an integer?

A positive/negative whole number (0, -20, 5)

7

What is a real number?

A positive/negative whole/fractional number (0, -20, 5, 4.5, 20,9)

8

What is true of operators?

Combine 2 numeric values + create a result. For most operators, if input values are integers, result will be integer. Tend to come in pairs where 1 is inverse of other and undoes its effect e.g. +/-, *//

9

What is true of 0?

We cannot divide by 0.

10

How do we type root in vdmlab?

c**(1/b). C is the number we root, b is the number which we are rooting by (e.g. b is 2 for square root)

11

How do we use power/root to find a variable?

Inverse of power is root (3**2=9 so 9**(1/2)). If a**b=c, c=a**(1/b). Can only be used to find c.
To find b, we must use log. if a**b=c, b=log↓ac e.g. 2**3=8 so 3 = log↓28. To type this in vdmlab, we say log (a,b) so 3 = log(2,8)

12

How do we divide when there is going to be a remainder?

We use div to get an integer + mod to get the remainder e.g. 13 div 5 = 2, 13 mod 5 = 3. The answer to the mod equation shouldn't be as big as what we divide by.

13

How do we find x from div + mod answer

If a div b = d + a mod b = m, then a = d*b+m
e.g. x div 5 = 2, x mod 5 = 3.

14

What is a sequence?

A list of values which are separated by commas + surrounded by square brackets. e.g. [1, 5, 7, 9] or [].

15

How do we find the length of a sequence?

Len function e.g. len([2, 3, 4]) = 3 or s=[1, 25, 7], then len (s) = 3.

16

How do we access an element of a sequence based on its position?

s = [4, 6, 1, 2]. s (3) = 1

17

How do we add up the elements of a sequence?

We use sigma (sum), we can use it for consecutive nums.
We will show these on ppt.

18

How do we find the product of a sequence?

Use pi, again used for consecutive numbers.

19

What must be aware of when combining operators?

The order of operations (BIDMAS). Operators with same precedence are evaluated left to right. ()is highest, then **, then *, /, div, mod, then +, -. If we have x^y^^z, then we evaluate top to bottom e.g. w = y^z, then w^x.

20

How do we find x in an equation?

We must apply the same modification to both sides of the equation until one side has become exactly x or search for x by guessing through trial + error.