Algebra

Question 1

What are the versions of these operators on vdmlab:

x, +, -, divide, ^x, root.

Answer 1

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

Question 2

What is a variable in maths?

Answer 2

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.

Question 3

What does algebra do?

Answer 3

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

Question 4

What is a constant?

Answer 4

A value which we know.

Question 5

What is a natural number?

Answer 5

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

Question 6

What is an integer?

Answer 6

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

Question 7

What is a real number?

Answer 7

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

Question 8

What is true of operators?

Answer 8

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. +/-, *//

Question 9

What is true of 0?

Answer 9

We cannot divide by 0.

Question 10

How do we type root in vdmlab?

Answer 10

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)

Question 11

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

Answer 11

Inverse of power is root (32=9 so 9(1/2)). If ab=c, c=a(1/b). Can only be used to find c.
To find b, we must use log. if ab=c, b=log↓ac e.g. 23=8 so 3 = log↓28. To type this in vdmlab, we say log (a,b) so 3 = log(2,8)

Question 12

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

Answer 12

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.

Question 13

How do we find x from div + mod answer

Answer 13

If a div b = d + a mod b = m, then a = d*b+m

e.g. x div 5 = 2, x mod 5 = 3.

Question 14

What is a sequence?

Answer 14

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

Question 15

How do we find the length of a sequence?

Answer 15

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

Question 16

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

Answer 16

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

Question 17

How do we add up the elements of a sequence?

Answer 17

We use sigma (sum), we can use it for consecutive nums.

We will show these on ppt.

Question 18

How do we find the product of a sequence?

Answer 18

Use pi, again used for consecutive numbers.

Question 19

What must be aware of when combining operators?

Answer 19

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.

Question 20

How do we find x in an equation?

Answer 20

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.