Revision of Basic Maths and Linear equations, straight lines and linear inequalities ( Week 1 and 2)

Question 1

We are now going to learn some indices rules?

Answer 1

Question 2

Answer 2

Question 3

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Question 4

Answer 4

Question 5

Answer 5

Question 6

Answer 6

Question 7

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Question 8

Answer 8

Question 9

Suppose you eat your house with gas for d days a year and on each day you use m cubic metres of gas. If gas costs £P per cubic metre. Suppose you also have to pay a fixed amount per year £81 per year to the gas company. Suppose that you pay gas bill in twelve monthly installements, write an expression for this?

Answer 9

Question 10

Suppose you eat your house with gas for d days a year and on each day you use m cubic metres of gas. If gas costs £P per cubic metre. Suppose you also have to pay a fixed amount per year £81 per year to the gas company. Suppose that you pay gas bill in twelve monthly installements,

Answer 10

Question 11

Answer 11

Question 12

When solving inequalities and we divide by a negative what must we always do?

Answer 12

We must reverse the direction of the inequality

Question 13

Start by subtracting 6x on both sides?

Answer 13

Question 14

Answer 14

Question 15

Express this expression in the simplest form?

Answer 15

Question 16

Answer 16

TBA

Question 17

Answer 17

TBA

Answer 18

TBA

Answer 19

TBA

Question 20

With a linear equation of one variable ax = c

What happens when A is not = 0

What happens when A = 0

What hapens when C = 0

Answer 20

Question 21

Draw the lines X = 2 and y=3

Answer 21

Question 22

What is the form of a linear straight line?

Answer 22

ax+by = c

Question 23

How do we find the x and y intercepts of a straight line?

Answer 23

We know ax + by = c

The x intercept is when y = 0 this will mean we will have ax = c

x = c/a, so the x intercept coordinate is ( c/a , 0)

The y intercept is when x = 0, this will mean we will have by = c

y = c/b, so the y intercept coordinate is ( 0, c/b)

Question 24

Say we have a line 2x + y = 4, find the x and y intercepts and draw the line?

Answer 24

Question 25

Lets say we are given a gradient and a point on a line what is the equation of the line using the gradient formula. e.g. the gradient is 10 and the coordinates are (2,3)

Answer 25

Question 26

How can we find gradient of a line given 2 points?

Answer 26

Question 27

If we have the coordinates (1,-7) and (2,3) are on the line, find the equation of the line?

Answer 27

Question 28

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Question 29

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Question 30

Find the equation of the line given these 2 points (-2,3) and (4,6) ( do it your way)

Answer 30

Question 31

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Question 32

Answer 32

Breakeven point is when profit is = 0 for i breakeven point is when x = 5 and for ii breakeven point is then x = 6

Question 34

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Question 35

Part A

Answer 35

Question 36

Part B

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Question 37

Answer 37

I DONT NEED TO DO THE TABLE OF X AND Y AS WE SKETCH

Question 38

a) Consider the line 2x+Y\<4 draw the line of a xy plane and shade this region? b) Then shade the region 2x+y\>4 Both are greater/less or equal to

Answer 38

Question 39

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Question 40

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Question 41

What is one useful economic application of simultaneous equations?

Answer 41

Linear programming, this is where a quanitity is determined by a linear expression e.g ax + by, we can use to find the optimum bundle given the money avaliable.

Question 42

When doing economic applications, can we have bundles that are negative?

Answer 42

No it doesnt make any sense.

Question 43

Lets say we want to buy apples and organces but we have a budget constraint what is the expression

Answer 43

x + y = T

Question 44

How can we find the maximum value of T i.e the bundles of goods he can afford given budget? Lets say we he X bananans and Y organes and a maxium of 4 pounds to spend find the bundle that satisfies this?

Answer 44

We draw the Budget set 'bricked region' and draw the lines T = x+y with T= 1,2,3,4,5,6, we can rewrite y=-x+T, where T is the y intercept, so we need to find the largest T, that is affordable Notice T = X+Y for T = 1,2,3 is drawn with dashed line, T =4 with a solid line and T\>4 dotted line

Question 45

Lets say for example Jane has a budget set 2x+y =4 and Ashley has a budget set x + 2y =4, how can we find a bundle that simuntaneously maxmises there ultitiy.

Answer 45

Question 46

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Question 47

Answer 47