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Ma110 > Revision of Basic Maths and Linear equations, straight lines and linear inequalities ( Week 1 and 2) > Flashcards

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

1
Q

We are now going to learn some indices rules?

A
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2
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9
Q

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?

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10
Q

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,

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11
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12
Q

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

A

We must reverse the direction of the inequality

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13
Q

Start by subtracting 6x on both sides?

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14
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15
Q

Express this expression in the simplest form?

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16
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TBA

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17
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TBA

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18
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TBA

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19
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TBA

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20
Q

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

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21
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Draw the lines X = 2 and y=3

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22
Q

What is the form of a linear straight line?

A

ax+by = c

23
Q

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

A

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)

24
Q

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

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25
Q

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)

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26
Q

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

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27
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If we have the coordinates (1,-7) and (2,3) are on the line, find the equation of the line?

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30
Q

Find the equation of the line given these 2 points

(-2,3) and (4,6) ( do it your way)

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32
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Breakeven point is when profit is = 0 for i breakeven point is when x = 5 and for ii breakeven point is then x = 6

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35
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Part A

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36
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Part B

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37
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I DONT NEED TO DO THE TABLE OF X AND Y AS WE SKETCH

38
Q

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

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41
Q

What is one useful economic application of simultaneous equations?

A

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.

42
Q

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

A

No it doesnt make any sense.

43
Q

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

A

x + y = T

44
Q

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?

A

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

45
Q

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.

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48
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Ma110 (19 decks)

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