How to convert from the Cartesian to parametric vector equation of a plane
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A2 doubles F block Tuesday 19th May 20 one and a half hours' work
Solving Inequalities: our first topic of Further Pure Maths Questions set from the blue FP1 book pages 93-98
1. Assignment test 3
2. Read examples 1 and 2 page 94 do Ex 4A page 95/96 questions 1-6
3. Read example 3 page 96 Ex 4B page 98 questions 1-5 upload onto Teams please
4. Start FP1 assignment 4 and from the VLE paper 16, paper 6 S and M and paper 7 S and M due after progression week Tuesday 9th June 20
Solving Inequalities: our first topic of Further Pure Maths Questions set from the blue FP1 book pages 93-98
1. Assignment test 3
2. Read examples 1 and 2 page 94 do Ex 4A page 95/96 questions 1-6
3. Read example 3 page 96 Ex 4B page 98 questions 1-5 upload onto Teams please
4. Start FP1 assignment 4 and from the VLE paper 16, paper 6 S and M and paper 7 S and M due after progression week Tuesday 9th June 20
Consider -1/4 < -1/5 true of false? true
multiply both sides by -1
1/4 < 1/5 true or false? false
1/4 > 1/5
Rule: if we multiply by a negative across an inequality sign we must change the sign.
We cannot therefore treat an inequality in the same way as an equals sign.
We cannot cross multiply across an inequality sign by an expression that COULD be negative like
(x-2) or (x+1) since for some values of x this is negative.
so we multiply by the square of the expression which is always positive.
multiply both sides by -1
1/4 < 1/5 true or false? false
1/4 > 1/5
Rule: if we multiply by a negative across an inequality sign we must change the sign.
We cannot therefore treat an inequality in the same way as an equals sign.
We cannot cross multiply across an inequality sign by an expression that COULD be negative like
(x-2) or (x+1) since for some values of x this is negative.
so we multiply by the square of the expression which is always positive.
Solving inequalities
a) To solve an inequality involving algebraic fractions
Step 1:multiply by an expression squared to remove fractions
Step 2: rearrange the inequality to get 0 on one side
Step 3 find the critical values (the values if the inequality was an equals sign)
Step 4 use a sketch* to identify the correct intervals.
*Make sure you check whether the inequality is < > ≤ or ≥
In general it's a bad idea to multiply out brackets, you need to make brackets and factorise
a) To solve an inequality involving algebraic fractions
Step 1:multiply by an expression squared to remove fractions
Step 2: rearrange the inequality to get 0 on one side
Step 3 find the critical values (the values if the inequality was an equals sign)
Step 4 use a sketch* to identify the correct intervals.
*Make sure you check whether the inequality is < > ≤ or ≥
In general it's a bad idea to multiply out brackets, you need to make brackets and factorise
b) To solve an inequality using graphical methods
Drawing graphs well:
use a ruler, draw axes with arrows to show the positive direction, mark on the origin, add any asymptotes (vertical: put the denominator to zero, horizontal: divide the bottom into the top) before you sketch the graph. The graph should never meet the asymptote but moves towards it as x tends to + or - infinity.
Note the term "sketch" does not mean "do it roughly" it means "do not plot the graph" so, as always, as double mathematicians set the standard high for sketching graphs in your assignments.
Drawing graphs well:
use a ruler, draw axes with arrows to show the positive direction, mark on the origin, add any asymptotes (vertical: put the denominator to zero, horizontal: divide the bottom into the top) before you sketch the graph. The graph should never meet the asymptote but moves towards it as x tends to + or - infinity.
Note the term "sketch" does not mean "do it roughly" it means "do not plot the graph" so, as always, as double mathematicians set the standard high for sketching graphs in your assignments.
fp1_summer_4.pdf | |
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fp1_summer_4_answers.pdf | |
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