Basic indefinite integrals, Basic definite integrals, integration by substitution

Missing: Area type question, solving diff eq application

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

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A question testing the application of the Cosine Rule when given three side lengths. In this question, the triangle is always acute. A secondary application is finding the area of a triangle.

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Find roots and the area under a parabola

The simplest case. Divisor is single digit. There is no remainder. 

Testing the understanding of the formal definition of $A\subseteq B$.

Example of a universal statement over the integers and its negation

Testing addition, multiplication and division involving negative numbers.

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A variety of worded fraction questions.

The simplest case. Divisor is single digit. There is no remainder. 

The simplest case. Divisor is single digit. There is no remainder. 

 Basics, percentage of an amount, converting to fractions and decimals.

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Practice with adding, subtracting and dividing basic algebraic fractions

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

This is the question for Lent Term week 10 of the MA100 course at the LSE. It looks at material from chapters 39.

This is the question for Lent Term week 9 of the MA100 course at the LSE. It looks at material from chapters 37 and 38.

This is the question for Lent Term week 8 of the MA100 course at the LSE. It looks at material from chapters 35 and 36.

This is the question for Lent Term week 7 of the MA100 course at the LSE. It looks at material from chapters 33 and 34.

The following is a description of parts a and b. In particular it describes the varaibles used for those parts.

This question (parts a and b) looks at optimisation problems using the langrangian method. parts a and b of the question we will ask the student to optimise the objective function f(x,y) = y + (a/b)x subject to the constraint function r^2 = (x-centre_x)^2 + (y-centre_y)^2.

The variables centre_x and centre_y take values randomly chosen from {6,7,...,10} and r takes values randomly chosen from {1,2,...,5}.

We have the ordered set of variables (a,b,c) defined to be randomly chosen from one of the following pythagorean triplets: (3,4,5) , (5,12,13) , (8,15,17) , (7,24,25) , (20,21,29). The a and b variables here are the same as those in the objective function. They are defined in this way because the minimum will occur at (centre_x - (a/c)*r , centre_y - (b/c)*r) with value centre_y - (b/c)r + (a/b) * centre_x - (a^2/bc)*r , and the maximum will occur at (centre_x + (a/c)*r , centre_y + (b/c)*r) with value centre_y + (b/c)r + (a/b) *centre_x + (a^2/bc)r. The minimisation problem has lambda = -c/(2br) and the maximation problem has lambda* = c/(2br).

We can see that all possible max/min points and values are nice rational numbers, yet we still have good randomisation in this question. :)

This is the question for Lent Term week 6 of the MA100 course at the LSE. It looks at material from chapters 31 and 32.

This is the question for Lent Term week 5 of the MA100 course at the LSE. It looks at material from chapters 29 and 30.

This is the question for Lent Term week 4 of the MA100 course at the LSE. It looks at material from chapters 27 and 28.

This is the question for Lent Term week 3 of the MA100 course at the LSE. It looks at material from chapters 25 and 26.