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

Integration by Parts

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Integration using partial fractions

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This question asks learners to use row operations to find the inverse of a 3x3 matrix.

This question asks learners to use row operations to find the inverse of a 3x3 matrix.

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

Elementary operations on vectors; sum, modulus, unit vector, scalar multiple. 

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

Calculating the new concentration of a diluted solution.

Example of a dilution calculation involving mass concentration and molarity calculations.

Working backwards from the concentration of a diluted solution to find the concentration of "stock" solution.

Practice at a longer calculation to work out how much glucose is needed to make a solution of a given concentration.

Practice calculating number of moles of a substance given the concentration and volume of a solution.

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A question to test integration by parts in a "pre-Fourier series" setting.

A copy of Amy Chadwicks block question, with adaptions to provide a diagram for the student.

A block of given mass is sliding down the plane, with given acceleration. Find the normal reaction force, the coefficient of friction, and the distance travelled before reaching a given speed.

Two masses in a box which is attached to a string. Finding acceleration by modelling the two masses as the whole system. Find forces exerted by the two masses.

A test of basic concepts to do with SI units and concentrations of solutions.

Arithmetic operations involving fractions; converting between decimals and fractions; deciding if fractions are equivalent.

This question asks learners to use row operations to find the inverse of a 3x3 matrix.

This question asks learners to use row operations to find the inverse of a 3x3 matrix.

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A test of basic concepts to do with SI units and concentrations of solutions.

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Order of precedence for multiplication, division, addition, subtraction.

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

Questions on vector arithmetic and vector operations, including dot and cross product, as well as the vector equations of planes and lines.

Find the common ratio of a given geometric sequence, write down the formula for the nth term and use it to calculate a given term in the sequence.