In 2013 alevel examiner’s report, it was reported that few candidates knew the factorisation of the difference of two cubes.
Here are the formulas students should remember:
Students can use the mnemonic “SOAP” to help them remember the formula.
S: Same sign
O: Opposite sign
Improper fraction can be expressed in proper fraction without doing long division.
Juggling is a shortcut to long division, especially in the case where the degree of the numerator is the same as the denominator. In H2 math, juggling is a useful technique in finding the asymptote of graphs and integration.
Trigo “Sum to Product” formula is given in the math formula list MF26. However, “Product to Sum” formula is not in the formula list. Yet, students are often required to use the “Product to Sum” formula in mathematical induction or integration. Hence, knowing how to derive the “Product to Sum” formula from “Sum to Product” formula is critical.
“Sum to Product” formula
To derive the “Product to Sum” formula
Let P = X+Y and Q= X-Y
Substitute into the “Sum to Product” formula, we derived the “Product to Sum” formula
Try out this question
2011 P1, 6iii
Synthetic division can be used to divide a polynomial by a linear divisor, which is commonly required in H2 math and Amath.
It is faster than the traditional long division.
How to do Synthetic division
Partial fraction is commonly used in binomial expansion, method of difference and integration.
When the divisor consists only of linear factors, cover up rule can be used to find the constants in the partial fraction quickly.
Express in partial fraction.
By cover up rule,
0 = A+C