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Proper, Improper and Mixed Fractions

Fractional Arithmetic

Changing the Subject of an Expression

Multiplying Expressions

Factorising Quadratic Expressions

Solving Linear Equations

Rationalising the Denominator

Solving Simultaneous (Linear) Equations

Solving Simultaneous Quadratic Equations

2 and 3 Part Ratios

Completing the Square

Sequences and Series

Ex. 0:
A sequence has the following terms: a3 = 32, a4 = 43, a5 = 54, a6 = 65, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 25th term (a25).
[Arithmetic, a1 = -1, d = 11, a25 = 263]
Ex. 1:
A geometric sequence has the following terms: u5 = 4.000, u6 = -4.000, u7 = 4.000, u8 = -4.000, u9 = 4.000, u10 = -4.000, ...
Find the first term and the common ratio, and hence the sum to infinity (Sinf) of the series.
[u1 = 4.00, r = -1.00, Sinf = 2.00]
Ex. 2:
A sequence has the following terms: a6 = 6, a7 = 4, a8 = 2, a9 = 0, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 37th term (a37).
[Arithmetic, a1 = 18, d = -2, a37 = -54]
Ex. 3:
A sequence has the following terms: u5 = -2.09, u6 = -1.32, u7 = -0.84, u8 = -0.53, u9 = -0.34, u10 = -0.21, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 16th term (a16).
[Geometric, u1 = -13.00, r = 0.63, u16 = -0.01]
Ex. 4:
A geometric sequence has the following terms: u3 = 0.889, u4 = 0.296, u5 = 0.099, u6 = 0.033, u7 = 0.011, u8 = 0.004, ...
Find the first term and the common ratio, and hence the sum to infinity (Sinf) of the series.
[u1 = 8.00, r = 0.33, Sinf = 12.00]
Ex. 5:
A sequence has the following terms: u4 = 4.63, u5 = -3.86, u6 = 3.22, u7 = -2.68, u8 = 2.23, u9 = -1.86, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 15th term (a15).
[Geometric, u1 = -8.00, r = -0.83, u15 = -0.62]
Ex. 6:
A sequence has the following terms: u3 = 0.17, u4 = -0.03, u5 = 0.00, u6 = -0.00, u7 = 0.00, u8 = -0.00, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 12th term (a12).
[Geometric, u1 = 6.00, r = -0.17, u12 = -0.00]
Ex. 7:
A geometric sequence has the following terms: u3 = -0.680, u4 = 0.136, u5 = -0.027, u6 = 0.005, u7 = -0.001, u8 = 0.000, ...
Find the first term and the common ratio, and hence the sum to infinity (Sinf) of the series.
[u1 = -17.00, r = -0.20, Sinf = -14.17]
Ex. 8:
A sequence has the following terms: u3 = -0.32, u4 = -0.06, u5 = -0.01, u6 = -0.00, u7 = -0.00, u8 = -0.00, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 12th term (a12).
[Geometric, u1 = -8.00, r = 0.20, u12 = -0.00]
Ex. 9:
A geometric sequence has the following terms: u3 = -1.188, u4 = 0.297, u5 = -0.074, u6 = 0.019, u7 = -0.005, u8 = 0.001, ...
Find the first term and the common ratio, and hence the sum to infinity (Sinf) of the series.
[u1 = -19.00, r = -0.25, Sinf = -15.20]

Polynomial Long Division

Factor and Remainder Theorem

Roots of a cubic

Differentials

Finding Turning Points

Pythagorus

Sine and Cosine Rules

Vectors