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The Algebra Buster


May 24th









May 24th

MATHEMATICAL FORMULAS

Pre sumed knowledge

Area of a parallelogram A = (b× h) , where b is the base, h is the height
Area of a triangle A = 1/2(b× h), where b is the base, h is the height
Area of a trapezium A = 1/2(a + b)h , where a and b are the parallel sides, h is the height
Area of a circle A = πr2 , where r is the radius
Circumference of a circle C = 2πr , where r is the radius

Topic 2— Number and algebra

2.2 Percentage error where is the exact value and is the approximate value of v
2.5 The nth term of an
arithmetic sequence

The sum of n terms of
an arithmetic sequence

2.6 The nth term of a
geometric sequence

The sum of n terms of a
geometric sequence

2.7 Solution of a quadratic
equation

Topic 3—Sets, logic and probability

3.8 Probability of an event A

 

Complementary events

3.10 Combined events P(A∪ B) = P(A) + P(B) − P(A∩ B)
  Mutually exclusive
events		 P(A∪ B) = P(A) + P(B)
  Independent events P(A∩ B) = P(A) P(B)
  Conditional probability

Topic 4—Functions

4.3 Equation of axis of
symmetry

Topic 5—Geometry and trigonometry

5.1 Distance between two
points (x1, y1) and (x2, y2)
  Coordinates of the
midpoint of a line
segment with endpoints
(x1, y1) and (x2, y2)
5.2 Equation of a straight
line		 y = mx + c; ax + by + d = 0
  Gradient formula
5.3 Sine rule
  Cosine rule
  Area of a triangle Area of a triangle where a and b are adjacent sides,
C is the included angle
5.5 Volume of a pyramid V = 1/3(area of base*vertical height)
  Volume of a cuboid V = l × w× h , where l is the length, w is the width, h is the height
  Volume of a cylinder V = πr2h , where r is the radius, h is the height
  Area of the curved
surface of a cylinder		 A = 2πrh , where r is the radius, h is the height
  Volume of a sphere , where r is the radius
  Surface area of a sphere A = 4πr2, where r is the radius
  Volume of a c one where r is the radius, h is the height
  Area of the curved
surface of a cone		 πrl , where r is the radius, l is the slant height

Topic 6—Statistics

6.4 Interquartile range
Outliers are points with value either less than or
greater than
6.5 Mean
6.6 Standard deviation
6.7 Pearson’s product–
moment correlation
coefficient

and is the covariance
6.8 Equation of regression
line for y on x
6.9 The χ 2 test statistic where are the observed frequencies, are
the expected frequencies

Topic 7—Introductory differential calculus

7.1 Derivative of f (x)
7.2 Derivative of axn
  Derivative of a
polynomial

Topic 8— Financial mathematics

8.2 Simple interest where = capital, % = interest rate, n = number of time periods, I = interest
8.3 Compound interest where = capital, % = interest rate, n = number of time periods, I = interest which is the special case

where C = capital, r% = nominal interest rate,
n = number of years, k = number of compounding periods
in a single year and I = interest

Critical values of the χ 2 distribution (topic 6.9)

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