Basic Mathematics Form 2

Contents

1. 1. Algebra

   1 tests 14 questions

   Topic lessons

   • Binary operations
   • Expanding brackets
   • Factorisation: common factors, grouping and difference of two squares
   • Factorising quadratic expressions
   • Using factorisation: arithmetic and algebraic fractions
   • Summary

   Building on Form One algebra In Form One you learned to simplify expressions and solve linear equations. In Form Two we learn to work with binary operations , to expand products of brackets and to factorise expressions. Factorising is the reverse of expanding and is the key to solving quadratic equations. Binary…

2. 2. Quadratic Equations

   1 tests 15 questions

   Topic lessons

   • Quadratic equations and solving by factorisation
   • Solving by completing the square
   • The quadratic formula and the discriminant
   • Quadratic graphs and their roots
   • Forming quadratic equations and word problems
   • Summary

   What is a quadratic equation? A quadratic equation is an equation in which the highest power of the unknown is 2. Its general form is ax 2 + bx + c = 0 , where a, b and c are numbers and a ≠ 0. Examples: x 2 − 9 = 0, 2x 2 + 3x − 5 = 0. A quadratic equation can have two, one or no real solutions (also called roots ).…

3. 3. Logarithms

   1 tests 17 questions

   Topic lessons

   • Laws of exponents
   • Standard form
   • What is a logarithm?
   • Laws of logarithms and equations
   • Using logarithm tables
   • Summary

   Exponents In 2 5 = 32, the number 2 is the base and 5 is the exponent (power or index). The laws of exponents are: a m × a n = a m+n and a m ÷ a n = a m−n (a m ) n = a mn a 0 = 1 (a ≠ 0) and a −n = 1/a n a 1/n = the nth root of a, and a m/n = (a 1/n ) m . For example 8 2/3 = (∛8) 2 = 2 2 = 4. Standard form A number is…

4. 4. Congruence of Simple Polygons

   1 tests 14 questions

   Topic lessons

   • What does congruent mean?
   • Tests for congruent triangles
   • Why AAA and SSA do not prove congruence
   • Writing congruence proofs
   • Summary

   What does congruent mean? Two figures are congruent if they have exactly the same shape and the same size. If you cut one out, it would fit exactly on top of the other (it may need to be turned over or rotated). The symbol for congruence is ≅. When we write ΔABC ≅ ΔPQR, the order of the letters matters: A matches P, B…

5. 5. Similarity and Enlargement

   1 tests 16 questions

   Topic lessons

   • Similar figures
   • Similar triangles
   • Ratio of areas and volumes
   • Enlargement
   • Scale drawings and maps
   • Summary

   Similar figures Two figures are similar if they have the same shape but not necessarily the same size. One is an exact enlargement or reduction of the other. For polygons this means: corresponding angles are equal, and corresponding sides are in the same ratio (proportional). Any two circles are similar, and so are any…

6. 6. Geometrical Transformations

   1 tests 15 questions

   Topic lessons

   • Reflection
   • Rotation
   • Translation
   • Enlargement, combined transformations and invariance
   • Summary

   What is a transformation? A transformation moves or changes a figure according to a rule. The original figure is the object and the result is the image . If a point is called A, its image is usually written A′ (read "A dash"). In this topic we study reflection, rotation, translation and enlargement. Reflection A…

7. 7. Pythagoras Theorem

   1 tests 15 questions

   Topic lessons

   • The right-angled triangle and Pythagoras' theorem
   • Finding a missing side
   • The converse and Pythagorean triples
   • Practical problems: ladders, diagonals and journeys
   • Distance between two points
   • Summary

   The right-angled triangle In a right-angled triangle, the longest side is opposite the right angle and is called the hypotenuse . The other two sides are sometimes called the legs. Pythagoras' theorem In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. If…

8. 8. Trigonometry

   1 tests 16 questions

   Topic lessons

   • Naming the sides and the three ratios
   • Special angles: 30°, 45° and 60°
   • Using tables and finding a missing side
   • Finding angles and relations between the ratios
   • Angles of elevation and depression
   • Summary

   What is trigonometry? Trigonometry is the study of the relationship between the sides and angles of triangles. It allows us to find heights and distances that are difficult to measure directly, such as the height of a tree or the width of a river. Naming the sides In a right-angled triangle, choose one of the acute…

9. 9. Sets

   1 tests 15 questions

   Topic lessons

   • What is a set?
   • Types of sets and the universal set
   • Subsets and the number of subsets
   • Operations on sets: union, intersection, complement, difference
   • Solving problems with Venn diagrams
   • Summary

   What is a set? A set is a well-defined collection of objects. "Well-defined" means we can always decide whether an object belongs to the set or not. The objects are called elements or members. Sets are named with capital letters and their elements are written inside curly brackets: A = {2, 4, 6, 8}. We write 4 ∈ A (4…

10. 10. Statistics

    1 tests 16 questions

    Topic lessons

    • Collecting and organising data
    • Bar charts and pie charts
    • Line graphs, histograms and frequency polygons
    • Mean, median, mode and range
    • Averages of grouped data and choosing an average
    • Summary

    What is statistics? Statistics is the branch of mathematics that deals with collecting, organising, presenting, analysing and interpreting data (facts and figures). A school might collect the marks of students, a hospital the number of patients per day, and a farmer the yield of maize per acre. Collecting and…