Mathematics Core topic HL for IBDP(Chapter1-9)

Mathematics Core topic HL for IBDP(Chapter1-9),for IBDP students who are at 10th grade,for revision.

Mathematics Core topic HL for use with IB Diploma Programme

• 7 RIGHT ANGLED TRIANGLE TRIGONOMETRY
  • A
    • Formulas:sinθ=OPP/HYP;cosθ=ADJ/HYP;tanθ=OPP/ADJ
    • tanθ=sinθ/cosθ
  • B
    • Fine the angle whose sine/tangent/cosine is ....:use the inverse sine/tangent/cosine to determine the angle.
  • C
    • isosceles triangle
    • equilateral triangle
    • Rectangle
    • square
    • rhombus
    • A tangent to a circle
    • semi-circle
    • chord
    • kite
  • D
    • Angles of elevation/depression
    • Two methods to calculate[AB]to the plane:
  • E
    • True bearing are measured clockwise from true north.They are always written in three digits,plus decimals if necessary.
    • When questions ask you to solve out the bearing of C from A: in Chinese meaning:C在A的什么方向（true bearing）.
  • F
    • The angle between a line and a plane is the angle between the line and its projection on the plane.
• 8 THE UNIT CIRCLE AND RADIAN MEASURE
  • A
    • degrees to radians=degree*π/180
    • radians to degrees=radian*180/π
    • π radians ≡180°
  • B
  • C
    • θ is positive for anticlockwise rotaitons and negative for clockwise rotations.
    • Especially important:
  • D
    • cos π/4=1/根号2；sinπ/4=1/根号2
    • cos π/3 = 1/2; sin π/.3=根号3/2
    • cos π/6=根号3/2;sin π/6 =1/2
  • E
    • For any angle θ，cos^2 θ+sin^2 θ=1
  • F
  • G
• 9 NON-RIGHT ANGLED TRIANGLE TRIGONOMETRY
  • A
    • Area=1/2*a*b*sinc=1/2*b*c*sina=1/2*a*c*sinb
  • B
  • C
  • D
    • Use the cosine rule when given:1.three sides 2.two sides and an included angle
    • Use the sine rule when given:1.one side and two angles 2.two sides and a non-included angle.
• 6 MEASUREMENT
  • A Circles,arcs and sectors
    • For a circle with radius r:the circumference C=2πr;A=πr^2
    • Arc length=Θπr/180
    • Sector area=Θπr^2/360
  • B Surface area
    • SOLIDS WITH PLANE FACES
      • The surface area of a three-dimensional figure with plane faces is the sum of the areas of the faces.
    • Solids with curved surfaces
  • C Volume
    • SOLIDS OF UNIFORM CROSS-SECTION
      • Volume=area of cross section*length
    • Other solids
      • Formulas:
  • D Capacity
• 5 SEQUENCES AND SERI ES
  • A
    • A number sequence is an ordered list of numbers defined by a rule.The numbers in a sequence are called the terms of the sequence.
  • B
    • Sample
  • C
    • For a geometric sequence with first term u1 and common ratio r,the general term or the n th term is Un = u1*r to the power of(n-1)
  • D
  • E
    • Compound interest
    • Example of compound interest
    • the real value of an investment:inflation.
    • Depreciation
      • The formula:Un=U1*(1-d)^n
    • Using technology for financial models
      • Some instructions about each term.
  • F
  • G
    • Sn=n/2(u1+un) or Sn=nu1+n(n-1)/2*d
  • H
    • Sn=u1(1-r^n)/1-r
  • I
    • S=u1/1-r
• 4 EQUATIONS
  • A
    • A power equation is an equation which can be written in the form x to the power if n =k,n≠0.
    • Principle
    • Example1
    • Example2
    • Example3
  • B
  • C
    • A quadratic equation is an equation which can be written in the form ax*x+bx+c=0,where a,b,c are constants,a≠0.
    • General method of solving the equation:(1)Solving by factorization(2)Solving by "Completing the square".(3)calculate the delta,solve out all solution.(Don't forget delta is >0,=0 or <0.)
  • D
    • Casio-cx991 can solve out the solutions of quadratic equation.
  • E
    • Look at the intersection of two lines:x-intercept
• 3 SURDS AND EXPONENTS
  • A surds and other radicals
    • surd:is a real,irrational radical:e.g:根号4=2，根号1/4=1/2;
    • radical:is any number which is written with the radical sign,根号；
  • B Division by surds
    • rationalizing denominators
  • C Exponents
    • Principle:
  • D Law of exponents
  • E Scientific notation
    • Scientific notation or standard form involves writing any given number as a number between 1 inclusive and 10,multiplied by a power of 10.
    • The result has the form a*10 to the power of k,where 1<=a<10,k∈Z；
    • Sample
• 2 SETS AND VENN DIAGRAMS
  • A Sets
    • A set is a collection of distinct numbers or objects.Each object is called an element or member of the set.
    • Set notation
    • Sample
      • About Q is a proper subset of P:it means that every element of Q is also an element of P,but Q isn't equal to P(Q or P has element(s)that another doesn't have.)About Q is a subset of P:it means that every element of Q is also an element in P(Q may equal to P,OR Q is a subset of P).In my opinion,the probability of appearing proper subset is more than appearing subset,you can distinguish the every element of P is or isn't appeared in Q.
  • B intersection and union
    • Intersection:the intersection of two sets A and B is the set of elements that are both in set A and set B.the intersection is written as A ∩ B；
    • Union:The union of two sets A and B is the set of elements that are either in A or set B.(elements that both A and B are included in the union of A and B.)
    • Sample
  • C Complement of a set
    • The universal set U is the set of all elements we are considering.
    • The complement of a set A is the set of all elements of U that are not elements of A.The complement of A is written as A'.
    • Sample(which usually do as incorrect)
  • D Special number sets
    • Following is a list of some special number sets you should be familiar with.
    • Sample
  • E Interval notation
    • interval notation:To describe the set of all integers between -3 and 5.We can write the set using interval notation as {x∈Z | -3<x<5};How to read it:the set of all integers x such that x lies between -3 and 5.(If it doesn't mention the category of the numbers we commonly regard it as a real number and write it in the form of interval notation:{x | -3<x<5})
    • Bracket notation
      • The way to represent it(from the upper one to the lower one):(1)the set of all real number x such that x lies between a and b,including a and b.(2)the set of all real number x such that x lies between a and b,including a.(3)the set of all real number x such that x lies between a and b,including b.(4)the set of all real number x such that x lies between a and b.
    • Sample
  • F Venn diagram
    • All conditions that can represent on the Venn diagram.
    • Sample
  • G Venn diagram region
    • Use diagram to tell you how to remember these meanings:
    • Sample1(direct tell you the number of elements in each area)
    • Sample2(indirectly;through calculating.)
  • H Problem solving with Venn diagrams
    • Sample 1(through a bit calcualting)
    • Sample 2(need to suppose an unknown number of intersection;two categories.)
    • Sample3(need to suppose an unknown number of intersection;three categories.)*:Face the percentage,you just need to transform the percentage by multiplying 100 to be a number(in the form of an interger)
• 1 STRAIGHT LINES
  • A
    • Some basic information about the lines in the Cartesian plane
    • the equation of a line
      • point-gradient form:y-y1 = m(x-x1)
      • gradient-intercept form:y = mx+c
      • In general form,the equation of a line is ax+by=d,where a,b,d are constants.
  • B
    • lines in gradient-intercept form
      • (1)use the y-intercept c to plot the point (0,c)(2)use x and y-steps(positive right,negative left,from the point of y-intercept) from the gradient m to locate another point on the line.(3)join the two points and extend the line in either direction.
    • lines in general form
      • find the y-intercept by letting x=0
      • find the x-intercept by letting y=0
      • join the points where the line cuts the axes and extend the line in either direction.
  • C
    • the perpendicular bisector of a line segment[AB]is the line perpendicular to [AB] which passes through its midpoint.(k1*k2=-1)
  • D
    • A system of two equations can be solved by:1.graphing the straight lines on the same set of axes.2.algebra using substitution or elimination. 3.technology.
• Made by Steven