pgdhhm

[shafali9]

i m doing Pgdhhm from symboisis and finding answer

 

[shafali9]

got my answer
Number Algebra Shape and Space
 Calculate a percentage of a given amount.
 Express one quantity as a percentage of another.
 How to calculate percentage gain or loss.
 Increase or decrease a given amount by a certain percentage.
 Calculate the original amount (100%) when a certain percentage of it is known.
 Calculate compound interest on a given amount in three ways.
 Round off to decimal places and significant figures.
 Approximate the result of a calculation.
 How to calculate the value of a number raised to any power, both integer (positive and negative) and fractional.
 How to multiply and divide integer and fractional powers of the same number.
 How to multiply and divide by powers of 100.
 How to write large and small numbers in standard form and compare their sizes.
 How to solve problems using numbers in standard form.
 What rational and irrational numbers are, and how to express a fraction as either a terminating decimal or a recurring decimal.
 What surds are and how to calculate with them.
 How to recognise direct and inverse variations, both linear and nonlinear.
 What a constant of proportionality is.
 How to find formulae describing direct and inverse variations.
 How to solve problems involving direct and inverse variations.
 To use limits of accuracy in calculations.
 The answer to a calculation may be affected by the accuracy of the values used in the calculation.  Substitute whole numbers, fractions and decimals into expressions and evaluate them.
 Solve simple linear equations.
 Solve equations by trial and improvement.
 Solve pairs of simultaneous linear equations by the elimination method.
 Solve practical problems which are expressed by pairs of simultaneous linear equations.
 Transpose a formula to change its subject.
 Expand and simplify expressions containing brackets.
 Factorise an expression into one or two brackets.
 Expand and factorise quadratic expressions.
 Solve quadratic equations by factorisation, using the quadratic formula and by completing the square.
 Simplify algebraic fractions.
 Solve, by the method of substitution, a pair of simultaneous equations where one is linear and the other is nonlinear.
 How to find the gradient of a straight line.
 How to draw and interpret straight-line distance–time graphs.
 The relevance of the gradient of a straight-line distance–time graph.
 How to find speeds from a straight-line distance–time graph.
 How to find acceleration and total distance travelled from a velocity–time graph.
 How to use graphs to describe and find rates of change in other practical situations.
 Find the equation of a straight line from its graph.
 Draw graphs of a square root, reciprocal, cubic and exponential functions, using values of their coordinates between given functions.
 Solve two simultaneous linear equations using their graphs.
 Solve quadratic and cubic equations using their graphs, including the method of intersection.
 Recognise a number pattern and explain how the pattern is made.
 Recognise a linear sequence and find its nth term.
 Form general rules from given number patterns.
 Recognise when a sequence is not linear and therefore look for a quadratic rule.
 Recognise when a sequence is based on n2 alone.
 Recognise when a sequence is not based on n2 alone, and therefore look for another quadratic rule.
 Rearrange a formula in which the subject appears more than once.
 Create algebraic inequalities from verbal statements.
 Represent a linear inequality on a graph.
 Depict a region on a graph satisfying more than one linear inequality.
 Solve practical problems through linear programming techniques.
 Sketch the following transformations of the known graph
• y = f(x): y = f(x) + a, y = f(x – a),
• y = kf(x), y = f(tx), y = –f(x) and y = f(–x).
 Describe from their graphs the transformation of one function into another.
 Identify equations from transformations of known graphs.
 Arc length of a sector.
 Area of a sector.
 Area of a trapezium.
 Curved surface area of a cylinder.
 Volume of a prism, pyramid, cylinder, sphere and cone.
 Curved surface area of a cone.
 Surface area of a sphere.
 Density of a substance.
 How to use Pythagoras to find the hypotenuse or a short side of a right-angled triangle, given the two other sides.
 How to draw out a right-angled triangle from a 2-D or 3-D practical problem and label it with necessary information.
 The three basic trigonometric ratios: sinx, cosx, tanx.
 How to calculate sides and angles in right-angled triangles.
 How to interpret a practical situation to obtain a right-angled triangle which can be used to solve the problem: examples involve angles of elevation and depression, bearings and distances, and isosceles triangles.
 Corresponding angles are equal and the sum of allied angles is 180°.
 How to find the sum of the interior angles of a polygon.
 The properties of equilateral and isosceles triangles, trapeziums, parallelograms rhombuses and kites.
 That an angle at the centre of a circle is twice any angle at the circumference subtended by the same arc.
 That every angle at the circumference of a semicircle that is subtended by the diameter of the semicircle is a right angle.
 The angles at the circumference in the same segment of a circle are equal.
 That the sum of the opposite angles of a cyclic quadrilateral is 180°.
 That a tangent is a straight line that touches a circle at one point only. The point is called the point of contact.
 That a tangent is perpendicular to the radius at the point of contact.
 The four conditions for two triangles to be congruent.
 What is meant by the terms ‘translation’, ‘reflection’, ‘rotation’ and ‘enlargement’.
 How to change shapes by using translations, reflections, rotations and enlargements.
 What is meant by the terms ‘negative enlargement’ and ‘fractional enlargement’, and how to apply them to shapes.
 How to construct a line bisector and an angle bisector.
 How to construct angles of 90° and 60°.
 How to drop a perpendicular from a point to a line.
 What is meant by the term ‘locus’.
 How to draw a locus about a point, a line or a plane shape.
 How to draw a locus that depends on the bisecting of lines or angles, or both.
 How to recognise when a locus is being asked for.
 Work out the scale factor between two similar shapes.
 Work out the unknown lengths, areas and volumes of similar 3-D shapes.
 Solve practical problems using similar shapes.
 Solve problems involving area and volume ratios.
 Solve problems in two and three dimensions using trigonometry.
 Draw the graphs of the three basic trigonometric functions: sinx, cosx, and tanx.
 Find the trigonometric ratios for angles between 0° and 360°.
 Find both angles between 0° and 360° that have the same trigonometric ratio.
 Use the sine and cosine rules for solving any triangle.
 Find the exact trigonometric ratios of 30°, 45° and 60°.
 Find the area of a triangle, knowing two sides and the included angle.
 Recognise whether a formula represents length, area or volume.
 Recognise when a formula is not consistent and state the reasons why.
 Add and subtract two non-parallel vectors.
 Apply vector methods to 2-D geometrical situations.