SECTION 1 - NUMBER THEORY AND COMPUTATION
1: Distinguish among sets of numbers. [cite: 296]
[cite_start]2: Compute powers of real numbers of the form x^a, where a is a rational number. [cite: 324]
[cite_start]3: Evaluate numerical expressions using any of the four basic operations on real numbers. [cite: 325]
[cite_start]4: Convert among fractions, percents and decimals. [cite: 326]
[cite_start]5: List the set of factors and multiples of a given integer. [cite: 327]
[cite_start]6: Compute the H.C.F. or L.C.M. of two or more positive integers. [cite: 328]
[cite_start]7: State the value of a digit of a numeral in a given base. [cite: 329]
[cite_start]8: Convert from one set of units to another. [cite: 330]
[cite_start]9: Express a value to a given number of significant figures and decimal places. [cite: 331, 341, 343]
[cite_start]10: Use properties of numbers and operations in computational tasks. [cite: 345]
[cite_start]11: Write any rational number in scientific notation. [cite: 347]
[cite_start]12: Calculate any fraction or percentage of a given quantity. [cite: 348]
[cite_start]13: Express one quantity as a fraction or percentage of another. [cite: 361]
[cite_start]14: Compare quantities. [cite: 364]
[cite_start]15: Order a set of real numbers. [cite: 367]
[cite_start]16: Compute terms of a sequence given a rule. [cite: 373]
[cite_start]17: Derive an appropriate rule given the terms of a sequence. [cite: 375]
[cite_start]18: Divide a quantity in a given ratio. [cite: 377]
[cite_start]19: Solve problems involving concepts in number theory and computation. [cite: 381]
SECTION 2 - CONSUMER ARITHMETIC
1: Calculate discount, sales tax, profit, and loss. [cite: 452]
[cite_start]2: Calculate percentage profit and percentage loss. [cite: 463]
[cite_start]3: Express a profit, loss, discount, markup and purchase tax, as a percentage of some value. [cite: 468]
[cite_start]4: Solve problems involving marked price, selling price, cost price, profit, loss or discount. [cite: 470]
[cite_start]5: Solve problems involving payments by instalments as in the case of hire purchase and mortgages. [cite: 473]
[cite_start]6: Solve problems involving simple interest. [cite: 485]
[cite_start]7: Solve problems involving compound interest. [cite: 486]
[cite_start]8: Solve problems involving appreciation and depreciation. [cite: 487]
[cite_start]9: Solve problems involving measures and money. [cite: 491]
[cite_start]10: Solve problems involving rates and taxes; utilities; invoices and shopping bills; salaries and wages; insurance and investments. [cite: 494]
SECTION 3 - SETS
1: Explain concepts relating to sets. [cite: 552]
[cite_start]2: Represent a set in various forms. [cite: 556]
[cite_start]3: List subsets of a given set. [cite: 565]
[cite_start]4: Determine elements in intersections, unions and complements of sets. [cite: 568]
[cite_start]5: Describe relationships among sets using set notation and symbols. [cite: 572]
[cite_start]6: Draw Venn diagrams to represent relationships among sets. [cite: 576]
[cite_start]7: Use Venn diagrams to represent the relationships among sets. [cite: 582]
[cite_start]8: Solve problems in Number Theory, Algebra and Geometry using concepts in Set Theory. [cite: 590]
SECTION 4 - MEASUREMENT
1: Convert units of length, mass, area, volume, capacity. [cite: 641]
[cite_start]2: Use the appropriate SI unit of measure for area, volume, capacity, mass, temperature and time (24-hour clock) and other derived quantities. [cite: 651]
[cite_start]3: Determine the perimeter of a plane shape. [cite: 653]
[cite_start]4: Calculate the length of an arc of a circle. [cite: 654]
[cite_start]5: Estimate the area of plane shapes. [cite: 655]
[cite_start]6: Calculate the area of polygons and circles. [cite: 656]
[cite_start]7: Calculate the area of a sector of a circle. [cite: 657]
[cite_start]8: Calculate the area of a triangle given two sides and the angle they form. [cite: 658]
[cite_start]9: Calculate the area of a segment of a circle. [cite: 659]
[cite_start]10: Calculate the surface area of solids. [cite: 673]
[cite_start]11: Calculate the volume of solids. [cite: 677]
[cite_start]12: Solve problems involving the relations among time, distance and speed. [cite: 678]
[cite_start]13: Estimate the margin of error for a given measurement. [cite: 679]
[cite_start]14: Use scales and scale drawings to determine distances and areas. [cite: 681]
[cite_start]15: Solve problems involving measurement. [cite: 691]
SECTION 5 - STATISTICS
1: Differentiate between sample and population attributes. [cite: 750]
[cite_start]2: Construct a frequency table for a given set of data. [cite: 754]
[cite_start]3: Determine class features for a given set of data. [cite: 758]
[cite_start]4: Construct statistical diagrams (Pie charts, bar charts, line graphs, histograms, frequency polygons). [cite: 761]
[cite_start]5: Determine measures of central tendency for raw, ungrouped and grouped data. [cite: 764]
[cite_start]6: Determine when it is most appropriate to use the mean, median and mode as the average for a set of data. [cite: 770]
[cite_start]7: Determine the measures of dispersion (spread) for raw, ungrouped and grouped data. [cite: 772]
[cite_start]8: Use standard deviation to compare sets of data. [cite: 773]
[cite_start]9: Draw cumulative frequency curve (Ogive). [cite: 783]
[cite_start]10: Analyse statistical diagrams. [cite: 787]
[cite_start]11: Determine the proportion or percentage of the sample above or below a given value from raw data, frequency table or cumulative frequency curve. [cite: 788]
[cite_start]12: Identify the sample space for simple experiment. [cite: 789]
[cite_start]13: Determine experimental and theoretical probabilities of simple events. [cite: 791]
[cite_start]14: Make inference(s) from statistics. [cite: 801]
SECTION 6 - ALGEBRA
1: Use symbols to represent numbers, operations, variables and relations. [cite: 856]
[cite_start]2: Translate between algebraic symbols and worded expressions. [cite: 861]
[cite_start]3: Evaluate arithmetic operations involving directed numbers. [cite: 865]
[cite_start]4: Simplify algebraic expressions using the four basic operations. [cite: 871]
[cite_start]5: Substitute numbers for variables in algebraic expressions. [cite: 876]
[cite_start]6: Evaluate expressions involving binary operations (other than the four basic operations). [cite: 884]
[cite_start]7: Apply the distributive law to factorise or expand algebraic expressions. [cite: 888]
[cite_start]8: Simplify algebraic fractions. [cite: 900]
[cite_start]9: Use the laws of indices to manipulate expressions with integral indices. [cite: 903]
[cite_start]10: Solve linear equations in one unknown. [cite: 911]
[cite_start]11: Solve simultaneous linear equations, in two unknowns, algebraically. [cite: 913]
[cite_start]12: Solve a simple linear inequality in one unknown. [cite: 915]
[cite_start]13: Change the subject of formulae. [cite: 918]
[cite_start]14: Factorise algebraic expressions. [cite: 920]
[cite_start]15: Rewrite a quadratic expression in the form a(x+h)²+k. [cite: 924]
[cite_start]16: Solve quadratic equations algebraically. [cite: 927]
[cite_start]17: Solve word problems (linear, simultaneous, quadratic equations). [cite: 941]
[cite_start]18: Solve a pair of equations in two variables when one equation is quadratic or non-linear and the other linear. [cite: 945]
[cite_start]19: Prove two algebraic expressions to be identical. [cite: 948]
[cite_start]20: Represent direct and inverse variation symbolically. [cite: 949]
[cite_start]21: Solve problems involving direct variation and inverse variation. [cite: 950]
SECTION 7 - RELATIONS, FUNCTIONS AND GRAPHS
1: Explain basic concepts associated with relations. [cite: 1022]
[cite_start]2: Represent a relation in various ways. [cite: 1028]
[cite_start]3: State the characteristics that define a function. [cite: 1029]
[cite_start]4: Use functional notation. [cite: 1030]
[cite_start]5: Distinguish between a relation and a function. [cite: 1032]
[cite_start]6: Draw graphs of linear functions. [cite: 1037]
[cite_start]7: Determine the intercepts of the graph of linear functions. [cite: 1040]
[cite_start]8: Determine the gradient of a straight line. [cite: 1041]
[cite_start]9: Determine the equation of a straight line. [cite: 1060]
[cite_start]10: Solve problems involving the gradient of parallel and perpendicular lines. [cite: 1072]
[cite_start]11: Determine from co-ordinates on a line segment: the length; and, the co-ordinates of the midpoint. [cite: 1074]
[cite_start]12: Solve a pair of simultaneous linear equations in two unknowns graphically. [cite: 1081]
[cite_start]13: Represent the solution of linear inequalities in one variable using set notation, the number line, and a graph. [cite: 1085]
[cite_start]14: Draw a graph to represent a linear inequality in two variables. [cite: 1093]
[cite_start]15: Use linear programming techniques to graphically solve problems involving two variables. [cite: 1101]
[cite_start]16: Derive the composition of functions. [cite: 1110]
[cite_start]17: State the relationship between a function and its inverse. [cite: 1111]
[cite_start]18: Derive the inverse of a function. [cite: 1112]
[cite_start]19: Evaluate a function f(x) at a given value of x. [cite: 1113]
[cite_start]20: Draw and use the graph of a quadratic function to identify its features. [cite: 1114]
[cite_start]21: Interpret the graph of a quadratic function. [cite: 1138]
[cite_start]22: Determine the equation of the axis of symmetry and the maximum or minimum value of a quadratic function expressed in the form a(x+h)²+k. [cite: 1151]
[cite_start]23: Sketch the graph of a quadratic function expressed in the form y=a(x+h)²+k and determine the number of roots. [cite: 1152]
[cite_start]24: Draw graphs of non-linear functions. [cite: 1157]
[cite_start]25: Interpret graphs of functions (including distance-time and speed-time graphs). [cite: 1160]
[cite_start]26: Solve problems involving graphs of linear and non-linear functions. [cite: 1164]
SECTION 8 - GEOMETRY AND TRIGONOMETRY
1: Explain concepts relating to geometry (points, lines, angles, etc.). [cite: 1232]
[cite_start]2: Draw and measure angles and line segments accurately using appropriate instruments. [cite: 1234]
[cite_start]3: Construct lines, angles, and polygons using appropriate instruments. [cite: 1242]
[cite_start]4: Identify the type(s) of symmetry possessed by a given plane figure. [cite: 1243]
[cite_start]5: Solve geometric problems using properties of lines, angles, polygons, congruent triangles, similar figures, and solids. [cite: 1258]
[cite_start]6: Solve geometric problems using properties of circles and circle theorems. [cite: 1277]
[cite_start]7: Represent translations in a plane using vectors. [cite: 1292]
[cite_start]8: Determine and represent the location of the image of an object under a transformation and an object given the image. [cite: 1293]
[cite_start]9: State the relationship between an object and its image in the plane under geometric transformations. [cite: 1314]
[cite_start]10: Describe a transformation given an object and its image. [cite: 1316]
[cite_start]11: Locate the image of an object under a combination of transformations. [cite: 1322]
[cite_start]12: Use Pythagoras' theorem to solve problems. [cite: 1339]
[cite_start]13: Define the trigonometric ratios (Sine, Cosine, Tangent) of acute angles in a right triangle. [cite: 1342]
[cite_start]14: Relate objects in the physical world to geometric objects. [cite: 1343]
[cite_start]15: Apply the trigonometric ratios to solve problems. [cite: 1345]
[cite_start]16: Use the sine and cosine rules to solve problems involving triangles. [cite: 1350]
[cite_start]17: Solve problems involving bearings. [cite: 1351]
SECTION 9 - VECTORS AND MATRICES
1: Explain concepts associated with vectors. [cite: 1417]
[cite_start]2: Simplify expressions involving vectors. [cite: 1426]
[cite_start]3: Write the position vector of a point P(a,b) as OP = (a b). [cite: 1429]
[cite_start]4: Determine the magnitude of a vector. [cite: 1431]
[cite_start]5: Determine the direction of a vector. [cite: 1432]
[cite_start]6: Use vectors to solve problems in geometry. [cite: 1433]
[cite_start]7: Explain basic concepts associated with matrices. [cite: 1434]
[cite_start]8: Solve problems involving matrix operations (addition, subtraction, scalar multiplication, multiplication). [cite: 1435]
[cite_start]9: Evaluate the determinant of a 2x2 matrix. [cite: 1450]
[cite_start]10: Define the multiplicative inverse of a non-singular square matrix. [cite: 1451]
[cite_start]11: Obtain the inverse of a non-singular 2x2 matrix. [cite: 1453]
[cite_start]12: Determine a 2x2 matrix associated with a specified transformation (reflection, rotation, enlargement). [cite: 1458]
[cite_start]13: Use matrices to solve simple problems in Arithmetic, Algebra and Geometry. [cite: 1467]