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The World of Mathematics

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IMBS Interactive Syllabus

CSEC Mathematics

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SECTION 1 - NUMBER THEORY AND COMPUTATION
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1: Distinguish among sets of numbers. [cite: 296]

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2: Compute powers of real numbers of the form x^a, where a is a rational number. [cite: 324]

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3: Evaluate numerical expressions using any of the four basic operations on real numbers. [cite: 325]

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4: Convert among fractions, percents and decimals. [cite: 326]

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5: List the set of factors and multiples of a given integer. [cite: 327]

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6: Compute the H.C.F. or L.C.M. of two or more positive integers. [cite: 328]

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7: State the value of a digit of a numeral in a given base. [cite: 329]

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8: Convert from one set of units to another. [cite: 330]

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9: Express a value to a given number of significant figures and decimal places. [cite: 331, 341, 343]

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10: Use properties of numbers and operations in computational tasks. [cite: 345]

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11: Write any rational number in scientific notation. [cite: 347]

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12: Calculate any fraction or percentage of a given quantity. [cite: 348]

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13: Express one quantity as a fraction or percentage of another. [cite: 361]

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14: Compare quantities. [cite: 364]

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15: Order a set of real numbers. [cite: 367]

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16: Compute terms of a sequence given a rule. [cite: 373]

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17: Derive an appropriate rule given the terms of a sequence. [cite: 375]

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18: Divide a quantity in a given ratio. [cite: 377]

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19: Solve problems involving concepts in number theory and computation. [cite: 381]

SECTION 2 - CONSUMER ARITHMETIC
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1: Calculate discount, sales tax, profit, and loss. [cite: 452]

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2: Calculate percentage profit and percentage loss. [cite: 463]

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3: Express a profit, loss, discount, markup and purchase tax, as a percentage of some value. [cite: 468]

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4: Solve problems involving marked price, selling price, cost price, profit, loss or discount. [cite: 470]

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5: Solve problems involving payments by instalments as in the case of hire purchase and mortgages. [cite: 473]

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6: Solve problems involving simple interest. [cite: 485]

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7: Solve problems involving compound interest. [cite: 486]

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8: Solve problems involving appreciation and depreciation. [cite: 487]

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9: Solve problems involving measures and money. [cite: 491]

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10: Solve problems involving rates and taxes; utilities; invoices and shopping bills; salaries and wages; insurance and investments. [cite: 494]

SECTION 3 - SETS
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1: Explain concepts relating to sets. [cite: 552]

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2: Represent a set in various forms. [cite: 556]

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3: List subsets of a given set. [cite: 565]

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4: Determine elements in intersections, unions and complements of sets. [cite: 568]

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5: Describe relationships among sets using set notation and symbols. [cite: 572]

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6: Draw Venn diagrams to represent relationships among sets. [cite: 576]

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7: Use Venn diagrams to represent the relationships among sets. [cite: 582]

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8: Solve problems in Number Theory, Algebra and Geometry using concepts in Set Theory. [cite: 590]

SECTION 4 - MEASUREMENT
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1: Convert units of length, mass, area, volume, capacity. [cite: 641]

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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]

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3: Determine the perimeter of a plane shape. [cite: 653]

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4: Calculate the length of an arc of a circle. [cite: 654]

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5: Estimate the area of plane shapes. [cite: 655]

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6: Calculate the area of polygons and circles. [cite: 656]

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7: Calculate the area of a sector of a circle. [cite: 657]

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8: Calculate the area of a triangle given two sides and the angle they form. [cite: 658]

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9: Calculate the area of a segment of a circle. [cite: 659]

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10: Calculate the surface area of solids. [cite: 673]

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11: Calculate the volume of solids. [cite: 677]

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12: Solve problems involving the relations among time, distance and speed. [cite: 678]

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13: Estimate the margin of error for a given measurement. [cite: 679]

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14: Use scales and scale drawings to determine distances and areas. [cite: 681]

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15: Solve problems involving measurement. [cite: 691]

SECTION 5 - STATISTICS
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1: Differentiate between sample and population attributes. [cite: 750]

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2: Construct a frequency table for a given set of data. [cite: 754]

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3: Determine class features for a given set of data. [cite: 758]

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4: Construct statistical diagrams (Pie charts, bar charts, line graphs, histograms, frequency polygons). [cite: 761]

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5: Determine measures of central tendency for raw, ungrouped and grouped data. [cite: 764]

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6: Determine when it is most appropriate to use the mean, median and mode as the average for a set of data. [cite: 770]

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7: Determine the measures of dispersion (spread) for raw, ungrouped and grouped data. [cite: 772]

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8: Use standard deviation to compare sets of data. [cite: 773]

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9: Draw cumulative frequency curve (Ogive). [cite: 783]

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10: Analyse statistical diagrams. [cite: 787]

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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]

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12: Identify the sample space for simple experiment. [cite: 789]

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13: Determine experimental and theoretical probabilities of simple events. [cite: 791]

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14: Make inference(s) from statistics. [cite: 801]

SECTION 6 - ALGEBRA
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1: Use symbols to represent numbers, operations, variables and relations. [cite: 856]

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2: Translate between algebraic symbols and worded expressions. [cite: 861]

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3: Evaluate arithmetic operations involving directed numbers. [cite: 865]

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4: Simplify algebraic expressions using the four basic operations. [cite: 871]

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5: Substitute numbers for variables in algebraic expressions. [cite: 876]

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6: Evaluate expressions involving binary operations (other than the four basic operations). [cite: 884]

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7: Apply the distributive law to factorise or expand algebraic expressions. [cite: 888]

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8: Simplify algebraic fractions. [cite: 900]

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9: Use the laws of indices to manipulate expressions with integral indices. [cite: 903]

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10: Solve linear equations in one unknown. [cite: 911]

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11: Solve simultaneous linear equations, in two unknowns, algebraically. [cite: 913]

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12: Solve a simple linear inequality in one unknown. [cite: 915]

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13: Change the subject of formulae. [cite: 918]

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14: Factorise algebraic expressions. [cite: 920]

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15: Rewrite a quadratic expression in the form a(x+h)²+k. [cite: 924]

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16: Solve quadratic equations algebraically. [cite: 927]

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17: Solve word problems (linear, simultaneous, quadratic equations). [cite: 941]

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18: Solve a pair of equations in two variables when one equation is quadratic or non-linear and the other linear. [cite: 945]

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19: Prove two algebraic expressions to be identical. [cite: 948]

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20: Represent direct and inverse variation symbolically. [cite: 949]

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21: Solve problems involving direct variation and inverse variation. [cite: 950]

SECTION 7 - RELATIONS, FUNCTIONS AND GRAPHS
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1: Explain basic concepts associated with relations. [cite: 1022]

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2: Represent a relation in various ways. [cite: 1028]

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3: State the characteristics that define a function. [cite: 1029]

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4: Use functional notation. [cite: 1030]

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5: Distinguish between a relation and a function. [cite: 1032]

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6: Draw graphs of linear functions. [cite: 1037]

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7: Determine the intercepts of the graph of linear functions. [cite: 1040]

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8: Determine the gradient of a straight line. [cite: 1041]

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9: Determine the equation of a straight line. [cite: 1060]

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10: Solve problems involving the gradient of parallel and perpendicular lines. [cite: 1072]

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11: Determine from co-ordinates on a line segment: the length; and, the co-ordinates of the midpoint. [cite: 1074]

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12: Solve a pair of simultaneous linear equations in two unknowns graphically. [cite: 1081]

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13: Represent the solution of linear inequalities in one variable using set notation, the number line, and a graph. [cite: 1085]

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14: Draw a graph to represent a linear inequality in two variables. [cite: 1093]

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15: Use linear programming techniques to graphically solve problems involving two variables. [cite: 1101]

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16: Derive the composition of functions. [cite: 1110]

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17: State the relationship between a function and its inverse. [cite: 1111]

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18: Derive the inverse of a function. [cite: 1112]

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19: Evaluate a function f(x) at a given value of x. [cite: 1113]

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20: Draw and use the graph of a quadratic function to identify its features. [cite: 1114]

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21: Interpret the graph of a quadratic function. [cite: 1138]

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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]

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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]

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24: Draw graphs of non-linear functions. [cite: 1157]

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25: Interpret graphs of functions (including distance-time and speed-time graphs). [cite: 1160]

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26: Solve problems involving graphs of linear and non-linear functions. [cite: 1164]

SECTION 8 - GEOMETRY AND TRIGONOMETRY
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1: Explain concepts relating to geometry (points, lines, angles, etc.). [cite: 1232]

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2: Draw and measure angles and line segments accurately using appropriate instruments. [cite: 1234]

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3: Construct lines, angles, and polygons using appropriate instruments. [cite: 1242]

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4: Identify the type(s) of symmetry possessed by a given plane figure. [cite: 1243]

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5: Solve geometric problems using properties of lines, angles, polygons, congruent triangles, similar figures, and solids. [cite: 1258]

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6: Solve geometric problems using properties of circles and circle theorems. [cite: 1277]

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7: Represent translations in a plane using vectors. [cite: 1292]

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8: Determine and represent the location of the image of an object under a transformation and an object given the image. [cite: 1293]

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9: State the relationship between an object and its image in the plane under geometric transformations. [cite: 1314]

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10: Describe a transformation given an object and its image. [cite: 1316]

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11: Locate the image of an object under a combination of transformations. [cite: 1322]

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12: Use Pythagoras' theorem to solve problems. [cite: 1339]

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13: Define the trigonometric ratios (Sine, Cosine, Tangent) of acute angles in a right triangle. [cite: 1342]

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14: Relate objects in the physical world to geometric objects. [cite: 1343]

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15: Apply the trigonometric ratios to solve problems. [cite: 1345]

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16: Use the sine and cosine rules to solve problems involving triangles. [cite: 1350]

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17: Solve problems involving bearings. [cite: 1351]

SECTION 9 - VECTORS AND MATRICES
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1: Explain concepts associated with vectors. [cite: 1417]

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2: Simplify expressions involving vectors. [cite: 1426]

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3: Write the position vector of a point P(a,b) as OP = (a b). [cite: 1429]

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4: Determine the magnitude of a vector. [cite: 1431]

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5: Determine the direction of a vector. [cite: 1432]

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6: Use vectors to solve problems in geometry. [cite: 1433]

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7: Explain basic concepts associated with matrices. [cite: 1434]

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8: Solve problems involving matrix operations (addition, subtraction, scalar multiplication, multiplication). [cite: 1435]

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9: Evaluate the determinant of a 2x2 matrix. [cite: 1450]

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10: Define the multiplicative inverse of a non-singular square matrix. [cite: 1451]

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11: Obtain the inverse of a non-singular 2x2 matrix. [cite: 1453]

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12: Determine a 2x2 matrix associated with a specified transformation (reflection, rotation, enlargement). [cite: 1458]

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13: Use matrices to solve simple problems in Arithmetic, Algebra and Geometry. [cite: 1467]

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