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NEM |
NSM |
NMC |
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Whole Numbers, Fractions, and Decimals |
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Review the four operations and order of operations with whole numbers, fractions, and decimals, some multistep word problems. |
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Use scientific calculators. |
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Understand prime numbers, prime factorization, greatest common factor, lowest common multiple. |
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Use commutative, associative, and distributive laws. |
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Real Numbers and the Four Operations |
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Understand integers, real numbers, and absolute value,use the symbols >, <, ≥, ≤, ≠. |
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Add, subtract, multiply, and divide rational numbers, apply order of operations, commutative, associative, and distributive properties. |
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Find the square roots and cube roots of given numbers using prime factorization. |
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Solve word problems involving real numbers |
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Perform mental calculations using various strategies. |
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Ratio, Rate, and Speed, and Proportion |
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Find the ratio of two or more quantities, identify equivalent ratio, find simplest ratio. |
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Solve problems involving increase and decrease in ratio. |
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Solve problems involving rate, ratio, average rate, speed, average speed. |
1 2 |
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Solve problems involving money exchange. |
1 2 |
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Solve problems involving direct and inverse proportions. |
1 2 |
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| Understand other forms of proportion, e.g. y is directly or inversely proporional to x2. |
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Record and make scale drawings and solve map problems given map scales or representative fractions. |
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Percentage |
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Solve word problems involving percentage |
1 2 |
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Solve problems involving personal finance |
1 2 |
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Solve problems involving earnings, profit and loss, commissions, discounts, and taxes. |
1 2 |
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Solve problems involving simple interest, compound interest and hire purchase. |
1 2 |
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Algebraic expressions, equations, and functions |
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Evaluate and simplify algebraic expressions and use the distributive property. |
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Represent the general term of a sequence by algebraic expressions. |
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1 5 |
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Factorize algebraic expressions of the form ax + ay and ax + bx + kay + kby |
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Solve linear equations with whole number, fractional, and decimal coefficients. |
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Solve algebraic word problems involving linear equations. |
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Solve simultaneous linear equations in two variables by elimination and by substitution, solve word problems involving simultaneous equations. |
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Use the following special algebraic rules: (a + b)2 = a2 + 2ab + b2, (a - b)2 = a2 - 2ab + b2 and a2- b2 = (a + b)(a - b) for calculating and expanding products of algebraic expressions, and for factorizing algebraic expressions. |
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Use special algebraic rules in mental calculations. |
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Perform addition, subtraction, multiplication, and division of algebraic fractions. |
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2 4 5 |
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Solve fractional equations involving numerical, linear, and quadratic denominators. |
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2 4 5 |
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Solve literal equations, including applying the results to solve equations of the same form. |
2 3 |
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Evaluate and transform a formula, including changing the subject of a formula. |
2 3 |
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Solve quadratic equations by factorization, solve word problems involving quadratic equations. |
2 3 |
2 3 |
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Solve quadratic equations by completing the square and by use of the formula. |
3 |
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Solve fractional equations that can be reduced to quadratic equations. |
3 |
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Understand the basic definition of functions. |
3 |
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Use function notation, understand domain and range, represent functions graphically. |
3 |
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Use inverse function notation to describe the inverse of a simple function. |
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Express direct variation and inverse variation in algebraic terms and use these forms of expressions to find unknown quantities. |
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Solve word problems involving direct variation and inverse variation. |
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Identify like terms in a polynomial, including stating the degree of an algebraic term. |
2 |
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Add, subtract, multiply, and divide polynomials. |
2 |
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Inequalities |
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Understand properties of order and use the inequality signs. |
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Use the number line to illustrate solutions of inequalities. |
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Solve simple inequalities (without change of sign). |
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Solve simple linear inequalities in one variable (including change of sign), solve problems involving inequalities) |
2 3 |
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Give upper and lower bounds for data and for solutions to simple problems to a specified accuracy. |
3 |
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Indices (Exponents and Radicals) |
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Use the laws of indices, simplify indices involving variable bases. |
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Understand and use fractional indices. |
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Demonstrate an understanding of the definition of standard form. |
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Use and compute numbers in standard form, including very large and small numbers. |
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Graphs |
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Understand Cartesian coordinates in two dimensions. |
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Identify simple rules connecting pairs of values of x and y. |
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Draw graphs of simple linear equations. |
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Graph equations of the form y = c, x = a, y = mx, y = yx + c and investigate how the graph change when m or c changes. |
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Interpret and draw graphs in practical situations. |
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Solve simultaneous linear equations by graphs. |
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Calculate the length of a line segment from the coordinates of its end points. |
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Find the gradient of a straight line or linear graph as the ratio of vertical change to horizontal change. |
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1 3 |
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Interpret and find the equation of a straight line in the form y = mx + c or ax + by = c. |
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Solve geometric problems involving use of coordinates. |
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Recognize graphs of quadratic functions and their properties, including positive and negative coefficients of x2, maximum and minimum points, and lines of symmetry. |
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Solve problems involving quadratic graphs. |
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3 5 |
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Demonstrate an understanding of the idea of gradient of a curve at a given point. |
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Graph cubic equations. |
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3 5 |
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Graph functions in the form y = axn and y = kan for -2 < n < 3 |
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3 5 |
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Solve equations approximately by using a given curve and an appropriate straight line. |
3 |
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Demonstrate an understanding of positive, zero and negative rates of change of distance from a given point. |
3 |
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Apply the idea of rate of change to easy kinematics involving distance-time and speed-time graphs including using graphs in practical situations. |
3 |
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Calculate the midpoint of a line segment from the coordinates of its end points. |
3 |
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Recognize that parallel lines have the same gradient, find the gradient of parallel lines, find the area of a quadrilateral given its vertices. |
3 |
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Measurement |
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Review: Understand the units in metric system of measurement. |
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Convert units of measurement for length, weight, and capacity, area, and volume. |
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Use formulae to find the perimeter and area of squares, rectangles, parallelograms, trapezoids, triangles, and circles. |
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Solve problems involving perimeter and area of composite figures. |
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Use formulae to find the volume and surface area of cubes, cuboids, prisms, and cylinders. |
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Solve problems involving volume and surface area of composite figures. |
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Use formulae to find the mass of a substance, solve problems involving volume and density. |
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Solve problems involving volume and surface area of pyramid, cone, and sphere. |
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Use the relationships between areas of similar figures and volumes of similar so lids.. |
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Solve problems involving arc length and sector area. |
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Understand and use radian measures. |
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Geometry |
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Understand some geometric terms for lines and angles, measure angles. |
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Recognize angle properties related to intersecting straight lines and angels formed by parallel lines and a transversal. |
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Recognize angle properties of polygons, solve geometrical problems involving triangles, quadrilaterals, and other polygons |
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Find the angle sum of interior and exterior angles of any convex polygon |
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Construct triangles and quadrilaterals with given data. |
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Identify line symmetries, plane symmetry, rotational symmetry, and order of symmetry of plane figures. |
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Identify symmetry in patterns. |
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Construct nets of solid figures and identify solid figures from their nets. |
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Use properties of similar and congruent figures to find unknown sides and angles. |
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| Relate enlargement to simiarl figures, inderstand scale factor. |
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Use similar and congruent figures to make design and tessellations and determine whether a figure can tessellate. |
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Demonstrate an understanding of the SAS, AAS, SSS and RHS tests for congruent triangles. |
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Solve problems involving applications of congruence and similarity. |
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Understand and apply the following symmetry and angle properties of circles and their converses: |
3 |
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Motion Geometry |
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Use and identify reflection, rotation, and translation to transform geometrical figures on the coordinate plane, including giving a full description of the transformation. |
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Use enlargement to transform geometrical figures on the coordinate plane. |
2 3 |
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Use column vectors to describe translations. |
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Draw the image of a given figure involving combined transformations, including using coordinates. |
2 3 4 |
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Use shear and stretch to transform geometrical figures on the coordinate plane. |
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Use transformations and their combinations, identify and give precise descriptions of transformations connecting given figures. |
3 4 |
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Trigonometry |
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Demonstrate an understanding of the Pythagoras’ Theorem, solve problems applying the Pythagoras' Theorem. |
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Use trigonometric ratios (sine, cosine, and tangent) of acute angles to calculate unknown sides and angles of right-angled triangles or related figures. |
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Solve simple trigonometrical problems in two dimensions, including angles of elevation and depression. |
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Express sine, cosine and tangent functions for obtuse angles and calculate the angle A between 0° and 180° given sin A or cos A. |
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Express tangent function for obtuse angles and calculate the angle A between 0° and 180° given tan A. |
3 |
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Solve problems using cosine rule, sine rul,e and the formula ˝ ab sin c for the area of a triangle. |
3 |
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Solve trigonometrical problems in three dimensions involving bearings. |
3 |
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Solve trigonometrical problems in two or three dimensions involving angles of elevation and depression and bearings. |
3 |
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Statistics |
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Collect, classify and tabulate data, construct and interpret tables, bar graphs, pictograms, line graphs and pie charts. |
2 |
1 2 |
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Construct and interpret histograms with equal intervals. |
2 |
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Find the mean, median and mode of a frequency distribution and understand their purpose. |
2 |
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Construct frequency distribution tables, frequency diagrams and frequency polygons for grouped data, identify the modal class and the class in which the median lies. |
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Use frequency density to construct and read histograms with unequal intervals. |
3 |
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Construct and use cumulative frequency diagram, estimate the median. |
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Interpret box and whisker plots. |
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Calculate the mean for grouped data, use percentiles, quartiles, and interquartile range. |
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Solve problems on cumulative frequency. |
3 |
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Probability |
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Understand the meaning of probability. |
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| Calculate the probability of single events. |
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Calculate the probability of combined events. |
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Add and multiply probabilities. |
4 |
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Understand mutually exclusive and independent events. |
4 |
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Set Language and Notation |
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Understand and use sets and set notations. |
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