South Africa
Skills available for South Africa grade 10 maths curriculum
Objectives are in black and IXL maths skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practise that skill.
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- National Curriculum Statement (CAPS) National Curriculum Statement (CAPS)
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10.1 Functions
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10.1.a Work with relationships between variables in terms of numerical, graphical, verbal and symbolic representations of functions and convert flexibly between these representations (tables, graphs, words and formulae). Include linear and some quadratic polynomial functions, exponential functions, some rational functions and trigonometric functions.
- Relations: convert between tables, graphs, mappings and lists of points (10-F.1)
- Domain and range of relations (10-F.2)
- Identify independent and dependent variables (10-F.3)
- Identify functions (10-F.4)
- Complete a function table from an equation (10-F.5)
- Find values using function graphs (10-F.6)
- Evaluate a function (10-F.7)
- Complete a function table from a graph (10-F.8)
- Interpret the graph of a function: word problems (10-F.9)
- Identify linear functions (10-G.1)
- Find the gradient of a graph (10-G.2)
- Find the gradient from two points (10-G.3)
- Find the gradient and y-intercept of a linear equation (10-G.5)
- Graph an equation in y=mx+c form (10-G.6)
- Write an equation in y=mx+c form from a graph (10-G.7)
- Write an equation in y=mx+c form (10-G.8)
- Write an equation in y=mx+c form from a table (10-G.9)
- Write an equation in y=mx+c form from a word problem (10-G.10)
- Write linear functions to solve word problems (10-G.11)
- Complete a table and graph a linear function (10-G.12)
- Compare linear functions: graphs, tables and equations (10-G.13)
- Write equations in standard form (10-G.14)
- Standard form: find x- and y-intercepts (10-G.15)
- Standard form: graph an equation (10-G.16)
- Equations of horizontal and vertical lines (10-G.17)
- Graph a horizontal or vertical line (10-G.18)
- Point-gradient form: graph an equation (10-G.19)
- Point-gradient form: write an equation (10-G.20)
- Point-gradient form: write an equation from a graph (10-G.21)
- Gradients of parallel and perpendicular lines (10-G.22)
- Write an equation for a parallel or perpendicular line (10-G.23)
- Evaluate an exponential function (10-J.1)
- Match exponential functions and graphs (10-J.2)
- Domain and range of exponential functions (10-J.3)
- Exponential growth: word problems (10-J.4)
- Characteristics of quadratic functions (10-O.1)
- Complete a function table: quadratic functions (10-O.2)
- Solve a quadratic equation using square roots (10-O.3)
- Solve a quadratic equation using the zero product property (10-O.4)
- Solve a quadratic equation by factorising (10-O.5)
- Complete the square (10-O.6)
- Solve a quadratic equation by completing the square (10-O.7)
- Solve a quadratic equation using the quadratic formula (10-O.8)
- Using the discriminant (10-O.9)
- Identify linear, quadratic and exponential functions from graphs (10-P.1)
- Identify linear, quadratic and exponential functions from tables (10-P.2)
- Write linear, quadratic and exponential functions (10-P.3)
- Linear functions over unit intervals (10-P.4)
- Exponential functions over unit intervals (10-P.5)
- Describe linear and exponential growth and decay (10-P.6)
- Rational functions: asymptotes and excluded values (10-S.1)
- Find properties of sine functions (11-S.1)
- Write equations of sine functions from graphs (11-S.2)
- Write equations of sine functions using properties (11-S.3)
- Graph sine functions (11-S.4)
- Find properties of cosine functions (11-S.5)
- Write equations of cosine functions from graphs (11-S.6)
- Write equations of cosine functions using properties (11-S.7)
- Graph cosine functions (11-S.8)
- Graph sine and cosine functions (11-S.9)
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10.1.b Generate as many graphs as necessary, initially by means of point-by-point plotting, supported by available technology, to make and test conjectures and hence generalise the effect of the parameter which results in a vertical shift and that which results in a vertical stretch and/or a reflection about the x-axis.
- Graph an equation in y=mx+c form (10-G.6)
- Complete a table and graph a linear function (10-G.12)
- Standard form: graph an equation (10-G.16)
- Point-gradient form: graph an equation (10-G.19)
- Transformations of linear functions (10-G.26)
- Match exponential functions and graphs (10-J.2)
- Graph a quadratic function (11-E.4)
- Match quadratic functions and graphs (11-E.5)
- Graph sine functions (11-S.4)
- Graph cosine functions (11-S.8)
- Graph sine and cosine functions (11-S.9)
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10.1.c Problem solving and graph work involving the prescribed functions.
- Solve linear equations: word problems (10-D.10)
- Interpret the graph of a function: word problems (10-F.9)
- Write linear functions to solve word problems (10-G.11)
- Exponential growth: word problems (10-J.4)
- Linear functions over unit intervals (10-P.4)
- Exponential functions over unit intervals (10-P.5)
- Describe linear and exponential growth and decay (10-P.6)
10.2 Number Patterns, Sequences and Series
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10.2.a Investigate number patterns leading to those where there is constant difference between consecutive terms, and the general term is therefore linear.
10.3 Finance, Growth and Decay
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10.3.a Use simple and compound growth formulae A = P(1 + in) and A = P(1 + i)n to solve problems (including interest, hire purchase, inflation, population growth and other real life problems).
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10.3.c The implications of fluctuating foreign exchange rates.
10.4 Algebra
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10.4.a Understand that real numbers can be irrational or rational.
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10.4.a Simplify expressions using the laws of exponents for rational exponents.
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10.4.b Establish between which two integers a given simple surd lies.
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10.4.c Round real numbers to an appropriate degree of accuracy (to a given number of decimal digits).
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10.4.a Manipulate algebraic expressions by:
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10.4.a.1 multiplying a binomial by a trinomial;
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10.4.a.2 factorising trinomials;
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10.4.a.3 factorising the difference and sums of two cubes;
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10.4.a.4 factorising by grouping in pairs; and
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10.4.a.5 simplifying, adding and subtracting algebraic fractions with denominators of cubes (limited to sum and difference of cubes).
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10.4.b Solve:
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10.4.b.1 linear equations;
- Model and solve equations using algebra tiles (10-D.1)
- Write and solve equations that represent diagrams (10-D.2)
- Solve one-step linear equations (10-D.3)
- Solve two-step linear equations (10-D.4)
- Solve advanced linear equations (10-D.5)
- Solve equations with variables on both sides (10-D.6)
- Solve equations: complete the solution (10-D.7)
- Find the number of solutions (10-D.8)
- Create equations with no solutions or infinitely many solutions (10-D.9)
- Solve linear equations: word problems (10-D.10)
- Solve linear equations: mixed review (10-D.11)
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10.4.b.2 quadratic equations;
- Solve a quadratic equation using square roots (10-O.3)
- Solve a quadratic equation using the zero product property (10-O.4)
- Solve a quadratic equation by factorising (10-O.5)
- Complete the square (10-O.6)
- Solve a quadratic equation by completing the square (10-O.7)
- Solve a quadratic equation using the quadratic formula (10-O.8)
- Using the discriminant (10-O.9)
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10.4.b.3 literal equations (changing the subject of a formula);
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10.4.b.4 exponential equations;
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10.4.b.5 linear inequalities;
- Graph inequalities (10-E.1)
- Write inequalities from graphs (10-E.2)
- Identify solutions to inequalities (10-E.3)
- Solve one-step linear inequalities: addition and subtraction (10-E.4)
- Solve one-step linear inequalities: multiplication and division (10-E.5)
- Solve one-step linear inequalities (10-E.6)
- Graph solutions to one-step linear inequalities (10-E.7)
- Solve two-step linear inequalities (10-E.8)
- Graph solutions to two-step linear inequalities (10-E.9)
- Solve advanced linear inequalities (10-E.10)
- Graph solutions to advanced linear inequalities (10-E.11)
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10.4.b.6 system of linear equations; and
- Is (x, y) a solution to the simultaneous equations? (10-H.1)
- Solve simultaneous equations by graphing (10-H.2)
- Solve simultaneous equations by graphing: word problems (10-H.3)
- Find the number of solutions to simultaneous equations by graphing (10-H.4)
- Find the number of solutions to simultaneous equations (10-H.5)
- Solve simultaneous equations using substitution (10-H.6)
- Solve simultaneous equations using substitution: word problems (10-H.7)
- Solve simultaneous equations using elimination (10-H.8)
- Solve simultaneous equations using elimination: word problems (10-H.9)
- Solve simultaneous equations using any method (10-H.10)
- Solve simultaneous equations using any method: word problems (10-H.11)
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10.4.b.7 word problems.
- Solve linear equations: word problems (10-D.10)
- Write linear functions to solve word problems (10-G.11)
- Solve simultaneous equations by graphing: word problems (10-H.3)
- Solve simultaneous equations using substitution: word problems (10-H.7)
- Solve simultaneous equations using elimination: word problems (10-H.9)
- Solve simultaneous equations using any method: word problems (10-H.11)
- Consecutive integer problems (10-CC.1)
- Rate of travel: word problems (10-CC.2)
- Weighted averages: word problems (10-CC.3)
- Word problems: mixed review (10-CC.4)
- Word problems with money (10-CC.5)
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10.5 Differential Calculus
10.6 Probability
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10.6.a Compare the relative frequency of an experimental outcome with the theoretical probability of the outcome.
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10.6.b Venn diagrams as an aid to solving probability problems.
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10.6.c Mutually exclusive events and complementary events.
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10.6.d The identity for any two events A and B: P(A or B) = P(A) + (B) - P(A and B)
10.7 Euclidean Geometry and Measurement
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10.7.a Revise basic results established in earlier grades.
- Transversals: name angle pairs (10-T.2)
- Transversals of parallel lines: find angle measures (10-T.3)
- Congruence statements and corresponding parts (10-V.1)
- Solve problems involving corresponding parts (10-V.2)
- Identify congruent figures (10-V.3)
- SSS, SAS, ASA and AAS Theorems (10-V.4)
- SSS Theorem in the coordinate plane (10-V.5)
- Congruency in isosceles and equilateral triangles (10-V.6)
- Classify triangles (10-W.1)
- Triangle Angle-Sum Theorem (10-W.2)
- Identify similar figures (10-Y.1)
- Similarity ratios (10-Y.2)
- Similarity statements (10-Y.3)
- Side lengths and angle measures in similar figures (10-Y.4)
- Similar triangles and indirect measurement (10-Y.5)
- Perimeters of similar figures (10-Y.6)
- Similarity rules for triangles (10-Y.7)
- Similar triangles and similarity transformations (10-Y.8)
- Pythagoras' Theorem (10-Z.1)
- Converse of Pythagoras' theorem (10-Z.2)
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10.7.b Investigate line segments joining the midpoints of two sides of a triangle.
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10.7.c Properties of special quadrilaterals.
- Classify quadrilaterals (10-X.2)
- Graph quadrilaterals (10-X.3)
- Properties of parallelograms (10-X.4)
- Proving a quadrilateral is a parallelogram (10-X.5)
- Properties of rhombuses (10-X.6)
- Properties of squares and rectangles (10-X.7)
- Properties of trapeziums (10-X.8)
- Properties of kites (10-X.9)
- Review: properties of quadrilaterals (10-X.10)
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10.7.a Solve problems involving volume and surface area of solids studied in earlier grades as well as spheres, pyramids and cones and combinations of those objects.
- Introduction to surface area and volume (10-BB.1)
- Surface area of prisms and cylinders (10-BB.2)
- Surface area of pyramids and cones (10-BB.3)
- Volume of prisms and cylinders (10-BB.4)
- Volume of pyramids and cones (10-BB.5)
- Surface area and volume of spheres (10-BB.6)
- Introduction to similar solids (10-BB.7)
- Surface area and volume of similar solids (10-BB.8)
- Surface area and volume review (10-BB.9)
10.8 Trigonometry
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10.8.a Definitions of the trigonometric ratios sin θ, cos θ and tan θ in a right-angled triangles.
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10.8.b Extend the definitions of sin θ, cos θ and tan θ to 0° ≤ θ ≤ 360°.
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10.8.c Derive and use values of the trigonometric ratios (without using a calculator for the special angles θ ∈ {0°; 30°; 45°; 60°; 90°})
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10.8.d Define the reciprocals of trigonometric ratios.
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10.8.a So Solve problems in two dimensions.
10.9 Analytical Geometry
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10.9.a Represent geometric figures in a Cartesian coordinate system, and derive and apply, for any two points (x1; y1) and (x2; y2), a formula for calculating:
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10.9.a.1 the distance between the two points;
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10.9.a.2 the gradient of the line segment joining the points;
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10.9.a.3 conditions for parallel and perpendicular lines; and
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10.9.a.4 the co-ordinates of the mid-point of the line segment joining the points.
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10.1 Statistics
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10.10.a Collect, organise and interpret univariate numerical data in order to determine:
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10.10.a.1 measures of central tendency;
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10.10.a.2 five number summary;
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10.10.a.3 box and whisker diagrams; and
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10.10.a.4 measures of dispersion.
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