Entrance Level Competencies For Alberta Apprenticeship Programs

MATHEMATICSSECTION FOUR . VARIABLES AND EQUATIONSA. Problem Solving Using Variables And EquationsOutcome:Use variables and equations to express, summarize and apply relationships asproblem-solving tools in a restricted range of contexts. (1,2,3,4,5)1. Write mathematical expressions that arise from problem-solving contexts.2. Evaluate expressions with and without concrete models.3. Illustrate the solution process for a one-step, single-variable, first-degree equation, using concretematerials or diagrams.4. Solve and verify one-step linear equations, using a variety of techniques.5. Explain how to solve simple problems, using informal algebraic methods.B. One And Two Step Linear EquationsOutcome:Solve and verify one-step and two-step linear equations with rational numbersolutions. (1,2,3,4,5)1. Illustrate the solution process for a two-step, single-variable, first-degree equation, using concretematerials or diagrams.2. Solve and verify one- and two-step, first-degree equations with integer coefficients.3. Create and solve problems, using first-degree equations.C. Linear Equations And Inequalities In One VariableOutcome:Solve and verify linear equations and inequalities in one variable. (1,2,3,4,5)1. Illustrate the solution process for a first-degree, single-variable equation, using concrete materials ordiagrams.2. Solve and verify first-degree, single-variable equations with rational coefficients (with a focus onintegers), and use equations of this type to model and solve problem situations.3. Solve, algebraically, first-degree inequalities in one variable, display the solutions on a number lineand test the solutions.D. Generalize Arithmetic Operations From Rational Numbers To PolynomialsOutcome:Generalize arithmetic operations from the set of rational numbers to the set ofpolynomials. (1,2,3,4,5)1. Identify constant terms, coefficients and variables in polynomial expressions.2. Evaluate polynomial expressions, given the value(s) of the variable(s).3. Represent and justify the addition and subtraction of polynomial expressions, using concretematerials and diagrams.4. Perform the operations of addition and subtraction on polynomial expressions.5. Represent multiplication, division and factoring of monomials, binomials, and trinomials usingconcrete materials and diagrams.6. Find the product of two monomials, a monomial and a polynomial, and two binomials.7. Determine equivalent forms of algebraic expressions by identifying common factors and factoringtrinomials.8. Find the quotient when a polynomial is divided by a monomial.Classification: Protected A8

MATHEMATICSE. Exponential, Logarithmic And Trigonometric Equations And IdentitiesOutcome:Solve exponential, logarithmic and trigonometric equations and identities. (5)1. Solve exponential equations having bases that are powers of one another.2. Solve and verify exponential and logarithmic equations and identities.3. Distinguish between degree and radian measure and solve problems using both.4. Determine the exact and approximate values of trigonometric ratios for any multiples of 0, 30, 45, 60,and 90 degrees.5. Solve first and second degree trigonometric equations over a domain of length 2pi algebraically andgraphically.6. Determine the general solution to trigonometric equations where the domain is the set of realnumbers.7. Verify trigonometric identities: numerically for any particular case; algebraically for general cases; andgraphically.8. Use sum difference and double angle identities for sine and cosine to verify and simplify trigonometricexpressions.SECTION FIVE . RELATIONS AND FUNCTIONSA. Exponential And Logarithmic Functions Using Appropriate TechnologyOutcome:Represent and analyze exponential and logarithmic functions, using technology asappropriate. (5)1. Graph and analyze an exponential function using technology.2. Model, graph and apply exponential functions to solve problems.3. Change functions from exponential form to logarithmic form and vice versa.4. Use logarithms to model practical problems.5. Explain the relationship between the laws of logarithms and the laws of exponents.6. Graph and analyze logarithmic functions with and without technology.B. Trigonometric Functions Using Appropriate TechnologyOutcome:Represent and analyze trigonometric functions, using technology as appropriate. (5)1. Describe the three primary trigonometric functions as circular functions with reference to the unitcircle and an angle in standard position.2. Draw using technology, sketch and analyze graphs of sine, cosine and tangent functions foramplitude, period, domain and range, asymptotes, behaviour under transformations.3. Draw using technology, sketch and analyze graphs of secant, cosecant and cotangent functions foramplitude, period, domain and range, asymptotes, behaviour under transformations.4. Use trigonometric functions to model and solve problems.Classification: Protected A9

MATHEMATICSSECTION SIX . . MEASUREMENT OF SHAPE AND SPACEA. Properties Of Circles, Angles And Time ZonesOutcome:Solve problems involving the properties of circles and their connections withangles and time zones. (1,2,3,4,5)1. Measure the diameters, radii and circumferences of circles, and establish the relationships amongthem.2. Solve problems involving the radii, diameters and circumferences of circles.3. Explain how time zones are determined.4. Research and report how measurement instruments are used in the community.B. Metric And Imperial MeasureOutcome: Solve problems involving Metric and Imperial measure. (1,2,3,4,5)1. Identify commonly used metric units of measurement.2. Convert between units of measurement.3. Convert imperial units:a. feet to inches and vice versa.b. square inches to square feet and vice versa.c.cubic inches to cubic feet and vice versa.d. cubic measures to gallons.C. Indirect Measurement ProceduresOutcome: Apply indirect measurement procedures to solve problems. (1,2,3,4,5)1. Use concrete materials and diagrams to develop the Pythagorean relationship.2. Use the Pythagorean relationship to calculate the measure of the third side, of a right triangle, giventhe other two sides in 2-D applications.D. Area, Perimeter, Surface Area And VolumeOutcome:Generalize measurement patterns and procedures, and solve problems involvingarea, perimeter, surface area and volume. (1,2,3,4,5)1. Describe patterns, and generalize the relationships by determining the areas and perimeters ofquadrilaterals and the areas and circumferences of circles.2. Estimate, measure and calculate the surface area and volume of any right prism or cylinder.3. Estimate and calculate the area of composite figures.4. Estimate, measure and calculate the surface area of composite 3-D objects.5. Estimate, measure and calculate the volume of composite 3-D objects.E. Trigonometric RatiosOutcome: Use trigonometric ratios to solve problems involving a right triangle. (1,2,3,4,5)1. Explain the meaning of sine, cosine and tangent ratios in right triangles.Classification: Protected A10

MATHEMATICS2. Demonstrate the use of trigonometric ratios (sine, cosine and tangent) in solving right triangles.3. Calculate an unknown side or an unknown angle in a right triangle, using appropriate technology.4. Model and then solve given problem situations involving only one right triangle.F. Problem Solving Involving Dimension Changes In Two And Three Dimensional ObjectsOutcome: Describe the effects of dimension changes in related 2-D shapes and 3-D objects insolving problems involving area, perimeter, surface area and volume. (1,2,3,4,5)1.Relate expressions for volumes of pyramids to volumes of prisms, and volumes of cones to volumes ofcylinders.2.Calculate and apply the rate of volume to surface area to solve design problems in three dimensions.3.Calculate and apply the rate of area to perimeter to solve design problems in two dimensions.SECTION SEVEN. 3-D OBJECTS AND 2-D SHAPESA. Angle Measures And Properties Of Parallel LinesOutcome: Link angle measures to the properties of parallel lines. (1,2,3,4,5)1. Measure and classify pairs of angles as complementary or supplementary angles.2. Investigate, identify and name pairs of angles pertaining to parallel lines and transversals, including:corresponding, vertically opposite, interior on the same side of the transversal, and exterior on thesame side of the transversal.)3. Describe the relationships between the pairs of angles pertaining to parallel lines and transversals.4. Explain, in more than one way, why the sum of the measures of the angles of a triangle is 18 .5. Use mathematical reasoning to determine the measures of angles in a diagram.6. Construct angle bisectors and perpendicular Bisectors.B. Angle Measures., Properties Of Parallel Lines And Properties Of QuadrilateralsOutcome:Link angle measures and the properties of parallel lines to the classification andproperties of quadrilaterals. (1,2,3,4,5)1. Identify, investigate and classify quadrilaterals, regular polygons and circles, according to theirproperties.2. Build 3-D objects from a variety of representations (nets, skeletons).C. Similar And Congruent TrianglesOutcome:Specify conditions under which triangles may be similar or congruent, and usethese conditions to solve problems. (1,2,3,4,5)1. Recognize when, and explain why, two triangles are similar, and use the properties of similartriangles to solve problems.2. Recognize when, and explain why, two triangles are congruent, and use the properties of congruenttriangles to solve problems.3. Relate congruence to similarity in the context of triangles.Classification: Protected A11

MATHEMATICSD. Describe And Analyze Geometric ShapesOutcome:Use spatial problem solving in building, describing and analyzing geometricshapes. (1,2,3,4,5)1. Draw the plan and elevations of a 3-D object from sketches and models.2. Sketch or build a 3-D object, given its plan and elevation views.3. Recognize and draw the locus of points in solving practical problems.E. Problem Solving Using Polygons And VectorsOutcome:Solve problems involving polygons and vectors, including both 3-D and 2-Dapplications. (5)1. Use and give 2D and 3D examples of vector terminology and notation including: vector direction &magnitude, scalar, unit vector, collinear vectors, opposite vectors, parallel vectors, resultant vectors.2. Assign meaning to the multiplication of a vector by a scalar.3. Perform vector addition and subtraction using triangle or parallelogram methods.4. Determine the magnitude and direction of a resultant vector, using triangle, parallelogram orcomponent methods.5. Use vector diagrams and trigonometry to analyze and solve practical problems in 2D and 3D.SECTION EIGHT . TRANSFORMATIONSA. Create And Analyse Patterns And DesignsOutcome:Create and analyze patterns and designs, using congruence, symmetry,translation, rotation and reflection. (1,2,3,4,5)1. Create, analyze and describe designs, using translations (slides), rotations (turns) and reflections(flips).2. Use informal concepts of congruence to describe images after translations, rotations andreflections.3. Draw designs, using ordered pairs, in all four quadrants of the coordinate grid, together withtranslation and reflection images.4. Relate reflections to lines and planes of symmetry.B. Architectural PatternsOutcome:Create and analyze design problems and architectural patterns, using theproperties of scaling, proportion and networks. (1,2,3,4,5)1. Represent, analyze and describe enlargements and reductions.2. Draw and interpret scale diagrams and colouring problems.3. Describe, analyze and solve network problems.C. Geometry And Pattern RecognitionOutcome:Classification: Protected AApply coordinate geometry and pattern recognition to predict the effects oftranslations, rotations, reflections and dilatations on 1-D lines and 2-D shapes.(1,2,3,4,5)12

MATHEMATICS1. Draw the image of a 2-D shape as a result of a single transformation, dilatation, combinations oftranslations, and/or reflections.2. Identify the single transformation that connects a shape with its image.3. Demonstrate that a triangle and its dilatation image are similar.4. Demonstrate the congruence of a triangle with its translation image, rotation image, and reflectionimage.SECTION NINE . STATISTICS AND PROBABILITYA. Data AnalysisOutcome:Develop and implement a plan for the collection, display and analysis of data,using measures of variability and central tendency. (5)1. Formulate questions for investigation, from a real-world context.2. Select, defend and use appropriate methods of collecting data; designing and using questionnaires,interviews, experiments, research.3. Describe issues to be considered when collecting data.4. Display data by hand or by computer in a variety of ways, including circle graphs.5. Read and interpret graphs.6. Determine measures of central tendency for a set of data: mode, median, mean.7. Determine measures of the distribution of a set of data: range, extremes, gaps and clusters,quartiles.8. Interpolate from data to make predictions.B. Plan For The Collection, Display And Analysis Of DataOutcome:Develop and implement a plan for the collection, display and analysis of data,using technology, as required. (5)1. Formulate questions for investigation, using existing data.2. Select, use and defend appropriate methods of collecting data; designing and using surveys,research, using electronic media.3. Display data by hand or by computer in a variety of ways, including box and whisker plots.C. Evaluate And Use MeasuresOutcome:Evaluate and use measures of central tendency and variability. (5)1. Determine and use the most appropriate measure of central tendency in a given context.2. Describe the variability of data sets, using such techniques as range, and box and whisker plots.3. Construct sets of data given measures of central tendency and variability.4. Determine the effect on the mean, median and/or mode when a constant is added or subtractedfrom each value; each value is multiplied or divided by the same constant; and a significantlydifferent value is included.Classification: Protected A13

MATHEMATICSD. Collect And Analyse Experimental DataOutcome:Collect and analyze experimental results expressed in two variables, usingtechnology, as required. (5)1. Design, conduct and report on an experiment to investigate a relationship between two variables.2. Create scatter plots for discrete and continuous variables.3. Interpret a scatterplot to determine if there is an apparent relationship.4. Determine the lines of best fit from a scatterplot for an apparent linear relationship, by inspectionand using technology (equations are not expected).5. Draw and justify conclusions from the line of best fit.6. Assess the strengths, weaknesses and biases of samples and data collection methods.7. Critique ways in which statistical information and conclusions are presented by the media and othersources.E. Chance And UncertaintyOutcome:Create and solve problems, using probability. (5)1. Use a table to identify all possible outcomes of two independent events.2. Create and solve problems, using the numerical definition of probability as favourable outcomesdivided by possible outcomes.3. Use the Monte Carlo simulation method to solve probability problems. (5)F. Theoretical And Experimental ProbabilityOutcome:Compare theoretical and experimental probability of independent events. (5)1. Use computer or other simulations to solve probability and data collection problems.2. Recognize that if n events are equally likely the probability of any one of them occurring is 1/n.3. Determine the probability of two independent events where the combined sample space has 52 orfewer elements.4. Predict population characteristics from sample data.G. Complex Problems Using Probability And StatisticsOutcome:Explain the use of probability and statistics in the solution of complex problems.(5)1. Recognize that decisions based on probability may be a combination of theoretical calculations,experimental results and subjective judgments.2. Demonstrate an understanding of the role of probability and statistics in society.3. Solve problems involving the probability of independent events.Classification: Protected A14

ENTRANCE LEVEL COMPETENCIES IN SCIENCE(Numbers in parentheses indicate which Entrance Examination(s) test for this competency)SECTION ONE: . PHYSICSA. Electricity And Magnetism Materials And SafetyOutcome:Demonstrate safe methods for the study of magnetism and electricity, identifymethods for measurement and control, and apply techniques for evaluatingmagnetic and electrical properties of materials. (1,2)1. Recognize and appreciate the potential dangers involved in using sources of electrical currents;understand that household electrical currents are potentially dangerous and not a suitable sourcefor experimentation; understand that small batteries are a relatively safe source of electricity, forexperimentation and study, but that care should be taken to avoid short circuits; understand thatshort circuits may cause wires to heat up, as well as waste the limited amount of energy in batteries.2. Describe and demonstrate example activities that show that electricity and magnetism are related;demonstrate that electricity can be used to create magnetism; demonstrate that a moving magnetcan be used to generate electricity.3. Demonstrate and interpret evidence of magnetic fields around magnets and around current-carryingwires, by use of iron filings or by use of one or more compasses.4. Demonstrate that a continuous loop of conducting material is needed for an uninterrupted flow ofcurrent in a circuit.5. Distinguish electrical conductors from insulators.6. Recognize and demonstrate that some materials, including resistors, are partial conductors ofelectricity.7. Predict the effect of placing an electrical resistance in a simple circuit.8. Recognize that the amount of electricity we use is measured in kilowatt-hours.9. Interpret and explain the reading on a household electrical meter and efficiency labels on electricalappliances.10. Draw and interpret, with guidance, circuit diagrams that include symbols for switches,

requirements of the relevant trade in Alberta. Classification: Protected A 4 ENTRANCE LEVEL COMPETENCIES IN MATHEMATICS (Numbers in parentheses indicate which Entrance Examination(s) test for this competency)