# Quantitative Assessment Topics

The following list of objectives was developed during the designing of the SFU’s Quantitative Placement Test. The purpose of the test is to determine whether incoming students have the necessary background to succeed in the “Q” courses they will be taking.

We placed an objective on the list below if it satisfied two criteria: 1) it was stated or implied in the B.C. high school curriculum documents; and 2) the objective is relevant for courses offered under the “Q” designation at SFU.

Some of the objectives are quite general, while others are more specific. In an effort to keep the list to a manageable number, we have attempted to refrain from being very specific except in those areas where experience suggests such specificity would be helpful.

The actual test has 30 questions, and will therefore only cover a subset of the list. However, we anticipate that the assessment test will evolve and change as time goes on, and we included items as objectives whether or not they appear on the first version of the test. Some test questions may be randomly drawn from a pool of possible questions of comparable difficulty but covering different objectives on the list.

1. Use fractions, decimals, and percents to solve problems;
2. Display skills such as simplifying a complex fraction and finding a percent equivalent to two or more sequentially applied percents;
3. Compare and order fractions, decimals, and percents and find their appropriate locations on a number line;
4. Interpret percent values greater than 100%;
5. Use ratios and proportions to represent quantitative relationships;
6. Solve problems involving proportions, such as scaling and finding equivalent ratios;
7. Use factors, multiples, prime factorization, and relatively prime numbers to solve problems;
8. Use arithmetic operations with fractions, decimals, and integers appropriately, as required in a given context;
9. Recognize connections among the operations of arithmetic;
for example, that certain operations are inverses of each other;
10. Apply rules of arithmetic operations (commutative, associative and distributive properties) correctly;
11. Use the correct order of operations in situations where more than one operation is performed;
12. Interpret exponential notation and use laws of exponents for variables with integer exponents;
13. Estimate the results of numerical computations and judge the reasonableness of the results;
14. Verify the reasonableness of numerical computations and their results in a given context using an appropriate number of significant digits;
15. Recognize and generalize numerical, geometrical, and other patterns;
16. Plot linear and non-linear data, using appropriate scales;
17. Given a verbal, graphical, or algebraic representation of a relationship, express it in a different form as required;
18. Determine whether a relationship is a function;
19. Distinguish among linear, exponential, and power functions;
20. Compare linear and non-linear functions with respect to their rates of change;
21. Interpret the meaning of intercept and slope of a linear function in a given context;
22. Interpret the meaning of the intercepts and vertex of the graph of a quadratic function in a given context;
23. Translate a verbal statement into algebraic language;
24. Translate an algebraic statement into words;
25. Evaluate algebraic expressions for specified values of the variables, including cases where a variable may take on negative or fractional values, and recognize that -x does not have to be negative and 1/x might be greater than 1.
26. Generate and/or recognize equivalent forms of expressions, equations, inequalities, and relations;
27. Determine any non-permissible values for the variable in an algebraic expression;
28. Solve linear equations and inequalities, and systems of linear equations;
29. Solve quadratic and rational equations;
30. Solve linear equations and inequalities involving absolute value;
31. Solve a literal equation for a specified variable, including cases when one or more variable(s) is (are) negative;
32. Model and solve contextualized problems using various representations, such as graphs, tables, and equations;
determine whether or not the results obtained fit the original context;
33. Recognize and apply properties of parallel and perpendicular lines;
34. Determine whether a given two-dimensional figure is a polygon;
classify polygons according to the number of sides and how their sides and angles are related;
35. Recognize and apply properties of isosceles and equilateral triangles;
36. Recognize and apply the property that the sum of the angle measures in a triangle is 180 degrees;
37. Classify three-dimensional objects with respect to the nature and number of their faces and angles;
38. Apply properties of three-dimensional objects such as prisms, pyramids, spheres, cylinders or cones in problem solving;
39. Recognize that if geometric objects are similar, then angle measures are preserved and side lengths are proportional;
40. Given two similar geometric figures in a specified ratio, determine the ratios of their perimeters, areas, or volumes;
41. Solve problems involving ratio and proportion in similar triangles;
42. Use congruence and similarity to solve problems involving classes of two- and three-dimensional geometric objects;
43. Use the Pythagorean Theorem to solve problems involving right triangles in various contexts;
44. Describe sizes, positions, and orientations of shapes under transformations such as flips, turns, slides, and scaling;
45. Use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume in problem solving;
46. Determine the circumference/perimeters and the area of triangles, parallelograms, trapezoids, and circles;
47. Determine the surface area and volume of selected prisms, pyramids, spheres and cylinders;
48. Decompose complex shapes into simpler ones to find areas or volumes;
49. Solve problems involving perimeter and area of two-dimensional geometric figures;
50. Solve problems involving surface area, and volume of three-dimensional geometric figures;
51. Solve simple problems involving rates and derived measurements for such attributes as velocity and density;
52. Use graphical representations of data to solve problems;
53. Find, use, and interpret mean, weighted mean, or median as appropriate in the context of a given problem;
54. Use principles of probability to make and test conjectures about the results of experiments and simulations;
55. Compute probabilities for compound events;
56. Construct sample spaces and distributions in simple cases;
57. Use the concepts of conditional probability and independent events in problem solving;
58. Differentiate between inductive and deductive reasoning;
59. Interpret and correctly use connecting words, such as “and”, “or”, and “not”;
60. Use examples and counterexamples to analyze conjectures;
61. Distinguish between “if-then” and “if and only if” statements;
62. Determine whether two statements are logically equivalent;
63. State and interpret correctly the negation of a given statement;
64. Analyze the validity of an argument.
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