ENAF

Grade 11 Mathematics

Choose a topic to learn how to identify which question type is being asked.

Paper 1

Algebra Equations Inequalities
- Solving a quadratic equation: "Solve for x", "Find the roots", "For which values of x"
- Completing the square: "Write in the form (x + a)² + b", "Express in the form..."
- Simultaneous equations: "Solve simultaneously", two equations are given
- Inequalities: "For which values of x is...", answer required in interval notation
- Nature of roots (discriminant): "Show that... has real/unequal/equal roots", "Determine the nature of the roots", "For which values of k will..."
- Word problems (disguised algebra): No x is given, you must define the variable yourself
Patterns Sequences
- Arithmetic sequences: "Linear pattern" (the term DBE actually uses, instead of "arithmetic sequence"), "constant difference", "Determine the general term, Tn"
- Quadratic sequences: "Quadratic pattern" (the term DBE uses), "second difference is constant"
- Identify the type of pattern first: No label given, the question doesn't say "linear" or "quadratic"
Finance Growth Decay
- Simple interest / simple decay: "Simple interest", "straight-line depreciation", "interest is not compounded"
- Compound interest / compound decay: "Compound interest", "compounded annually/monthly", "the value depreciates by r% of its value each year"
- Nominal vs effective interest rates: "Nominal annual interest rate", "effective annual interest rate", "compounded monthly/quarterly"
- Combination growth and decay (two-phase) problems: "...for the first n years... thereafter...", a value that grows for one period then changes rate or type partway through
Functions Graphs
- x- and y-intercepts: "Determine the x-intercept(s)", "Calculate the coordinates of A and B", "Where does the graph cut the y-axis?"
- Turning point of a parabola: "Determine the coordinates of the turning point", "the minimum/maximum value of f"
- Asymptotes (hyperbola and exponential graphs): "Write down the equations of the asymptotes", "the equation of the horizontal/vertical asymptote"
- Determining the equation of a function from its graph: "Determine the equation of f", "Determine the values of a, p and q"
Probability
- Venn diagrams: "Draw a Venn diagram", "represented on the Venn diagram", overlapping circles already given
- Mutually exclusive and complementary events: "Mutually exclusive", "complementary events", "P(not A)"
- Independent events: "Independent events", "Show that A and B are independent", "with replacement"
- Tree diagrams and contingency tables for dependent events: "Without replacement", "Draw a tree diagram", a two-way table of results is given

Paper 2