Math 20-1: Alberta Curriculum & Final Exam Prep

Math 20-1 curriculum: 6 units, 44 lessons (Alberta Mathematics 20-1)

Unit 1: Quadratic Functions & Equations

• Introduction to Quadratic Functions, Meet the parabola, the curve at the heart of Math 20-1 — explore a quadratic's vertex, axis of symmetry, direction of opening, and range.
• Properties & Transformations of Quadratic Functions, Graph parabolas from vertex form y = a(x − p)² + q, reading how a, p, and q stretch, reflect, and slide the basic curve around the grid.
• Standard Form, Work with standard form y = ax² + bx + c and complete the square to rewrite it in vertex form, pinning down the vertex without a graph.
• Number of X-Intercepts & Writing Quadratic Functions, Predict how many x-intercepts a parabola has, then reverse the process — write a quadratic function from its zeros or its vertex and a point.
• Factoring Review, Sharpen the factoring toolkit Math 20-1 leans on — common factors, difference of squares, and trinomials of the form ax² + bx + c.
• Solving by Factoring, Solve quadratic equations by factoring — rewrite as a product, set each factor equal to zero, and read the roots straight off.
• Completing the Square, Turn a quadratic equation into a perfect square equal to a constant, then square-root both sides for exact answers — no formula required.
• The Quadratic Formula & Nature of the Roots, The quadratic formula solves any quadratic equation, and the discriminant b² − 4ac predicts two distinct, one repeated, or no real roots.
• Applications of Quadratics, Model area, revenue, and projectile-height problems with quadratics, using the vertex to nail down the maximum or minimum value.

Unit 2: Systems of Equations & Inequalities

• Linear Functions & Systems of Equations Review, Refresh slope, graphing lines, and the substitution and elimination methods — groundwork before Math 20-1 mixes lines with parabolas.
• Solving Systems of Equations Graphically, Graph a line and a parabola on the same grid and read solutions from the intersection points — systems can cross twice, once, or never.
• Solving Linear-Quadratic Systems Algebraically, Substitute the line into the parabola to solve linear-quadratic systems exactly, and let the resulting quadratic reveal how many intersections exist.
• Solving Quadratic-Quadratic Systems Algebraically, Find where two parabolas meet by setting the quadratics equal or eliminating a term, then solving and verifying each point of intersection.
• Linear Inequalities in One Variable, Isolate the variable in a linear inequality, reverse the sign when multiplying or dividing by a negative, and graph the solution on a number line.
• Linear Inequalities in Two Variables, Graph the boundary line solid or dashed, then use a test point to decide which half-plane to shade for a two-variable linear inequality.
• Quadratic Inequalities in Two Variables, Shade above or below the parabola to represent a two-variable quadratic inequality, letting a test point confirm the correct region.
• Quadratic Inequalities in One Variable, Solve quadratic inequalities in one variable — find the roots, break the number line into intervals, and test a value from each.
• Applications of Quadratic Inequalities, Translate word problems into quadratic inequalities, solve for the acceptable interval, and state the range of values that fits the context.

Unit 3: Sequences & Series

• Arithmetic Sequences, Spot the common difference, write the general term, and find any term or its position in an arithmetic sequence.
• Arithmetic Series, Add up an arithmetic series two ways — one sum formula uses the last term, the other the common difference — and learn when each shines.
• Geometric Sequences, Identify the common ratio of a geometric sequence and build its general term to reach any term in a doubling or decaying pattern.
• Geometric Series, Compute the sum of a geometric series with the ratio-based formula, watching signs carefully when r is negative.
• Infinite Geometric Series, An infinite geometric series converges only when |r| < 1 — test the ratio first, then compute the exact sum in one step.
• Sigma Notation, Read and write sigma notation — unpack the index and limits to expand a sum, or compress a long series into one compact expression.

Unit 4: Trigonometry

• Pythagorean Theorem & Trigonometric Ratios, Revisit the Pythagorean theorem and the sine, cosine, and tangent ratios — the right-triangle toolkit all Grade 11 trig builds on.
• Angles in Standard Position, Draw angles in standard position — initial arm on the positive x-axis, terminal arm rotating — and find coterminal angles by adding or subtracting 360°.
• Exact Values of Trig Ratios / CAST, Use the CAST rule to track which trig ratios stay positive in each quadrant and state exact values without touching a calculator.
• Special Triangles, Build the 30-60-90 and 45-45-90 triangles from scratch and read exact sine, cosine, and tangent ratios directly from their sides.
• The Unit Circle & Trigonometric Reciprocals, The unit circle turns angles into coordinates — cosine as x, sine as y — and introduces the reciprocal ratios cosecant, secant, and cotangent.
• The Sine Law & The Cosine Law, Solve triangles with no right angle: the sine law pairs each side with its opposite angle, while the cosine law covers SAS and SSS cases.
• Applications, Navigate bearings and distance problems — sketch the scenario, choose sine law or cosine law, and solve for the missing side or angle.
• The Ambiguous Case, The ambiguous case of the sine law: SSA information can produce two triangles, one, or none — learn to catch the second possible angle.

Unit 5: Radical Expressions & Equations

• Working with Radical Expressions, Convert between entire and mixed radicals, simplify by factoring out perfect powers, and order radical expressions from least to greatest.
• Adding & Subtracting Radical Expressions, Combine like radicals the way you combine like terms — simplify each term first, so √8 and 3√2 become like radicals.
• Multiplying & Dividing Radical Expressions, Multiply radical expressions by pairing coefficients together and radicands together, then divide and simplify the result completely.
• Rationalizing the Denominator, Clear radicals out of a denominator — multiply by the radical itself for one-term denominators, or by the conjugate for binomials.
• Solving Radical Equations, Isolate the radical, square both sides, and solve — then check every answer, since squaring can smuggle in extraneous roots.

Unit 6: Rational Expressions & Functions

• Review & Preview, A checkpoint before rational expressions: brush up on factoring and fraction operations, then preview where Math 20-1 takes them next.
• Simplifying Rational Expressions & Non-Permissible Values, Factor, cancel, and state the non-permissible values — the x-values that would make a rational expression's denominator zero.
• Multiplying & Dividing Rational Expressions, Multiply rational expressions by factoring and cancelling first; to divide, flip the second fraction and keep tracking non-permissible values.
• Adding & Subtracting Rational Expressions, Build the lowest common denominator from factored form, rewrite each rational expression over it, and combine the numerators carefully.
• Solving Rational Equations, Multiply every term by the lowest common denominator to clear the fractions, solve, and reject roots that land on non-permissible values.
• Applications of Rational Equations, Tackle work and rate problems with rational equations — combine two rates over a common denominator and solve for the unknown time.
• Reciprocal Functions, Sketch reciprocal functions such as y = 1/x — vertical and horizontal asymptotes, two branches, and invariant points where y is 1 or −1.

Frequently asked questions

What's the difference between Math 20-1 and Math 20-2?

Math 20-1 is Alberta's pre-calculus stream for Grade 11, more algebra-heavy, and the only route to Math 30-1. Math 20-2 leads to Math 30-2 and suits programs that don't need calculus. Pick 20-1 if engineering, computer science, or most science programs are on your radar.

Do universities require Math 20-1?

Not directly. University admission requirements name 30-level courses, not 20-level ones. But if your program requires Math 30-1 (common for engineering, computer science, and science), you need Math 20-1 first, because it's the prerequisite. Programs that accept Math 30-2 can be reached through Math 20-2 instead.

How many units are in Math 20-1?

Math 20-1 on Studyio has 6 units: Quadratic Functions & Equations, Systems of Equations & Inequalities, Sequences & Series, Trigonometry, Radical Expressions & Equations, Rational Expressions & Functions. That's 44 lessons in total, matching the Alberta curriculum from the first unit through exam review.

Is Studyio aligned to the Alberta curriculum?

Yes. Every Math 20-1 lesson on Studyio follows the Alberta Program of Studies: the same units, in the same order, they're taught in class. The course has 6 units and 44 lessons, each with a voice-over walkthrough, worked examples, and a practice quiz with step-by-step solutions.

Is Studyio free?

Yes. Studyio is free to start, with no credit card required. The free plan includes lesson access, unlimited quizzes, and step-by-step solutions. Pro, $7.99 a month or $73.99 a year after a 7-day free trial, unlocks unlimited Math 20-1 Final Exam practice and unlimited help from Ms. Emma, Studyio's AI tutor.