Math 20-1 Help, Built for Alberta's Curriculum

Math 20-1 curriculum: 6 units, 45 lessons (Alberta Mathematics 20-1)

Unit 1: Quadratic Functions & Equations

Vertex and standard form, factoring, completing the square, and the quadratic formula.

• Function Review
• 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.
• X-Intercepts & Writing Quadratic Equations
• 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: Linear Functions & Systems of Equations

Linear-quadratic and quadratic-quadratic systems, plus linear and quadratic 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 and Series

Arithmetic and geometric sequences and series, infinite geometric series, and sigma notation.

• 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

Angles in standard position, exact values and the unit circle, and the sine and cosine laws.

• Pythagorean Theorem, Primary Trig Ratios & Solving Right Triangles
• 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
• 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 and Equations

Simplifying, combining and rationalizing radicals, and solving radical 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 and 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 and 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 and Equations

Simplifying rational expressions, non-permissible values, rational equations, and reciprocal functions.

• Operations with Fractions & Reducing Rational Expressions
• Non-Permissible Values & Simplifying Rational Expressions
• 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 is Math 20-1 in Alberta?

Math 20-1 is Alberta's pre-calculus stream for Grade 11. It follows Math 10C, runs through quadratics, systems and inequalities, sequences and series, trigonometry, radicals, and rational expressions, and it is the required stepping stone to Math 30-1. It is the more algebra-intensive of the two Grade 11 academic streams.

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

They lead to different Grade 12 courses. Math 20-1 is the pre-calculus route and the only way into Math 30-1, which calculus-based programs like engineering, computer science and most sciences require. Math 20-2 leads to Math 30-2, which satisfies programs that don't need calculus. Choose based on the admission requirements of programs you're considering.

Does Math 20-1 lead to Math 30-1?

Yes, Math 20-1 is the prerequisite for Math 30-1. University admission requirements name 30-level courses rather than 20-level ones, but if your program wants Math 30-1, you have to come through 20-1 first, so the mark and the habits you build here matter more than most students expect.

What units does Math 20-1 cover?

Six units: Quadratic Functions & Equations, Systems of Equations & Inequalities, Sequences & Series, Trigonometry, Radical Expressions & Equations, and Rational Expressions & Functions. On Studyio that's 44 lessons, each with a voice-over walkthrough, worked examples, and a practice quiz with step-by-step solutions.

Will this help with the Math 20-1 final exam?

Yes. There's no provincial exam for Math 20-1, so the school final carries the weight, and it usually samples the whole course. Studyio's unit quizzes and final-exam-style practice cover every unit with instant feedback, so you can rehearse the full course before exam week instead of cramming it.

Can Studyio plan my studying for a Math 20-1 test?

Yes. Add a unit test or the final exam, its date and the units it covers, and pick the days you can study. Studyio builds a study plan, a day by day list of the Math 20-1 lessons, quizzes and practice tests to do before then, recommends how many minutes a day will finish everything with a few days kept free, and reshuffles on its own if you miss a day. Free accounts can plan one test; Pro plans every test.

Do I need a credit card to start the trial?

Starting the 7-day trial does ask for a card, because the trial is set up through Stripe, but no charge happens until the trial is over and you can cancel before then in a couple of clicks. Prefer no card? The free version requires no payment details.

What's the difference between the free version and the trial?

The free version is 5 lessons of your choosing plus 5 quiz attempts, with step-by-step solutions and limited access to Ms. Emma, the AI tutor. The 7-day trial opens up everything Pro offers: all 44 Math 20-1 lessons, unlimited quizzes, unit tests and final exam practice, and unlimited Ms. Emma.