Math For Grade 7

Explore direct proportions with algebra by forming equations like y = kx, identifying k as the constant, and solving for x or y in cost and rides problems.

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Explore inverse proportions by linking speed to time, applying the unitary method and the X1Y1 = X2Y2 formula through taps filling a tank and workers painting houses.

solve inverse proportions with algebra by using x1y1 = x2y2 and the constant key method to find y2 when x changes, demonstrated with x1=10, y1=20 and x2=40.

Learn how inverse proportionality connects P and Q using P1Q1 = P2Q2 and the constant K method, then apply it to a shelter food problem to find remaining days.

Learn how to solve inverse proportional problems in algebra, derive the constant from before–after values, apply root-based variations, and practice with a dosage-time example.

Explore how to find the gradient of a straight line by analyzing x and y axes, coordinates, and rise-over-run methods, with examples illustrating positive and negative slopes.

Apply rise over run to determine horizontal and vertical line gradients. A horizontal line yields zero gradient, while a vertical line has an undefined gradient using points A and B.

Learn what a linear equation is, its two variables and straight-line graph, and how to write y = mx + c, identify gradient and y-intercept, and compute y from x.

Solve simultaneous linear equations using the elimination method to find the intersection point of two lines. Practice canceling a variable by matching coefficients and substituting to get x and y.

Learn to solve simultaneous linear equations using the substitution method, expressing one variable in terms of another, substituting into the other equation, and finding x and y.

Identify quadratic expressions in the form x^2 + Bx + C. Practice adding and subtracting them by combining like terms and handling bracket signs.

Multiply quadratic expressions by expanding the product, distributing each term across brackets, and combining like terms to form polynomials such as 12x squared minus 9x and 5x squared plus 13x.

Master factorization of quadratic expressions by simplifying first when possible, then using the product of the leading coefficient and constant term to factor by grouping.

This lecture shows two methods for factoring quadratic expressions, including the traditional ac method and a simpler middle-term split, with emphasis on accurate copying and practice.

Explore simplifying and expanding algebraic expressions with two variables, applying distributive law, combining like terms, and multiplying coefficients to obtain forms like x^2 + 6xy + 6y^2.

Learn to multiply algebraic expressions, expand binomials such as A+B with C+D, and simplify resulting polynomials while reviewing factorization and common expansion formulas.

Learn to factor algebraic expressions with multiple variables by applying a trick similar to quadratics, using first and last coefficients to form binomial factors in X and Y.

Learn to expand algebraic expressions using three formulas: (A+B)^2, (A−B)^2, and (A+B)(A−B), with practice problems and a final X and Y example.

Learn to factorise by reversing expansion using the three formulas for perfect squares. Identify the sign to choose the correct formula, and factor expressions into (a+b)^2, (a-b)^2, or (a+b)(a-b).

Learn to factorize algebraic expressions using the grouping method by pulling out common factors and rearranging terms to create grouped pairs, with step-by-step practice.

Explore functions as relations between domain and code domain, identify one-to-one mappings, and learn function notation F(X) and G(X) with evaluation and solving F(X)=G(X).

Explore congruence and similarity in geometry, applying translation, rotation, and reflection to test congruent figures and distinguish similar shapes by equal angles and proportional sides.

Learn to work with scales and grids to convert map distances to real sizes. Apply scale factors and similarity to find missing sides, such as 1:2 or 1:500.

Learn how sets in grade seven mathematics collect related elements, use ∈ and ∉ to denote membership, express sets with {…}, and perform union, intersection, and the empty set concept.

Explore how Venn diagrams visualize universal sets, complements, and basic set operations like union and intersection, with counting elements and using set notation in grade 7 math.

Explore intersection and union of sets using universal sets, Venn diagrams, and A and B notation, illustrating A ∩ B, A ∪ B, and complements.

Learn the basics of probability by defining the sample space and outcomes, and calculating probability as favorable outcomes over total outcomes. Apply it to coin flips, dice, and cards.

Apply probability formulas to real lecture examples, calculating favorable over total outcomes for letters in painting, vowels, and classroom scenarios to build practice.