ACT

11:10 Topic 1 English: purpose, organisation and style Relevance asks whether a detail serves the paragraph's actual purpose. In a paragraph about queue manage… 11:09 Topic 2 English: conventions and punctuation Conventions depend on grammar, not a preferred sound. “The group of volunteers records outcomes” uses si… 4:29 Topic 3 Mathematics: models, functions and higher maths A complex conjugate changes the imaginary sign. The product of a plus b i times a minus b i equals a squ… 9:18 Topic 4 Reading: details, structure and integration A detail is directly stated; an inference joins clues. “The neighbour waited without complaint” does not… 10:30 Topic 5 Optional Science: data, investigations and models A controlled comparison changes the proposed cause while holding alternative causes fixed. An engineerin… 9:16 Topic 6 Optional Writing: perspectives and argument An argument needs a position, a reason and an explained connection. A counterargument tests the position… 4:27 Topic 7 Real numbers, rational powers and complex arithmetic A complex conjugate changes the imaginary sign. The product of a plus b i and a minus b i equals a squar… 3:30 Topic 8 Vectors and matrices as organised quantitative models A matrix uses labelled rows and columns. A quantity row, two comma three, and a price column, four comma… 4:07 Topic 9 Linear, quadratic and polynomial relationships An identity holds for every permitted input. Start with a x plus b equals c x plus d. Collect terms: ope… 3:48 Topic 11 Functions, composition, transformations and inverses Composition applies the inside rule first. If f of u equals one over u minus 2, and g of x equals x squa… 4:55 Topic 13 Trigonometric graphs, identities and general triangles Amplitude is half the peak-to-trough distance. In y equals A sine of B x plus D, it is the absolute valu… 5:51 Topic 14 Plane transformations, coordinate reasoning and proof Rigid motions preserve lengths and angles. A 90-degree anticlockwise rotation sends x, y to negative y, … 5:10 Topic 15 Conics, circle relationships and geometric measurement An ellipse, x minus h squared over a squared plus y minus k squared over b squared equals 1, has centre … 5:31 Topic 16 Data displays, normal distributions and association A frequency counts repeated observations. Values one, three, seven with frequencies two, one, one repres… 6:02 Topic 17 Sampling inference, expected value and counting A margin of error is added and subtracted in percentage points. Estimate 63% with margin 4 points gives … 3:20 Topic 18 Essential skills in a multi-step practical model A rate compares quantities with their units. Velocity equals distance divided by time, which is ninety k… 11:10 Topic 19 English: purpose, focus and argumentative support Relevance asks whether a detail serves the paragraph's actual purpose. In a paragraph about queue manage… 11:20 Topic 20 English: paragraph order, cohesion and introductions Cohesion makes each reference and relationship followable. Introduce an arrangement before writing “This… 11:03 Topic 21 English: precision, concision and consistent style Concision removes repetition while preserving meaning. “Recorded the outcomes and wrote the results down… 9:18 Topic 23 Reading: explicit detail, inference and relationships A detail is directly stated; an inference joins clues. “The neighbour waited without complaint” does not… 9:22 Topic 24 Reading: contextual meaning, structure and point of view Point of view limits access to motives. First-person narration tells us what the narrator notices and th… 7:00 Topic 25 Reading: arguments, paired texts and graphic evidence Integration uses each source for the claim it actually supports. A retrieval-time table can test a claim… 10:30 Topic 26 Science: research summaries, controls and engineering tests A controlled comparison changes the proposed cause while holding alternative causes fixed. An engineerin…