Study Plan A

Every property on Monday’s list comes from one fact, which is exactly what the learning target is asking you to say: water is polar, so its molecules stick to each other with hydrogen bonds.

Oxygen pulls the shared electrons harder than hydrogen does, so the oxygen end is slightly negative and the hydrogen ends slightly positive. Opposite ends of neighbouring molecules attract. That is the whole mechanism — now read the five properties as five results of it:

• Cohesion — water sticks to water. Hydrogen bonds pulling inward.
• Adhesion — water sticks to other polar surfaces. Same bonds, different partner. Cohesion + adhesion together pull water up a narrow tube (capillary action), which is how a tree moves water to its leaves.
• Surface tension — molecules at the surface have no neighbours above, so the inward pull is unbalanced and the surface behaves like a skin. A water strider stands on it.
• High specific heat — you must break hydrogen bonds before the molecules can speed up, so water absorbs a lot of energy for a small temperature rise. This is why lakes and bodies buffer temperature swings.
• High heat of vaporization — escaping as vapour means breaking all a molecule’s hydrogen bonds, which takes a lot of energy and carries it away. This is why sweating cools you.

The exam move: if a question asks “why does water do X”, the answer almost always ends at hydrogen bonding. Say polarity → hydrogen bonds → the property → the consequence for life.

Oops! Cohesion and adhesion get swapped constantly. Cohesion = companions, water to water. Adhesion = adhesive, water to something else.

Water splits, very slightly, into H⁺ and OH⁻. pH is just a way of writing how much H⁺ is present without using tiny decimals.

pH = −log[H⁺]. Read that backwards and it is easier: pH 3 means [H⁺] = 10⁻³ M.

• pH < 7 acidic (more H⁺) · pH = 7 neutral · pH > 7 basic (more OH⁻)
• The scale is logarithmic: each whole step is a factor of 10.

Worked example. How much more acidic is pH 4 than pH 6? Two steps → 10 × 10 = 100 times more H⁺. Not “twice”, and not “20”.

Worked example. A solution has [H⁺] = 10⁻⁹ M. pH = 9, so it is basic.

Connect it back to Monday: pH exists because water is polar enough to ionise at all, and buffers matter to life because enzymes only work in a narrow pH band.

Oops! Because of the minus sign, lower pH = more H⁺ = more acidic. A pH of 2 is stronger acid than a pH of 5, even though 2 is the smaller number.

Your teacher named the sections rather than the topics, so read them first. In almost every text, that span runs: atoms and bonding (2.1) → water and its properties (2.2) → pH, acids, bases and buffers (2.3). Monday and Wednesday map onto the second and third of those, which means 2.1 is the part no class period covered directly — bonding types, ionic vs covalent, and why polarity happens at all.

If you have one hour, spend it: 20 minutes on 2.1 bonding, 20 minutes re-deriving the five water properties from polarity, 20 minutes on pH arithmetic.

A power function is a single term: f(x) = kx^p. A polynomial is a sum of power functions with whole-number exponents. Everything in 3.1 is about reading a polynomial’s shape without plotting it.

Only two things decide what the graph does at the far left and far right — the degree (highest exponent) and the sign of the leading coefficient:

• Even degree, positive lead — both ends up. (x², x⁴: a bowl.)
• Even degree, negative lead — both ends down.
• Odd degree, positive lead — down on the left, up on the right. (x³.)
• Odd degree, negative lead — up on the left, down on the right.

Worked example. f(x) = −2x³ + 5x² − 1. Degree 3 (odd), lead −2 (negative) → up on the left, down on the right. Notice the 5x² and the −1 had no say: only the leading term survives at the extremes.

Two more counts worth memorising for a degree-n polynomial: at most n x-intercepts, and at most n − 1 turning points.

Oops! The degree is the highest exponent after you have written the polynomial in standard form — not the exponent of the first term you happen to see. In 4x + 7x⁵ − 2, the degree is 5.

Every quadratic is the same parabola written three ways. Choosing the right form is the skill.

• Standard f(x) = ax² + bx + c — c is the y-intercept, free.
• Vertex f(x) = a(x − h)² + k — vertex (h, k), free.
• Factored f(x) = a(x − r₁)(x − r₂) — x-intercepts r₁, r₂, free.

From standard form the vertex is at x = −b/2a, then substitute back for y.

Worked example. f(x) = 2x² − 12x + 7. x = −(−12)/(2·2) = 3. f(3) = 18 − 36 + 7 = −11. Vertex (3, −11), opening up because a = 2 > 0, so −11 is the minimum.

Completing the square, same example. 2(x² − 6x) + 7 → 2(x² − 6x + 9 − 9) + 7 → 2(x − 3)² − 18 + 7 → 2(x − 3)² − 11. Same vertex, now readable straight off.

Oops! Watch the sign in vertex form: a(x − h)² + k means f(x) = (x + 4)² has h = −4, so the vertex is at x = −4, not +4.

The target asks about rhetorical choices, not who was right. Both sides preached from scripture to congregations who already accepted its authority — so the interesting question is which appeals each side reached for.

The Loyalist case leans on Romans 13 (“let every soul be subject unto the higher powers”), on order against chaos, and on oaths already sworn. Rhetorically it is heavy on ethos (established authority, the minister’s office) and on fear of consequence — rebellion as sin and as ruin.

The Patriot case leans on Exodus and the deliverance narrative, on covenant and on liberty as a gift that may be defended. Rhetorically it is heavy on pathos and on redefinition — arguing that obeying God is resisting an unjust magistrate, which reframes the Loyalist proof text rather than denying it.

That reframing move is the thing to name in your notes. The strongest counter-argument rarely rejects the opponent’s evidence; it accepts the evidence and disputes what it means.

A counter-argument paragraph that earns credit does four things in order. Practise on the sermons:

1. State the opposing claim fairly — in its strongest form, not a weak version. (“Loyalist ministers argued that Romans 13 forbids armed resistance to a lawful king.”)
2. Concede what is true — this buys you credibility. (“Scripture does command submission to governing authority.”)
3. Pivot — one word does the work: however, yet, but.
4. Show why your reading survives anyway — the actual argument.

Oops! The most common loss of marks is a straw man: summarising the other side so weakly that beating it proves nothing. If your opponent would not recognise their own view in your sentence, rewrite it.

You are reading toward a final project on themes, so read with a pen. These four chapters are the turn of the whole book.

• Ch. 20 “The Minister in a Maze” — Dimmesdale, having decided to flee, finds every impulse in him suddenly wicked. Watch how freedom from concealment reads as temptation, not relief.
• Ch. 21–22 “The New England Holiday” / “The Procession” — the whole town on display. Note the gap between public ceremony and private knowledge; it is the book’s central irony, staged.
• Ch. 23 “The Revelation of the Scarlet Letter” — the confession. Note who is released by it and who is not.

For a themes project, the three that pay: concealment vs. confession (and what each costs the body), public identity vs. private self, and whether the scarlet letter’s meaning is fixed or made by the community.

This target is listed on both posted rows, which usually means it is the essay hinge. The passage’s argument is short: “You were called to freedom… only do not use your freedom as an opportunity for the flesh, but through love serve one another.”

So liberty here is defined against two opposites, not one:

• not bondage — being compelled; and
• not licence — doing whatever one wants.

True liberty is freedom for something — self-restraint chosen rather than imposed. That is the bridge to the founding-era material: the argument that a free people must be a virtuous people, because a republic removes external compulsion and has to replace it with internal restraint.

Essay shape that works: define liberty against both opposites → show a founding-era voice making the same move → apply it to a concrete Unit 1 event → say what follows.

Oops! An essay that defines liberty only as “freedom from tyranny” answers half the prompt. The Galatians framing is specifically about the second danger.

Thursday asks for 4 individuals and 7 events in any format but a timeline — so learn it as a chain, which is easier to retell anyway.

Cause: British colonial expansion meets French forts in the Ohio River valley; both claim it, Native nations hold it and ally strategically.

Chain: disputed Ohio country → Washington’s 1754 skirmish and surrender at Fort Necessity → Braddock’s defeat 1755 → war widens into the global Seven Years’ War → Pitt commits resources and Britain turns it around → Quebec falls 1759 → Treaty of Paris 1763, France out of mainland North America.

Consequence — the part that matters for the next unit: Britain wins the continent and inherits an enormous war debt plus a frontier to garrison. That produces the Proclamation of 1763 and then the taxes. The war that removed the French threat is what made colonists dispensable to Britain and Britain intolerable to colonists.

Individuals worth having ready: George Washington, Edward Braddock, William Pitt, and Pontiac.

The posted spec repeats four required parts per page: a prayer, a scripture, a summary of that scripture, and a picture. The summary is the part people skip and lose marks on — it is the only place the booklet shows you understood the verse rather than just liked it.

A structure that fills ten pages without repeating itself is to give the booklet a shape — for example one page each for: praise, thanks, confession, asking for others, asking for yourself, guidance, hard days, gratitude for a specific person, a psalm you return to, and a closing blessing. Ten categories, ten pages, no page competing with another.

For each summary, one sentence answering “what is this verse actually saying?” in your own words beats three sentences of quotation.