Both courses, against the syllabus

Applications and Interpretation

78 of 78 sub-topics written.

Topic 1: Number and Algebra 15 of 15

• 1.1 · Each step along is ten times, not one more. shared
• 1.2 · The minus one is the whole formula. shared
• 1.3 · Same start, same second term, 51 times apart. shared
• 1.4 · It grew to 1628.89 and buys 1212.03 of things. shared
• 1.5 · A logarithm answers one question: what power? shared
• 1.6 · Each side is out by 4%. The area is out by 12%.
• 1.7 · Your first payment is 77.6% interest.
• 1.8 · A solution is where they cross.
• 1.9 HL · log x + log y is log(xy), never log(x + y).
• 1.10 HL · 16 to the power a half is 4.
• 1.11 HL · It bounces for ever and travels 18 metres.
• 1.12 HL · Multiplying by i is a quarter turn.
• 1.13 HL · Multiply the lengths, add the angles.
• 1.14 HL · AB and BA are different matrices.
• 1.15 HL · Two directions survive. The rest all swing.

Topic 2: Functions 10 of 10

• 2.1 · A gradient is not an angle shared
• 2.2 · The range is not the y-axis shared
• 2.3 · Sketch is an instruction, not a lesser draw shared
• 2.4 · A graph can cross its own asymptote shared
• 2.5 · Three points cannot choose the model
• 2.6 · The model is fine. The week you asked about is not
• 2.7 HL · The order is worth seven baht
• 2.8 HL · Stretch then shift is not shift then stretch
• 2.9 HL · Nothing grows for ever, so model the ceiling
• 2.10 HL · Which plot comes out straight tells you the model

Topic 3: Geometry and Trigonometry 16 of 16

• 3.1 · The triangle you need is hiding shared
• 3.2 · The angle your calculator cannot see shared
• 3.3 · The angle at the turn is neither bearing shared
• 3.4 · The number does not tell you which
• 3.5 · Every point on it is the same distance from both
• 3.6 · The middle is not the answer
• 3.7 HL · Put degrees in and you are out by 57
• 3.8 HL · Two triangles from the same three facts
• 3.9 HL · Same determinant, different transformation
• 3.10 HL · Three plus four is anything from one to seven
• 3.11 HL · One line, many equations
• 3.12 HL · The closest they ever get
• 3.13 HL · Zero is the answer, not a failure
• 3.14 HL · Count the handshakes, not the edges
• 3.15 HL · The diagonal is not zero
• 3.16 HL · Nearest neighbour is a bound, not an answer

Topic 4: Statistics and Probability 19 of 19

• 4.1 · Where the data came from shared
• 4.2 · The picture is a choice shared
• 4.3 · Where it sits, and how far it spreads shared
• 4.4 · A strong correlation is one point away from a weak one shared
• 4.5 · Counting outcomes, then testing the count shared
• 4.6 · Move the overlap and everything changes shared
• 4.7 · The expected value is where it balances shared
• 4.8 · Which bars does your event actually cover? shared
• 4.9 · The probability is the area, not the boundary shared
• 4.10 · One point moves. Only one of the two numbers cares.
• 4.11 · How different is different enough?
• 4.12 HL · Asking a question that does not answer itself
• 4.13 HL · When a line is the wrong shape
• 4.14 HL · Moving it does not spread it out
• 4.15 HL · The data stays skewed. The averages do not.
• 4.16 HL · 95% is a claim about the method, not your answer.
• 4.17 HL · λ belongs to the interval, not to the situation.
• 4.18 HL · The two errors sit on opposite sides of one line.
• 4.19 HL · Three different starts. One ending.

Topic 5: Calculus 18 of 18

• 5.1 · A curve has no gradient until you stop using two points shared
• 5.2 · A zero gradient does not mean a maximum shared
• 5.3 · Multiply by the power, then knock one off it shared
• 5.4 · The tangent that touches nothing shared
• 5.5 · Differentiating backwards, and what it measures shared
• 5.6 · The highest point is not always the top of the hill
• 5.7 · Bigger corners, taller box, smaller base
• 5.8 · Straight lines across a curve, and which way they miss
• 5.9 HL · The radius grows steadily. The area does not.
• 5.10 HL · Which way is the curve bending?
• 5.11 HL · Run the chain rule backwards
• 5.12 HL · Spin the curve and a solid appears
• 5.13 HL · It ends up 1.33 m away, having travelled 4 m
• 5.14 HL · A differential equation has a family, not an answer
• 5.15 HL · A picture of every solution at once
• 5.16 HL · Follow the gradient, in straight lines
• 5.17 HL · Two numbers decide the whole story
• 5.18 HL · One substitution turns it into something you can already do

Analysis and Approaches

83 of 83 sub-topics written.

Topic 1: Number and Algebra 16 of 16

• 1.1 · Each step along is ten times, not one more. shared
• 1.2 · The minus one is the whole formula. shared
• 1.3 · Same start, same second term, 51 times apart. shared
• 1.4 · It grew to 1628.89 and buys 1212.03 of things. shared
• 1.5 · A logarithm answers one question: what power? shared
• 1.6 · Thirty-nine times right, and still wrong.
• 1.7 · The law that turns 5 into 6
• 1.8 · A sum of positive numbers that comes out negative
• 1.9 · Every number is the sum of the two above it.
• 1.10 HL · Ten choices, sixty arrangements.
• 1.11 HL · One awkward curve is two simple ones added.
• 1.12 HL · The inverse tangent loses the quadrant
• 1.13 HL · You cannot add in polar form
• 1.14 HL · Find one root and you have found them all.
• 1.15 HL · Both halves are load-bearing.
• 1.16 HL · One, none, or infinitely many.

Topic 2: Functions 16 of 16

• 2.1 · A gradient is not an angle shared
• 2.2 · The range is not the y-axis shared
• 2.3 · Sketch is an instruction, not a lesser draw shared
• 2.4 · A graph can cross its own asymptote shared
• 2.5 · Square it then add, or add then square it
• 2.6 · One parabola, three ways of writing it
• 2.7 · The value the interval has to throw out
• 2.8 · Two asymptotes, and which coefficient each comes from
• 2.9 · They agree twice and then part company
• 2.10 · You cannot tell from looking which method it needs
• 2.11 · Stretch then shift is not shift then stretch
• 2.12 HL · The product of the roots is plus six
• 2.13 HL · The asymptote that is not horizontal
• 2.14 HL · The root of a square is not the number
• 2.15 HL · Multiplying by x throws half the answer away
• 2.16 HL · Inside the modulus is not outside it

Topic 3: Geometry and Trigonometry 18 of 18

• 3.1 · The triangle you need is hiding shared
• 3.2 · The angle your calculator cannot see shared
• 3.3 · The angle at the turn is neither bearing shared
• 3.4 · The sector is 5.78 times the segment
• 3.5 · The sine stays and the cosine flips
• 3.6 · You never need the angle
• 3.7 · Three cycles where you expected one
• 3.8 · Two answers or four, and the question decides
• 3.9 HL · The minus one is not a reciprocal
• 3.10 HL · Sine does not distribute over addition
• 3.11 HL · Adding pi leaves the tangent alone
• 3.12 HL · Lengths do not add
• 3.13 HL · Two non-zero vectors with a product of zero
• 3.14 HL · Your answer and the book's can both be right
• 3.15 HL · Crossing on the floor plan is not crossing
• 3.16 HL · Fifteen is the parallelogram, not the triangle
• 3.17 HL · The coefficients point out of the plane
• 3.18 HL · Sixty-three to the normal is twenty-six to the plane

Topic 4: Statistics and Probability 14 of 14

• 4.1 · Where the data came from shared
• 4.2 · The picture is a choice shared
• 4.3 · Where it sits, and how far it spreads shared
• 4.4 · A strong correlation is one point away from a weak one shared
• 4.5 · Counting outcomes, then testing the count shared
• 4.6 · Move the overlap and everything changes shared
• 4.7 · The expected value is where it balances shared
• 4.8 · Which bars does your event actually cover? shared
• 4.9 · The probability is the area, not the boundary shared
• 4.10 · There are two regression lines.
• 4.11 · Multiplying only works once.
• 4.12 · 70 and 102.5 are the same mark.
• 4.13 HL · A 99% accurate test, and you probably do not have it.
• 4.14 HL · P(X = 1) is zero. The density is not.

Topic 5: Calculus 19 of 19

• 5.1 · A curve has no gradient until you stop using two points shared
• 5.2 · A zero gradient does not mean a maximum shared
• 5.3 · Multiply by the power, then knock one off it shared
• 5.4 · The tangent that touches nothing shared
• 5.5 · Differentiating backwards, and what it measures shared
• 5.6 · Three rules, and a decision before you use them
• 5.7 · Three graphs that have to agree
• 5.8 · The cheapest can, and the bend that is not a turn
• 5.9 · Four metres away, twelve metres travelled
• 5.10 · Every integral is a chain rule someone already did
• 5.11 · Top minus bottom, every time
• 5.12 HL · Cancel the h, then let it go
• 5.13 HL · Close enough, every curve is its own tangent
• 5.14 HL · A curve that is not a function, differentiated anyway
• 5.15 HL · A longer table, and a fraction worth splitting
• 5.16 HL · Pick u badly and it gets worse
• 5.17 HL · Same curve, two axes, two different solids
• 5.18 HL · Four methods, and the thirty seconds that picks one
• 5.19 HL · A polynomial that learns the shape of a curve

How to use this

Every lesson has a student page and a teacher page, and the teacher page carries the answers, the marks, what each wrong answer tells you and a calculator plan. Nothing is stored and nothing needs a sign-in.