g10-01-01 · 5–10 min
An element or a subset?
Does changing 3 into {3} change the question?
Before you start: Numbers and braces
SENIOR 1 · PAPER AND PROJECTION
Senior 1 · short mathematical inquiries
85 bilingual, 5–10 minute inquiries across 14 chapters. Predict, compare cases and explain on paper.
Core topics · 4 short inquiries
01 Sets
g10-01-02 · 5–10 min
Containment, equality and the empty set
When is a subset proper?
Before you start: Set notation
g10-01-03 · 5–10 min
Operations select different elements
Can union, intersection and difference use the same rule?
Before you start: Membership
g10-01-04 · 5–10 min
Can these class counts coexist?
How many pupils choose neither option?
Before you start: Set operations and integer counts
Core topics · 4 short inquiries
02 Mathematical logic
g10-02-01 · 5–10 min
A counterexample to an implication
When does p⇒q fail?
Before you start: Inequalities and truth values
g10-02-02 · 5–10 min
Necessary or sufficient?
Which interval is contained in which?
Before you start: Implications and intervals
g10-02-03 · 5–10 min
All or at least one?
Can a statement be existentially true but universally false?
Before you start: Squares and quantifier language
g10-02-04 · 5–10 min
Negating a quantified statement
Does negating “all are greater” mean “all are smaller”?
Before you start: Quantifiers and strict inequalities
Core topics · 4 short inquiries
03 Quadratic inequalities
g10-03-01 · 5–10 min
Does the middle always solve it?
What changes when the leading coefficient changes sign?
Before you start: Factor signs and number lines
g10-03-02 · 5–10 min
How many real zeros?
Can a quadratic be positive without crossing the axis?
Before you start: Quadratic equations and squares
g10-03-03 · 5–10 min
Do the endpoints belong?
What is the difference between < and ≤ at a root?
Before you start: Root signs and endpoint notation
g10-03-04 · 5–10 min
A profitable value may be impossible
Which non-loss solutions are feasible in the context?
Before you start: Polynomial signs and intersections
Core topics · 4 short inquiries
04 Polynomial division and remainders
g10-04-01 · 5–10 min
What does division preserve?
How can the quotient and remainder reconstruct f?
Before you start: Polynomial expansion
g10-04-02 · 5–10 min
Where did the missing terms go?
Can missing coefficients be omitted in synthetic division?
Before you start: Polynomial coefficient order
g10-04-03 · 5–10 min
Read a remainder from one point
Why is the remainder f(a)?
Before you start: Division identity and substitution
g10-04-04 · 5–10 min
Design a factor by changing one coefficient
What constant makes x−a a factor?
Before you start: Remainder theorem
Core topics · 15 short inquiries
05 Functions and their properties
g10-05-01 · 5–10 min
Repair one mapping arrow
Can two inputs share an output? Which single input breaks the function rule?
Before you start: Read function inputs, outputs and the stated domain; write your first prediction on paper.
g10-05-02 · 5–10 min
Same formula: the same function?
Does x = 0.5 distinguish a finite domain from the interval [−2,2]?
Before you start: Read function inputs, outputs and the stated domain; write your first prediction on paper.
g10-05-03 · 5–10 min
Which endpoint belongs?
Why is 3 allowed in √(x−3), while 2 is forbidden in 1/(x−2)?
Before you start: Read function inputs, outputs and the stated domain; write your first prediction on paper.
g10-05-04 · 5–10 min
Keep every restriction after simplification
Does cancelling x−1 restore the missing input x=1?
Before you start: Read function inputs, outputs and the stated domain; write your first prediction on paper.
g10-05-05 · 5–10 min
Should the points be joined?
The same cost formula y=2x+4 describes time or item count. Which graph permits x=2.5?
Before you start: Read function inputs, outputs and the stated domain; write your first prediction on paper.
g10-05-06 · 5–10 min
A missing boundary or two outputs?
If both pieces include the boundary, is the relation always invalid?
Before you start: Read function inputs, outputs and the stated domain; write your first prediction on paper.
g10-05-07 · 5–10 min
Swap two function machines
Does doubling then adding 3 give the same result as adding 3 then doubling?
Before you start: Read function inputs, outputs and the stated domain; write your first prediction on paper.
g10-05-08 · 5–10 min
Can the largest value be reached?
Does y=x on (0,2) have a maximum just because the graph approaches 2?
Before you start: Read function inputs, outputs and the stated domain; write your first prediction on paper.
g10-05-09 · 5–10 min
Decreasing on each piece or the whole domain?
Is 1/x decreasing on all nonzero real numbers?
Before you start: Read function inputs, outputs and the stated domain; write your first prediction on paper.
g10-05-10 · 5–10 min
Symmetry needs the matching input
Is x² still even when its domain is restricted to [0,3]?
Before you start: Read function inputs, outputs and the stated domain; write your first prediction on paper.
g10-05-11 · 5–10 min
Five powers, different forbidden inputs
Which of x, x², x³, √x and 1/x are defined at −1 and at 0?
Before you start: Read function inputs, outputs and the stated domain; write your first prediction on paper.
g10-05-12 · 5–10 min
When does the larger exponent give less?
For positive x, does x³ always exceed x²?
Before you start: Read function inputs, outputs and the stated domain; write your first prediction on paper.
g10-05-13 · 5–10 min
Undo the input rule in the right order
If f(2x+1)=6x+5, how do you obtain f(u) rather than f((u−1)/2)?
Before you start: Read function inputs, outputs and the stated domain; write your first prediction on paper.
g10-05-14 · 5–10 min
Cheapest at this quantity or most within budget?
Can the best plan change when the decision question changes?
Before you start: Read function inputs, outputs and the stated domain; write your first prediction on paper.
g10-05-15 · 5–10 min
Squaring can create a false root
Why does squaring √(x+2)=x produce two candidates but only one solution?
Before you start: Real-number operations and reading coordinates; write a prediction on paper.
Core topics · 9 short inquiries
06 Exponential and logarithmic functions
g10-06-01 · 5–10 min
A negative exponent is a reciprocal
Does 2⁻³ mean a negative number or a reciprocal?
Before you start: Real-number operations and reading coordinates; write a prediction on paper.
g10-06-02 · 5–10 min
A fractional exponent names a root
What does 16^(3/4) ask you to do?
Before you start: Real-number operations and reading coordinates; write a prediction on paper.
g10-06-03 · 5–10 min
Equal additions or equal ratios?
Does adding 20 each round match growing by 20% each round?
Before you start: Real-number operations and reading coordinates; write a prediction on paper.
g10-06-04 · 5–10 min
Crossing the base 1 reverses growth
What changes in aˣ when a passes through 1?
Before you start: Real-number operations and reading coordinates; write a prediction on paper.
g10-06-05 · 5–10 min
A logarithm asks for an exponent
What number does log₂8 ask for, and why is log₂0 impossible?
Before you start: Real-number operations and reading coordinates; write a prediction on paper.
g10-06-06 · 5–10 min
Swap coordinates for inverse graphs
If (2,4) lies on y=2ˣ, which point lies on y=log₂x?
Before you start: Real-number operations and reading coordinates; write a prediction on paper.
g10-06-07 · 5–10 min
Products become sums of logarithms
Is logₐ(u+v)=logₐu+logₐv?
Before you start: Real-number operations and reading coordinates; write a prediction on paper.
g10-06-08 · 5–10 min
The threshold between two integer rounds
When does 100rⁿ first reach a target, and why might rounding a logarithm fail?
Before you start: Real-number operations and reading coordinates; write a prediction on paper.
g10-06-09 · 5–10 min
A decreasing base reverses the inequality
Does logₐx<logₐb always imply x<b?
Before you start: Real-number operations and reading coordinates; write a prediction on paper.
Core topics · 12 short inquiries
07 Trigonometric functions
g10-07-01 · 5–10 min
What does one radian measure?
Does doubling a circle radius double its angle or its arc?
Before you start: Angles, coordinates and basic function graphs.
g10-07-02 · 5–10 min
One circle, two coordinates
Which coordinate is sine, and which signs depend on the quadrant?
Before you start: Angles, coordinates and basic function graphs.
g10-07-03 · 5–10 min
Reflect an angle without recalculating
Why do θ and180°−θ share a sine but not always a cosine?
Before you start: Angles, coordinates and basic function graphs.
g10-07-04 · 5–10 min
A square loses a sign
Does sin²θ+cos²θ=1 determine the sign of cosine?
Before you start: Angles, coordinates and basic function graphs.
g10-07-05 · 5–10 min
Unroll the circle into a wave
How does a moving circle point produce a sine graph?
Before you start: Angles, coordinates and basic function graphs.
g10-07-06 · 5–10 min
Where does tangent break?
Can a tangent graph pass through90°?
Before you start: Angles, coordinates and basic function graphs.
g10-07-07 · 5–10 min
Can sine distribute over addition?
Is sin(α+β)=sinα+sinβ?
Before you start: Angles, coordinates and basic function graphs.
g10-07-08 · 5–10 min
Double an angle, not its sine
How does sin2θ relate to sinθ?
Before you start: Angles, coordinates and basic function graphs.
g10-07-09 · 5–10 min
Amplitude and a reflected wave
Does a negative coefficient mean a negative amplitude?
Before you start: Angles, coordinates and basic function graphs.
g10-07-10 · 5–10 min
Frequency squeezes the horizontal axis
Why is the period2π/|ω| rather than2πω?
Before you start: Angles, coordinates and basic function graphs.
g10-07-11 · 5–10 min
Phase is divided by frequency
Does adding φ shift every sine graph by−φ?
Before you start: Angles, coordinates and basic function graphs.
g10-07-12 · 5–10 min
A wheel needs a starting position
Can amplitude and period alone determine a height model?
Before you start: Angles, coordinates and basic function graphs.
Syllabus supplement · 6 short inquiries
08 Plane vectors
g10-08-01 · 5–10 min
Move the arrow without changing the vector
Must equal vectors start at the same point?
Before you start: Coordinates, displacement and Pythagoras.
g10-08-02 · 5–10 min
A detour and its final displacement
Does changing the order of two displacements change the destination?
Before you start: Coordinates, displacement and Pythagoras.
g10-08-03 · 5–10 min
A negative scalar reverses direction
What does multiplication by−2 change?
Before you start: Coordinates, displacement and Pythagoras.
g10-08-04 · 5–10 min
Two directions need to be independent
Can any pair of vectors locate every point uniquely?
Before you start: Coordinates, displacement and Pythagoras.
g10-08-05 · 5–10 min
What does the sign of a dot product tell us?
Does a dot product of0 always mean a right angle?
Before you start: Coordinates, displacement and Pythagoras.
g10-08-06 · 5–10 min
Translate a midpoint and a distance
What changes when both endpoints receive the same translation?
Before you start: Coordinates, displacement and Pythagoras.
Syllabus supplement · 5 short inquiries
09 Solving triangles
g10-09-01 · 5–10 min
A triangle and three equal ratios
If one side changes scale, what happens to a/sinA?
Before you start: Triangle angles, sine and cosine.
g10-09-02 · 5–10 min
Pythagoras with a correction term
What changes when the included angle is not90°?
Before you start: Triangle angles, sine and cosine.
g10-09-03 · 5–10 min
The same SSA data can make two triangles
How can two sides and a nonincluded angle give0,1 or2 solutions?
Before you start: Triangle angles, sine and cosine.
g10-09-04 · 5–10 min
The same two sides, different areas
Which included angle gives the greatest area for fixed sides?
Before you start: Triangle angles, sine and cosine.
g10-09-05 · 5–10 min
Measure a distance without crossing the river
What can a baseline and two sighting angles determine?
Before you start: Triangle angles, sine and cosine.
Syllabus supplement · 6 short inquiries
10 Solid geometry
g10-10-01 · 5–10 min
Classify by structure, not by viewpoint
Does rotating a solid change its type?
Before you start: Plane area, Pythagoras and units.
g10-10-02 · 5–10 min
A drawing does not preserve every length
Can equal perpendicular sides look unequal in an oblique drawing?
Before you start: Plane area, Pythagoras and units.
g10-10-03 · 5–10 min
A cone height is not its slant height
Which length belongs in the lateral-area formula?
Before you start: Plane area, Pythagoras and units.
g10-10-04 · 5–10 min
The same base and vertical height
Which height determines a prism or cone volume?
Before you start: Plane area, Pythagoras and units.
g10-10-05 · 5–10 min
A frustum is a difference of cones
Can the volume use the average of the two end areas?
Before you start: Plane area, Pythagoras and units.
g10-10-06 · 5–10 min
Double a sphere: four or eight times?
Do surface area and volume scale at the same rate?
Before you start: Plane area, Pythagoras and units.
Additional mathematics · 4 short inquiries
11 Variation
g10-11-01 · 5–10 min
Which power controls the multiplier?
Does doubling x always double y?
Before you start: Powers and ratios
g10-11-02 · 5–10 min
A fixed product instead of a fixed ratio
What remains fixed in inverse variation?
Before you start: Division and domain restrictions
g10-11-03 · 5–10 min
Change one factor or both?
In joint variation, do two doublings still give a doubling?
Before you start: Products and direct variation
g10-11-04 · 5–10 min
The fixed part changes the ratio
Does a straight graph always mean direct proportion?
Before you start: Affine functions and ratios
Additional mathematics · 3 short inquiries
12 Polynomial factors and multiples
g10-12-01 · 5–10 min
Which factor copies are shared?
Why does a greatest common divisor use the lower exponent?
Before you start: Factorisation and divisibility
g10-12-02 · 5–10 min
The smallest shared multiple
Why is multiplying A and B usually excessive?
Before you start: GCD and factor counts
g10-12-03 · 5–10 min
Why do remainders preserve the GCD?
Can replacing A by a remainder lose a common factor?
Before you start: Polynomial division and factors
Additional mathematics · 4 short inquiries
13 Partial fractions
g10-13-01 · 5–10 min
Two denominators, one identity
How can substituting a forbidden value still find a coefficient?
Before you start: Rational domains and coefficient identities
g10-13-02 · 5–10 min
Why include every repeated power?
Can one term represent every numerator over (x−a)²?
Before you start: Coefficient comparison
g10-13-03 · 5–10 min
Divide before decomposing
Where does the polynomial part come from?
Before you start: Polynomial division and simple fractions
g10-13-04 · 5–10 min
Does cancellation repair a hole?
Are equal values on a shared domain the same as equal domains?
Before you start: Domains, cancellation and function equality
Additional mathematics · 5 short inquiries
14 Parallelism and perpendicularity in space
g10-14-01 · 5–10 min
Not intersecting does not imply parallel
Can two space lines neither intersect nor run parallel?
Before you start: Points, lines, planes and vector directions.
g10-14-02 · 5–10 min
A parallel line must lie outside the plane
Can the outside-plane condition be omitted?
Before you start: Points, lines, planes and vector directions.
g10-14-03 · 5–10 min
Two test lines must intersect
Do two parallel test lines prove that two planes are parallel?
Before you start: Points, lines, planes and vector directions.
g10-14-04 · 5–10 min
Perpendicular to two parallel lines is not enough
Why must the two lines in the perpendicularity test intersect?
Before you start: Points, lines, planes and vector directions.
g10-14-05 · 5–10 min
Perpendicular planes do not make every line normal
If two planes are perpendicular, is every line of one perpendicular to the other?
Before you start: Points, lines, planes and vector directions.