Alpenrise is a practice tool, not a school, a course or a tutor. It does not teach lessons and it does not replace your child’s teacher. What it gives you is a reading: which rung each strand of maths is on, and why marks are lost. This page shows how the questions are organised, which official curriculum documents they follow, and what we do not claim, so you can judge it yourself.
The quickest check is the placement. It is free, takes about twenty minutes a subject and needs no sign-up. Sit it with your child. If the rung it gives does not match what you see at home, tell us.
Every curriculum below divides maths a little differently. Alpenrise measures four strands separately (number, algebra, geometry and statistics), so a strong number and a weak geometry never average out. This is where each official heading lands:
| Official document | Its headings, and where they land in our four strands |
|---|---|
| New Zealand | number · algebra · measurement · geometry · statistics · probabilityMeasurement goes with geometry; probability with statistics. |
| England | number · algebra · ratio, proportion and rates of change · geometry and measures · probability · statisticsRatio, proportion and rates go with number; measures with geometry; probability with statistics. |
| Australia | number · algebra · measurement · space · statistics · probabilityMeasurement and space go with geometry; probability with statistics. |
| Singapore | number and algebra · geometry and measurement · statistics and probabilityNumber and algebra are split into our first two strands. |
| Cambridge Lower Secondary | number · algebra · geometry and measure · statistics and probabilityOne to one. |
| Cambridge IGCSE 0580 | number · algebra and graphs · coordinate geometry · geometry · mensuration · trigonometry · transformations and vectors · probability · statisticsCoordinate geometry, mensuration, trigonometry and vectors go with geometry. |
| IB MYP | number · algebra · geometry and trigonometry · statistics and probabilityOne to one. |
Calculus sits on the algebra strand from rung 7; logarithms on the number strand from rung 6.
A rung is pinned to an age, not to any one school’s scheme of work: rung 1 is about 11–12 years old, rung 7 about 17–18, and rung 8 goes beyond school-leaving level. The year names below come from each system’s own age table, and the same table runs inside Alpenrise.
| Rung | Age | New Zealand | Australia | United Kingdom | Singapore | Cambridge | IB | US / Canada |
|---|---|---|---|---|---|---|---|---|
| R1 | 11–12 yrs | Year 7 | Year 6 | Year 7 | ≈ P6 | Stage 7 | MYP 1 | Grade 6 |
| R2 | 12–13 yrs | Year 8 | Year 7 | Year 8 | ≈ Sec 1 | Stage 8 | MYP 2 | Grade 7 |
| R3 | 13–14 yrs | Year 9 | Year 8 | Year 9 | ≈ Sec 2 | Stage 9 | MYP 3 | Grade 8 |
| R4 | 14–15 yrs | Year 10 | Year 9 | Year 10 · GCSE yr 1 | ≈ Sec 3 | IGCSE Yr 1 | MYP 4 | Grade 9 |
| R5 | 15–16 yrs | Year 11 | Year 10 | Year 11 · GCSE | ≈ Sec 4 · O-Level | IGCSE Yr 2 | MYP 5 | Grade 10 |
| R6 | 16–17 yrs | Year 12 | Year 11 | Year 12 · AS | ≈ JC 1 | AS Level | DP 1 | Grade 11 · AP |
| R7 | 17–18 yrs | Year 13 | Year 12 · senior cert | Year 13 · A Level | ≈ JC 2 | A Level | DP 2 | Grade 12 · AP |
| R8 | 18+ yrs | NZ Scholarship | beyond Year 12 | beyond A Level | ≈ H3 | STEP prep | DP HL+ | AP capstone · college |
The table scrolls sideways: every system has a column.
These names are an approximation. Birthdays, states and individual schools move them by a year either way, and schools teach topics in different orders. So Alpenrise never assumes a child’s rung from their year: the placement measures it.
Year names for 40 countries are built in, plus Cambridge and IB. Where a country is not listed, the rung reads as an age.
These are the published documents the maths questions are written to, and the rungs each one covers.
Years 11–12 (rungs 6–7) are set by each state and territory, so there is no single national document to link.
Rung 1 is about Primary 6; rungs 6–7 are about the junior-college years.
US and Canada, China, Hong Kong and the other countries in the list: Alpenrise shows your year name for each rung, matched by age, but does not write questions to those countries’ standards.
The links open each publisher’s own page or document. Publishers move their pages; if a link breaks, tell us.
For each strand: what the rung covers, how many questions the bank holds for it, and one question from it. Every sample is one of the free questions already on the mountain.
| Rung | What it covers, and one question from it |
|---|---|
| R1 | Whole-number operations, rounding, order of operations, equivalent fractions, money and time problems114 questions in the bankFill in the missing number: 3/4 = ?/12General |
| R2 | Decimals, negative numbers, fractions and percentages, sharing in a ratio, index notation, HCF and LCM, unit conversion630 questions in the bankRuby and Ana earn $45 together for babysitting. They share it in the ratio 2:3. How much does Ana get?IB style |
| R3 | Standard form, bounds, significant figures, percentage change, direct and inverse proportion, recurring decimals, speed546 questions in the bank-4 × -7 =General |
| R4 | Compound interest, reverse percentages, depreciation, exchange rates, multi-step proportion480 questions in the bankAfter a 40% discount, a tablet cover costs $24. What was the ORIGINAL price?IB style |
| R5 | Surds, density, GST and tax, successive percentage changes, rates, changing ratios462 questions in the bankThe exchange rate is NZ$1 = 0.6 EUR. How many EUR does NZ$100 buy?New Zealand style |
| R6 | Logarithms, sums of sequences, simple versus compound interest, choosing the best option under a constraint204 questions in the bankLeila owes $81. Every month, Leila pays off 1/3 of whatever is STILL owed (not of the original amount). How much has been PAID OFF in total after 3 months?Singapore style |
| R7 | Exponential growth and doubling time, complex numbers, kinematics, calculations in standard form, rationalising surds48 questions in the bankWork out (6 × 10^9) × (5 × 10^4), giving your answer in standard form as m × 10^n. What is n?General |
| R8 | Infinite geometric series, the modulus of a complex number, binomial coefficients, logarithmic equations48 questions in the bankEvaluate: (√11 + √2)(√11 − √2)General |
| Rung | What it covers, and one question from it |
|---|---|
| R1 | One-step equations, number machines, number patterns, substitution48 questions in the bankA number machine multiplies by 2 and then adds 6. What is the output when the input is 6?General |
| R2 | Two-step equations, expanding brackets, collecting like terms, simple inequalities, term-to-term and position-to-term rules156 questions in the bankIsla buys w raffle tickets, each costing $6. Write an expression, in terms of w, for the total cost in dollars.Cambridge style |
| R3 | Equations with brackets, double brackets, factorising, index laws, simultaneous equations, the nth term, rearranging formulae210 questions in the bankExpand and simplify: (p + 6)(p + 3)Cambridge style |
| R4 | Factorising and solving quadratics, algebraic fractions, functions and inverses, negative and fractional indices, quadratic sequences270 questions in the bankWrite down all the integer values of x that satisfy 7 < 3x + 1 ≤ 19.Cambridge style |
| R5 | Solving quadratics, rearranging, simplifying algebraic fractions, simultaneous equations in context54 questions in the bankMake x the subject of: y = 7x + 9General |
| R6 | The discriminant, turning points, exponential equations, geometric sequences and series, comparing two pricing plans162 questions in the bankFind the x-coordinate of the turning point of y = x² + 4x + 3General |
| R7 | Differentiation including the chain rule, stationary points, tangents, integration, optimisation78 questions in the bankIf f(x) = 2x⁴, find f′(2).General |
| R8 | Area between curves, the remainder theorem, sums and products of roots, optimisation with a constraint, related rates60 questions in the bankThe equation x² + 4x + 4 = 0 has roots α and β. Find the value of α² + β².General |
| Rung | What it covers, and one question from it |
|---|---|
| R1 | Perimeter, area of rectangles, angles on a line and around a point, volume of cuboids48 questions in the bankA rectangle is 8 cm long and 7 cm wide. Find its perimeter (in cm).General |
| R2 | Angles in triangles and with parallel lines, area of triangles and parallelograms, compound shapes, transformations on a grid, nets and surface area132 questions in the bankA triangle has base 10 cm and height 7 cm. Find its area (in cm²).General |
| R3 | Circles, Pythagoras, polygons, bearings, enlargement, similar shapes, loci, map scales222 questions in the bankCalculate the size of one interior angle of a regular 24-sided polygon (24 sides).Cambridge style |
| R4 | Right-angled trigonometry, circle theorems, volume of cones, spheres and prisms, area and volume of similar shapes, vectors192 questions in the bankIn triangle ABC, angle B = 90° and angle A = 44°. The hypotenuse AC = 10 cm. Calculate the length of BC (the side opposite angle A). Give your answer correct to 3 significant figures.Cambridge style |
| R5 | Interior and exterior angles of polygons, back bearings, scale factors for area48 questions in the bankThe bearing of B from A is 103°. Find the bearing of A from B. (Give a three-figure bearing.)General |
| R6 | Arc length and sector area, exact trigonometric values, equations of straight lines, midpoints, the sine rule, volume problems132 questions in the bankA conical paper cup has radius 3 cm and height 10 cm. Using V = (1/3)πr²h, find its volume in terms of π (write your answer like 12π).IB style |
| R7 | Equations of circles, distance between points, perpendicular gradients, area of a triangle using sine, magnitude of a vector48 questions in the bankFind the radius of the circle x² + y² = 25General |
| R8 | Scalar product and perpendicular vectors, distance in three dimensions, exact areas, tangent lengths48 questions in the bankFind the distance between the points (3, 3, -3) and (4, 15, 9).General |
| Rung | What it covers, and one question from it |
|---|---|
| R1 | Mean, median, mode and range, tally charts and frequency tables, simple probability48 questions in the bankFind the mode of: 6, 4, 4, 6, 25, 25, 6General |
| R2 | Frequency tables, bar charts and line graphs, the probability scale, mutually exclusive events, two-way tables, comparing data sets168 questions in the bankCharlotte records 5 numbers: 5, x, 8, 7, 8. The mean of these 5 numbers is 7. Show that x = 7. Hence, write down the range of the 5 numbers.Cambridge style |
| R3 | Grouped data, stem-and-leaf diagrams, pie charts, scatter graphs and correlation, tree diagrams, Venn diagrams, relative frequency171 questions in the bankIn a class survey: 11 girls play a sport and 9 girls do not; 13 boys play a sport and 7 boys do not. One student is picked at random. What is the probability they play a sport? (fraction)General |
| R4 | Box plots, cumulative frequency, histograms, conditional probability from tables, combined means108 questions in the bankThe table shows the time taken to complete a jigsaw puzzle (min) for 38 students. 0–12 min: 5 | 12–24 min: 8 | 24–36 min: 12 | 36–48 min: 9 | 48–60 min: 4 The cumulative frequency polygon for this data is shown below. Estimate the median time taken to complete a jigsaw puzzle. Give your answer correct to 1 decimal place.Cambridge style |
| R5 | Probability without replacement, estimating from a sample, capture–recapture54 questions in the bankThere are 7 name cards in a hat: 3 are Year 8 cards and 4 are not. Two are drawn WITHOUT replacement. What is the probability that BOTH are Year 8 cards? Give a fraction in simplest form.New Zealand style |
| R6 | Expected value, conditional probability, tree diagrams, weighted averages, the normal distribution (empirical rule)108 questions in the bankIn a survey, 21 girls and 9 boys said they cycle to school; 9 girls and 11 boys said they do not. A girl is chosen at random. What is the probability that she cycles to school? Give a fraction in simplest form.IB style |
| R7 | Binomial probability, combinations, variance, two-stage (Bayes-style) problems, interpreting a regression line54 questions in the bankA raffle sells 80 tickets at $5 each, with one prize of $40. What is the expected VALUE of buying one ticket (winnings minus cost), in dollars? Give a decimal or a fraction.IB style |
| R8 | Permutations and combinations, at-least-once probability, conditional probability48 questions in the bankHow many different teams of 3 can be chosen from 12 players?General |
Twenty minutes with your child is a better test of this page than anything written on it. If the rung looks wrong, write to us and say why.
Written 7 October 2026. Question counts are read from the live question bank each time this page is built.