Geometry and measurement: angles, shapes, area and volume, transformations, Pythagoras and trigonometry, and the units all of it is measured in.
Walk to this campThree questions light the next lantern. Nothing to install, no sign-up.
Eight rungs, one trail
Every camp on the mountain has the same eight rungs: the eight altitudes Alpenrise measures, read back in the words of your own school system. Rung 1 is the bottom of secondary school; rung 8 is beyond the final exam.
Rung
New Zealand
United Kingdom
Cambridge
IB
R1Explorer
Year 7
Year 7
Stage 7
MYP 1
R2Pathfinder
Year 8
Year 8
Stage 8
MYP 2
R3Voyager
Year 9
Year 9
Stage 9
MYP 3
R4Navigator
Year 10
Year 10 · GCSE yr 1
IGCSE Yr 1
MYP 4
R5Pioneer
Year 11
Year 11 · GCSE
IGCSE Yr 2
MYP 5
R6Summit
Year 12
Year 12 · AS
AS Level
DP 1
R7Apex
Year 13
Year 13 · A Level
A Level
DP 2
R8Beyond
NZ Scholarship
beyond A Level
STEP prep
DP HL+
One question from each rung
The mountain draws three questions per rung from the same slice as the free placement. Here is one from each rung of Geometry, shown without its answer.
Rung 1 · Explorer · Year 7A rectangle is 16 m long and 18 m wide. Find its area (in m²).
Rung 2 · Pathfinder · Year 8A herb patch is a rectangle 12 m long and 11 m wide. What is its area, in m²?
Rung 3 · Voyager · Year 9On a tape measure laid out straight, O is the centre of an enlargement. A point A is 6 units from O, and its image A' is 24 units from O, on the OPPOSITE side of O from A. Work out the scale factor of the enlargement.
Rung 4 · Navigator · Year 10In triangle ABC, angle B = 90° and angle A = 37°. The hypotenuse AC = 22 cm. Calculate the length of AB (the side adjacent to angle A). Give your answer correct to 1 decimal place.
Rung 5 · Pioneer · Year 11A regular nonagon has 9 sides. Find the size of each INTERIOR angle (in degrees).
Rung 6 · Summit · Year 12A 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).
Rung 7 · Apex · Year 13A triangle has two sides of 16 cm and 5 cm with an angle of 150° between them. Work out its area in cm². (sin 150° = 1/2)
Rung 8 · Beyond · NZ ScholarshipFind the EXACT area of an equilateral triangle with side 8 cm. (Answer in the form k√3.)