Algebra: expressions, equations and inequalities, sequences, functions and graphs. From “find x” at rung 1 to quadratics and simultaneous equations near the top.
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 Algebra, shown without its answer.
Rung 1 · Explorer · Year 7Solve for x: x + 27 = 44
Rung 2 · Pathfinder · Year 8Isla buys w raffle tickets, each costing $6. Write an expression, in terms of w, for the total cost in dollars.
Rung 3 · Voyager · Year 9Expand and simplify: (p + 6)(p + 3)
Rung 4 · Navigator · Year 10A car park holds motorbikes and cars, 23 in total. Counting wheels gives 68. How many cars are there?
Rung 6 · Summit · Year 12A car wash pass charges a fixed fee of $40 plus $3 per wash. Zoe uses 10 washes in a month. What is the total cost, in dollars?
Rung 7 · Apex · Year 13An open box is made from a 30 cm by 30 cm square of card by cutting a square of side x from each corner and folding up the sides. The volume is V = x(30 − 2x)². The maximum occurs at x = 5 cm. What is the MAXIMUM volume, in cm³?
Rung 8 · Beyond · NZ ScholarshipA square's side length grows at 3 cm per second. Using A = s², the rate of area growth is dA/dt = 2s × ds/dt. How fast is the AREA growing when the side is 5 cm, in cm² per second?