The mountain · Maths ridge · camp 1 of 4

Number

Number is the first camp on the Maths ridge: place value, fractions, decimals and percentages, ratio and rates, powers and roots, and the arithmetic everything else stands on. The low rungs ask for a sum; the high rungs ask why the sum works.

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.

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 Number, shown without its answer.

1. Rung 1 · Explorer · Year 7In basketball this season Isla scored 19 points and Charlotte scored 29 points. How many more points did Charlotte score than Isla?
2. Rung 2 · Pathfinder · Year 8Maia has 21 seedlings. Leila has 12 more seedlings than Maia. How many seedlings does Leila have?
3. Rung 3 · Voyager · Year 9-4 × -7 =
4. Rung 4 · Navigator · Year 10A passenger train on the main line travels at 36 km/h. What is that speed in metres per second?
5. Rung 5 · Pioneer · Year 11After Maia gives 16 seedlings to Aroha, the ratio of Maia's seedlings to Aroha's seedlings is 3 : 4, and together they have 84 seedlings. How many seedlings did Maia have at the very START, before giving any away?
6. Rung 6 · Summit · Year 12Priya has 800 g of flour. Recipe A uses 75 g per batch and sells for $1.50 each. Recipe B uses 160 g per batch and sells for $2.20 each. Priya can only pick ONE recipe, and makes as many whole batches of it as the flour allows. What is the highest total revenue possible, in dollars?
7. Rung 7 · Apex · Year 13Rationalise the denominator of 20/√10 and write it as c√10. What is c?
8. Rung 8 · Beyond · NZ ScholarshipSolve for x: log_3(x) + 1 = log_3(30)

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