Every year, 15 percent flunk at attempt one with basic school final state examinations in mathematics.

For Pärnu Rääma school headmaster Elmo Joa, the ado around basic school math exams is quite a mystery: in his house, even the not-so-bright got good grades at it.

«We did have some anomalies, though: some who always had a 5 [excellent] in math, now fell to 3 [satisfactory],» said Mr Joa, having analysed the results. «But those we feared would fail and repeat the exam got a 4 [good] or even a 5.»

Last week, the media wrote about almost half the students at Tallinn Art Gymnasium flunking the math exam. Cases like that also occurred at other schools.

«The problems were not difficult and if some students did not make it, there must have been some other reason,» said Gustav Adolf Gymnasium math teacher Agu Ojasoo. What’s more: he assessed the exam, by new compilers, to be interesting. Mr Ojasoo admitted that not all teachers have embraced the new curriculum which makes the students apply more of logical thinking; so the teachers just keep on «cramming it in» as before.

According to Mr Joa, the math exam was compiled for the thinking person. «For those used to solve the standard problems, it was harder; but for those not too smart at math by possessing good functional reading skills and ability to think – whose essays are interesting to read and debating them ones has to really think what to answer –, these did better,» said Mr Joa. «Even kids with special needs, such as have needed help with studies – even they did the math exam.»

Also satisfied is Palivere school headmaster Tõnis Peikel, in Lääne County – despite having two kids flunk, out of ten. «But we had more of these who got a 5 – whoever had been studying got it and passed the exam,» said Mr Peikel.

**Cramming not enough**

For the first time, this year’s exam was based on the new curriculum in force since 2011 which, according to Mr Ojasoo, is easier than the former one. «Basic school math has been freed from the larger part of trigonometry; of algebra formulas for, seven needed to be known – now only three,» said Mr Ojasoo citing a few examples.

The main difference, said Mr Ojasoo is that stuff isn’t just crammed; rather, the student really has to get it: «There’s a bit more of real life in the problems, but there were the totally traditional ones as well.»

As an example, Mr Ojasoo tells of the cinema problem where a point could be earned not by mathematical calculation, but by just understanding the text. Namely, among other things the problem stated that Estonia’s most viewed movie, in 2011, was «Mushrooming», and the very first question to be answered was just what was the most viewed Estonian film. Not everyone earned the point, noted Mr Ojasoo.

According to Anneli Aab, PR manager of Foundation Innove organising the exams, it will not be known before the fall if this year featured more failures than before – at Innove, they are only about to look at the basic school final exams. «A selection has been made of ten percent of students whose exam papers are sent to us by the schools; on the basis of these, we will do a general analysis,» explained Ms Aab. «But that will not be school-based. Every school will do their own analysis.»

**Repeat exam voluntary**

According to earlier analysis by Innove, an average of 15 percent flunk math at first attempt. Data on success of repeat exams, however, is not nationally collected.

In Palivere, one of the two that failed repeated the exam and got a positive mark on his certificate. «Of the four-five last year’s examination papers, he had one choice – like drawing a ticket,» explained the headmaster, Mr Peikel. «The teacher said thus it would not be possible to say, later, if the repeat exam was easier or harder.»

However a school organises the repeat exam, is the responsibility of its headmaster. According to Mr Ojasoo, the customs vary. Last year, at a small school the repeat exam was arranged by a teacher who never taught them that year. «The only thing they knew was the topics would be the same,» recalls Mr Ojasoo. Both passed, at attempt two.

Mr Ojasoo knows, however, that at some schools students are trained with problems which will be the very ones used in repeat exams. «They think: let’s give them a 3. But the certificate may feature a 2 [non-satisfactory] and one will still graduate – better be honest that to play some tricks,» underlined Mr Ojasoo.

In Palivere, two students did graduate from basic school with non-satisfactory marks. «A basic school graduation certificate may feature two non-satisfactory remarks, but not year’s result and exam both 2 in one subject,» said Mr Peikel, explaining the rules set by law. In Palivere, one student got a 2 for the year, in math; the other had a 2 for the exam. The repeat exam isn’t compulsory. For that, a parent must file an application.

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**Some select problems**

A flowerbed was dug, in a park. Its middle part is a square, the diagonal of which is 4 meters. A semi-circle was designed at each side of the square (see drawing).

1) Calculate the area of the flowerbed.

2) Unto the diagonal of the square, sunflowers will be planted. How many sunflowers need to be planted if they need to be 25 centimetres apart and the first one will be planted at the tip of the square?

• • •

To package gifts, Mom took two cuboid boxes. The large box’s main edges are 50 cm and 30 cm, and the box’s volume is 18,000 cm^{3}. The bottoms of the small and big box are similar and perimeters thereof relate as 5 : 2. The large box is higher by 3 cm.

1) Calculate the side area of large box.

2) Calculate volume of small box.

3) All facets of large box will be covered with paper. The paper roll is 1 meter wide. What is the most economical way to use the paper, with a fitting piece cut for each facet? Explain by a drawing of a calculation.

• • •

Two kilograms of grapes and one kg of pears cost €5 in total. Cutting volume of grapes 4 times and increasing pears by 200 grams, one would pay €2.58.

Calculate kg price of grapes and pears.

• • •

The given function is y = x2 – 2x – 3.

1) Calculate zero points of it.

2) Calculate its graph peak coordinates.

3) Find its graph and y-axis intersection coordinates.

4) Draw the function’s graph as x values change from -2 to 4.