Grade 11

Mathematics, three units

The compulsory level of the mathematics bagrut, from equations and word problems through the straight line and the parabola to growth and decay and the reading of data.

7 lessons

  1. 1How do you turn a word problem into an equation without going wrong at the start?Begin by defining the unknown and writing that definition down: x is Danny's age today. Then translate each sentence separately into an expression, join them into one equation, and only then solve. Most of the marks lost on a three-unit paper go missing not in the algebra but in this translation step, before a single equals sign is written.45m
  2. 2When do you use a distance-speed-time table and when the part done in one hour?For motion problems build a table of distance, speed and time with one row per traveller, and use distance equals speed times time. Work-rate problems have no distance, so switch to the fraction of the job done in one hour: someone who finishes in 6 hours does one sixth an hour, and those fractions add.45m
  3. 3How do you find the equation of the line through two given points?First compute the slope: the difference in the y values over the difference in the x values, taken in the same order in both. Then substitute the slope and one of the points into y equals mx plus n and solve for n. Finally check that the second point also satisfies the equation you obtained.45m
  4. 4How do you sketch a parabola without computing a whole table of values?You need only three things: the sign of the leading coefficient, which says whether the parabola opens upwards or downwards; the vertex, whose x value is minus b over 2a; and where the curve meets the axes. Anyone holding those three can draw the graph accurately enough for any question on the paper.45m
  5. 5Why does a 10 percent rise followed by a 10 percent fall not return the original price?Because the two percentages are taken from different bases. The rise is computed on the original price, but the fall is computed on the higher price already reached, so in shekels it is the larger of the two. A hundred becomes 110 and then 99. The result is always below the original, in any order and at any percentage.50m
  6. 6Two classes share an average — what else do you need to compare them?The spread. The average says where the centre of the marks sits, but not how far from it they lie. A small standard deviation means a uniform class whose marks cluster near the average; a large one means a split class, with high achievers and failures, whose average describes nobody in it.45m
  7. 7How do you find an average from a frequency table rather than from a list?Multiply each value by its frequency, add all those products, and divide by the sum of the frequencies — not by the number of rows in the table. If a mark of 80 appears 7 times it contributes 560 to the total and 7 to the count. Dividing by the row count is the commonest error on this item.45m