Estonian Basic-School Mathematics Exam flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Order of operations

Evaluate brackets first, then powers and roots, then multiplication and division from left to right, and finally addition and subtraction from left to right. This order removes ambiguity in expressions like 2+3·4².

Rational number

A number expressible as a fraction a/b where a and b are integers and b is not zero. Its decimal form either terminates or repeats periodically, unlike irrational numbers such as the square root of two.

Absolute value

The distance of a number from zero on the number line, always non-negative. For example the absolute value of minus seven is seven, and the absolute value of five is five.

Standard form

Writing a number as a times ten to the power n, where a is at least one and less than ten. For instance 45 000 is written as 4.5 times ten to the fourth power.

Difference of squares

The identity a squared minus b squared equals (a+b)(a−b). It factorises expressions such as x²−9 into (x+3)(x−3) and speeds up mental multiplication like 51·49.

Expanding brackets

Multiplying each term inside a bracket by the factor outside. For two brackets, multiply every term of the first by every term of the second, then collect like terms.

Solving a linear equation

Isolate the unknown by applying inverse operations to both sides in reverse order: undo addition or subtraction first, then undo multiplication or division. Check by substituting the result back.

Inequality reversal rule

When both sides of an inequality are multiplied or divided by a negative number, the inequality sign flips. Adding or subtracting the same number never changes its direction.

Discriminant

The expression b squared minus four a c in a quadratic equation. Positive gives two real roots, zero gives one repeated root, negative gives no real roots.

Slope of a line

The change in y divided by the change in x between two points on the line. It measures steepness; positive slopes rise, negative slopes fall, zero is horizontal.

Direct proportionality

A relationship of the form y equals k times x, whose graph is a straight line through the origin. Doubling x doubles y; k is the constant rate.

Inverse proportionality

A relationship y equals k divided by x, where the product x·y stays constant. Its graph is a hyperbola whose branches approach the axes without touching them.

Parabola vertex

The highest or lowest point of a quadratic graph y=ax²+bx+c. Its x-coordinate is minus b divided by two a, and it lies on the axis of symmetry.

Zero of a function

An input value for which the function equals zero, shown where the graph crosses the horizontal axis. A function may have none, one, or several zeros.

Pythagorean theorem

In a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides. It also converts into a test for a right angle.

Similar figures

Figures with equal corresponding angles and proportional corresponding sides. If the length ratio is k, areas scale by k squared and volumes by k cubed.

Sine, cosine, tangent

In a right triangle: sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, tangent is opposite over adjacent. They link an acute angle to side ratios.

Volume of a cone

One third of the base area multiplied by the height. A cone with base radius r and height h has volume one third pi r squared h.

Circle circumference and area

Circumference equals two pi r, the distance around the circle. Area equals pi r squared, the surface enclosed. Both use the radius, not the diameter.

Trapezium area

Half the sum of the two parallel sides multiplied by the perpendicular distance between them. Written as A equals half (a+b) h.

Arithmetic mean

The sum of all data values divided by how many there are. It uses every value, so a single very large or small value can pull it noticeably.

Median of a data set

Order the values and take the middle one; with an even count, average the two middle values. It is resistant to extreme values unlike the mean.

Range of data

The largest value minus the smallest value. It shows the total spread quickly but ignores how the remaining values are distributed.

Probability of an event

The number of favourable outcomes divided by the number of equally likely outcomes. The result always lies between zero and one inclusive.

Complementary event

The event that A does not happen. Its probability equals one minus the probability of A, which is often the quicker route to an answer.

Pie chart sector angle

The angle for a category equals its frequency divided by the total, multiplied by 360 degrees. A percentage converts to an angle by multiplying by 3.6.

Average speed

Total distance travelled divided by total time taken for the whole journey. It is not the average of the separate speeds unless the times are equal.

Percentage change

New value minus old value, divided by the old value, times one hundred. A positive result is an increase, a negative result a decrease.

Successive percentage changes

Apply changes one after another by multiplying factors, such as 1.2 then 0.8. The combined effect is 0.96, a net decrease of four percent, not zero.

Distance, speed, time

Distance equals speed multiplied by time. Rearranged, speed is distance divided by time and time is distance divided by speed. Keep units consistent.

Counterexample

A single case where a general claim fails, which is enough to disprove it. Testing zero, one, negatives and fractions exposes many false statements.

Rounding and significant figures

Keep exact values during working and round only the final answer, stating the accuracy used. Write approximately equals for rounded results and equals only for exact values.