Full Grade 8 test

The box count must be an integer. Write inequalities for the minimum count and the total mass. Check the largest integer count that stays below the mass limit.

The magnitude of (a, b) is √(a² + b²), by Pythagoras. Magnitude is always nonnegative.

Relative frequency percentage = interval frequency ÷ total frequency × 100. For example, 6 out of 20 is 30%.

Sort the data. Q2 is the overall median; Q1 is the median of the lower half and Q3 the median of the upper half. In these tasks, an even-length list is split into two equal halves; the median of an even-sized group is the average of its two middle values.

The opposite vector has the same magnitude and reversed direction. Both coordinates change sign: (a, b) → (−a, −b).

Perpendicular lengths form the legs of a right triangle. By Pythagoras, hypotenuse c = √(a² + b²). Square the lengths, add and take the square root; do not simply add the lengths.

Interquartile range IQR = Q3 − Q1. It describes the spread of the middle approximately 50% of the data. A greater IQR means greater spread in this middle portion.

Natural numbers belong to the integers Z. Every integer is rational because it can be written n/1. Rational numbers Q belong to the real numbers R: N ⊂ Z ⊂ Q ⊂ R. For a negative integer, Z is the smallest of these sets.

Natural numbers belong to the integers Z. Every integer is rational because it can be written n/1. Rational numbers Q belong to the real numbers R: N ⊂ Z ⊂ Q ⊂ R. For a negative integer, Z is the smallest of these sets.