Full Grade 6 test

Use the complement: every toss gives B. Count all equally likely outcomes, find the probability of that single path, and subtract it from 1.

Trace the branch backwards from the question mark and identify the number-letter pair. Write the number first.

Find the price difference. Divide by the original price and multiply by 100; do not divide by the new price.

p% of n = n × p ÷ 100. Useful shortcuts: 10% is one tenth, 20% one fifth, 25% one quarter and 50% one half.

Divide the original total price by the original item count to find the unit price, then multiply by the new count. For example, if 3 items cost €12, then 5 cost 12 ÷ 3 × 5 = €20.

First find the area of the whole square by multiplying its side length by itself.

The diagonals divide the square into four triangles of equal area, so each has one quarter of the square area. The segment from the intersection of the diagonals to the midpoint of a side divides one of those triangles in half, so each small triangle has one eighth of the square area.

1. Use the letters of the shape to identify which parts it contains.
2. Add the required parts, or subtract the parts outside the shape from the area of the whole square.

Find the difference between the percentages. The difference in pupil counts represents that percentage of all pupils.

Multiplying or dividing two numbers with the same sign gives a positive result; different signs give a negative result. Determine the sign, then operate on the absolute values. For example, (−6) × (−2) = 12 and 12 ÷ (−3) = −4.

Count outcomes meeting both conditions together. Divide by the total number of terminal outcomes.

The total of four numbers equals their mean multiplied by 4. Subtract the sum of the three known numbers. Unknown number = 4 × mean − a − b − c.

Divide both sides of a × (x − b) = c by a to obtain x − b = c ÷ a. Add b: x = c ÷ a + b. Check the solution in the original equation.

If x ÷ b = c, the unknown dividend equals the divisor times the quotient: x = b × c. Check by division.

A sector is part of a circular region. Its fraction of the total area equals its central angle as a fraction of a full turn.

1. Use the sector name to identify its bounding radii. Count the equal small sectors inside the required sector and the total number in the circle.
2. Find the area of the whole circle: A = π · r². Use the radius given in the question, not a length measured from the drawing.
3. Multiply the whole area by the required fraction: A_sector = π · r² · m / N, where m is the number of parts in the required sector and N is the total number of equal parts.
4. If the central angle α is known, the same fraction is α / 360°.

Use π = 3.14 in this question. Round only the final sector area to the nearest whole number, not intermediate calculations.

An event and its complement cover all outcomes. Subtract the given probability from 1.

Select the column for the requested club. Compare the two class counts in that column and find their difference.

For each first-digit branch, check the allowed second digits. Add the two digit values and keep only codes whose sum reaches or exceeds the stated threshold. Add the counts from the separate branches.