Full Grade 6 test

An angle bisector divides the whole angle into two equal parts. Divide the given angle by two.

Convert the actual distance to centimetres and divide by the scale denominator.

The interior angles of a quadrilateral total 360°. Subtract the sum of the three known angles.

Sort the data from smallest to greatest. With an odd number of values, the median is the middle value. With an even number, add the two middle values and divide by 2.

Remaining capacity equals total capacity minus the amount already filled. Use the same units for both amounts. For example, a 12 l container holding 7 l can take 12 − 7 = 5 l more.

The mode is the value that occurs most often in a data set.

1. Count how many times each number appears.
2. Find the number with the greatest frequency.

The data does not have to be sorted. The mode is not necessarily the largest number or the mean.

Reflecting across the y-axis changes the sign of the first coordinate and leaves the second unchanged.

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

Interest is calculated from the current balance each year, so in the second year it is also earned on the first year’s interest.

1. Convert the annual percentage into a multiplier: 1 + percentage ÷ 100.
2. Multiply the initial deposit by this multiplier once for the first year.
3. Multiply the new balance by the same multiplier again for the second year.

Formula: final amount = initial deposit × (1 + annual percentage ÷ 100)².

To find the stated part of a number, multiply the number by the fraction or decimal multiplier given in the question.

Result = a · b.

If a is given as a percentage, first convert it to a fraction: a% = a / 100.

The whole distance represents 100%. Add the percentages for both days because both refer to the whole distance. Remaining percentage = 100% − first-day percentage − second-day percentage.

Subtracting a number means adding its opposite: a − b = a + (−b). Subtracting a negative therefore becomes addition. For example, −4 − (−7) = −4 + 7 = 3.

The range equals the greatest value minus the smallest value. Find these two extremes and subtract; there is no need to add intermediate values.

Divide both ratio terms by their greatest common divisor. Keep their order. For example, 12:18 = 2:3 because both terms were divided by 6.

Distance = speed × time. Speed in km/h and time in hours give distance in kilometres. For example, 60 km/h × 3 h = 180 km.

Multiply the aquarium length, width and height to find its volume. Dimensions in decimetres give dm³. Since 1 dm³ = 1 l, the same number gives the water capacity in litres.

Subtract delivery from the total. Divide by the quantity to find the discounted unit price. Subtract it from the original unit price.

When two fractions have the same denominator, compare only their numerators.

1. Check that both fractions have the same denominator.
2. Compare the numerators: the larger numerator means the larger fraction.
3. Choose <, > or = according to the comparison.

This works because both wholes are divided into the same number of equal parts. If denominators differ, first rewrite the fractions with a common denominator or use another reliable comparison method.

Align the decimal points and corresponding place values. Add trailing zeros if needed. Add from the right, carrying when necessary, and keep the decimal point aligned. For example, 2.35 + 1.4 = 3.75.

Use a common denominator. Add the numerators with their signs, then simplify.

Arithmetic mean = sum of all values ÷ number of values. Count every value, including repetitions. For example, the mean of 2, 4 and 9 is (2 + 4 + 9) ÷ 3 = 5.

The base angles of an isosceles triangle are equal, and all angles of a triangle add up to 180°.

1. Subtract the given vertex angle from 180°.
2. Divide the remaining angle sum by 2 because the two base angles are equal.

Formula: required angle = (180° − vertex angle) ÷ 2.

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

Multiplication by 10 moves the decimal point one place right; multiplication by 100 moves it two places. Add zeros if needed. For example, 2.35 × 10 = 23.5 and 2.35 × 100 = 235.

Write coordinates in the order (x; y). From origin O, read the horizontal displacement: right gives positive x and left gives negative x. Then read the vertical displacement: up gives positive y and down gives negative y. Check both axis scales.

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.

Replace division by a fraction with multiplication by its reciprocal: invert the second fraction. Then multiply numerators and denominators and simplify. For example, 2/3 ÷ 4/5 = 2/3 × 5/4 = 5/6.