Full Grade 4 test

If the remainder were equal to or larger than the divisor, another divisor could still be subtracted. Therefore the final remainder is smaller.

The sign ≥ includes equality. Since the given boundary is an integer, it is itself the smallest integer satisfying the inequality. Smaller numbers do not satisfy it.

A fair game needs equal numbers of A and B sectors. Find half the total and compare it with the current A count. Relabelling does not change the total sector count.

Multiply the box count by the quantity per box, then subtract the distributed quantity.

Select only numbers from 1 to 6 satisfying both conditions together. Divide the number of suitable outcomes by six. Satisfying just one condition is insufficient.

The area of a right triangle is S = a · b / 2, where a and b are the lengths of its legs.

1. Multiply the given area S by 2.
2. Divide the result by the length of the known leg.
3. This gives the length of the other leg.

Formula: unknown leg = 2 · S / known leg. Write the answer in centimetres.

Multiply each group mean by its pupil count. Add the group totals and divide by the total number of pupils.

Perimeter is the distance around a shape, so add the lengths of all its sides.

Speed tells you how many kilometres are travelled in one hour. Divide the distance in kilometres by the time in hours.

For example, 24 km in 3 h gives 24 ÷ 3 = 8 km/h. Check by multiplying speed by time.

A rectangle’s area is length × width. Measure both lengths in the same units.

For example, a floor 5 m long and 3 m wide has an area of 5 × 3 = 15 m². Area uses square units such as cm² or m². Do not add the side lengths.

First find how many full boxes remain. Multiply that number by the quantity per box.

Divide the numerator by the denominator with a remainder. The whole-number quotient becomes the whole part of the mixed number.

The remainder becomes the new numerator, and the denominator stays the same. For example, 17 ÷ 5 gives 3 with remainder 2, so 17/5 = 3 2/5.

Compare the whole parts first. If they match, compare tenths, then hundredths.

You may add a trailing zero: 2.5 = 2.50. For example, 2.50 > 2.45. Compare the values, rather than the number of digits.

Find the total by multiplying the mean by the number of pupils. A mean does not mean everyone has the same result.

Look at the thousands digit. For 5–9, round to the higher multiple of 10,000; otherwise use the lower multiple. The last four digits become zeros.

Check the highlighted digit’s place after the decimal point. The first place is tenths; the second is hundredths.

For example, in 4.37 the digit 3 means 0.3, while 7 means 0.07. Choose the digit’s value, not just the digit itself.

The area of a right triangle is half the product of its legs.

1. Multiply the lengths of the two legs: a · b.
2. Divide the product by 2.

Formula: A = (a · b) / 2. Give the answer in square centimetres (cm²).

The sign > means “greater than”, so the boundary number itself is not allowed.

The smallest integer above a given integer is one more. Add 1 to the boundary. For example, for x > 12, the smallest integer allowed is 13.

With only addition and subtraction, work from left to right. Subtract the second number from the first, then add the third.

For example, 350 − 120 + 40 = 230 + 40 = 270. Do not add the second and third numbers before subtracting.

Count how many values are in the list, counting every occurrence of repeated values. Add all the values and divide their sum by the number of values. The mean is neither the sum alone nor the middle number in the list.

Find the missing addend by subtracting the known addend from the total.

For example, for 240 + ? = 560, the missing amount is 560 − 240 = 320. Check that the known and found addends make the given total.

Line up the decimal points. Put tenths under tenths and hundredths under hundredths.

Add as with whole numbers, carrying to the next place when needed. Keep the decimal point in the same column. For example, 2.35 + 1.40 = 3.75.

Add all three given numbers, then divide their sum by the number of values, which is 3 here. Check that the mean lies between the smallest and largest given values.

Multiply the mean by three to find the total. Subtract the first two days’ quantities.

A percent means one hundredth. To find a percentage of a number, divide the number by 100 and multiply by the percentage.

For example, 20% of 60 is 60 ÷ 100 × 20 = 12. Useful shortcuts: 10% is one tenth, 25% is one quarter, and 50% is one half.

For whole numbers, 0–4 rounds down and 5–9 rounds up. If the digit being increased was 9, a carry into the next column may be needed.

Calculate the expression on the left and the expression on the right separately, then compare the results.

Choose > if the left result is greater, < if it is smaller, and = if they are equal. The open side of the sign faces the greater number.

1 euro = 100 cents. Multiply the euros by 100 and add the remaining cents.

Use the unit shown beside the sides: mm, cm, m or km. Perimeter is a length, so it uses that same unit; area counts square units, so it is written with ².

Use long division or split the dividend into convenient parts.

For example, 168 ÷ 7 = 140 ÷ 7 + 28 ÷ 7 = 20 + 4 = 24. Check that result × divisor gives the starting number.

Read the operation sign first.

• For addition or subtraction, work with ones, tens and hundreds. Regroup when needed: 10 ones = 1 ten.
• For multiplication, split a number: 6 × 24 = 6 × 20 + 6 × 4.
• Check division by multiplying: result × divisor must give the starting number.

To find how many thousands a number contains, divide it by 1,000.

1 m = 100 cm. Convert metres to centimetres, then add the centimetres already given.

Find the shortfall and divide by the weekly savings. If any shortfall remains, allow one more full week.

Divide the command sequence into matching blocks. Count the blocks, not individual arrows.

For a division with no remainder, quotient × divisor = dividend.

Line up the ones, tens and hundreds. Add starting with the ones.

If a place adds to 10 or more, carry a ten to the next place. For example, 268 + 157 = 425. Check by subtracting one addend from the result.

Check every column separately and do not forget carried tens. A quick check is to divide the shown result by one factor.