Full Grade 4 test

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 distance by multiplying speed by travelling time. Calculate the distance covered in the first hour and the distance covered in the second hour separately, then add them. Each stage lasts one hour. Give the total distance in kilometres.

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.

Starting with the first term, repeatedly add the stated step. Compare each expected term with the displayed term in that position.

Removing B leaves the A count unchanged but reduces the total by one. Use the remaining total, rather than the original total, as the denominator.

All four sides of a square have the same length.

1. Divide the perimeter by 4 to find the length of one side.
2. Multiply the side length by itself.
3. Write the answer in square centimetres.

Formula: side = perimeter ÷ 4, area = side × side.

Use the number of heads as the numerator and the total number of tosses as the denominator. Simplify the fraction if possible. This is the observed fraction of the tosses already performed.

1 t = 1,000 kg. Count complete thousands of kilograms to find the tonnes. Write the remainder in kilograms; it must be less than 1,000.

“Older than” means the age must be above the stated limit. The limit age itself is not allowed.

Add 1 to find the smallest whole-number age allowed. For example, someone older than 18 must be at least 19 when age is counted in whole years.

Multiply the whole part of the mixed number by the denominator, then add the numerator. This gives the new numerator.

Keep the same denominator. For example, 2 3/5 = (2 × 5 + 3)/5 = 13/5.

Calculate each rectangle’s area separately by multiplying its length by its width.

Compare the products and choose the rectangle with the larger area. One longer side is not enough: 6 × 2 = 12, while 4 × 4 = 16.

30 minutes is half an hour. To find the speed in kilometres per hour, work out how far the train would travel in a full hour at the same speed.

Multiply the distance travelled in 30 minutes by 2. For example, 25 km in half an hour means 50 km/h.

Line up the decimal points. Add trailing zeros if needed: 4.2 = 4.20.

Subtract from the right, regrouping from the next higher place when needed. Keep the decimal point in the same column. For example, 4.20 − 1.35 = 2.85.

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.

All four sides of a square are equal. Multiply one side length by 4 to find the perimeter.

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.

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

Determine which of the two alternating steps comes next. Add only that step’s fraction.

After step 1, only the pupil count is known. Include the accompanying adults before calculating the cost of all tickets.

Read the digits from left to right. Every column has a position: write zeros too so the other digits stay in their correct places.

When the denominators are the same, add the numerators and keep the denominator unchanged.

For example, 2/7 + 3/7 = 5/7. Do not add the denominators: you are still counting sevenths. If the numerator equals the denominator, the fraction is one whole.

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

Add all three numbers. You can first add the first two, then add the third to the result.

Alternatively, line up ones, tens and hundreds and add in columns. Remember to carry to the next place whenever a column total reaches 10.

Check the condition again after each addition. Stop once the number reaches or exceeds the limit. Count only the additions actually performed.