Full Grade 5 test

An acute angle is less than 90°, a right angle equals 90°, an obtuse angle is greater than 90° but less than 180°, and a straight angle equals 180°. Compare the opening with a right angle; rotating the drawing does not change the angle type.

Find the interval value. Subtract the left-hand labelled number from the required number and divide by the interval value. Move that many gaps to the right and read the letter at that tick.

Find the unknown starting amount or addend by subtracting the known added amount from the final total. For x + a = b, the solution is x = b − a. Check by addition.

Read the value of A from the scale. A positive change means moving right and adding; a negative change means moving left and subtracting. Add or subtract the amount shown above the arrow. Remember that each gap may represent more than one unit.

For x − a = b, find the starting number by adding the difference and the amount subtracted: x = b + a. Substitute the result into the original equation and check by subtraction.

Subtract the smaller number from the larger. Alternatively, count the gaps between A and B and multiply by the value of one gap. The number of ticks or gaps alone is not the distance in units.

For x ÷ a = b, find the dividend by multiplying the quotient by the divisor: x = b × a. Check that dividing the result by a gives b.

With equal denominators, add only the numerators. Keep the denominator because the size of each part is unchanged. Reduce the result by dividing numerator and denominator by a common factor.

Rewrite the fractions with a common denominator, scaling numerator and denominator by the same factor. Then subtract the numerators, not the denominators. Reduce the result by dividing numerator and denominator by a common factor.

A zero inside the number does not change the place values of other digits. Keep digits aligned by place value, calculate both partial products and add them.

A point farther to the right represents a greater number. If A is to the left of B, choose <; if A is to the right, choose >. The sign = applies only to equal values.

For the letters to be equally likely, both types must have equal counts. Find how many balls the smaller group needs. Added balls also increase the total.

Convert both Roman numerals to ordinary numbers. Perform the indicated addition or subtraction, then convert the result back. I = 1, V = 5, X = 10, L = 50, C = 100; IV = 4, IX = 9, XL = 40, XC = 90. For example, VIII + IV = 8 + 4 = 12 = XII.

Rectangle area is S = length × width. Use the same units for both lengths. If the lengths are in centimetres, express the area in cm².

Look beside the vertical scale for the unit. Letters A–D identify groups, not units. The title helps confirm which quantity is measured.

Work inside brackets first, then multiply and divide, and finally add and subtract. Perform operations of equal priority from left to right. Find the product first, then add the remaining number.

These two angles add up to 180°. Find the unknown angle by subtracting the known angle from 180°. Check that the two angles total 180°.

Subtract each earlier term from the following term. A positive difference means adding that amount; a negative difference means subtracting its magnitude. Check the same operation against every neighbouring pair.

The numerator is above the fraction bar and counts the equal parts taken. The denominator is below it and counts the equal parts in the whole. In 3/5, the numerator 3 means three parts are taken.

Divide the whole amount by the denominator to find one equal part. Multiply that amount by the numerator. Choose the expression that uses both operations with the correct parts of the fraction.

The equally likely outcomes are sectors, not distinct labels. Count every sector with the target number and divide by the total number of sectors.

Find the unknown starting amount or addend by subtracting the known added amount from the final total. For x + a = b, the solution is x = b − a. Check by addition.

Divide the total by the number of equal parts. For a × x = b, the solution is x = b ÷ a. In the pack problem, divide the total price by the number of packs and check by multiplication.

Equivalent fractions are made by multiplying or dividing both numerator and denominator by the same non-zero number. Changing only one, or adding the same number to both, does not preserve the value. Check whether numerator and denominator were scaled by the same factor.

Calculate the differences between neighbouring terms. Two different amounts are added alternately. Write their order and determine which of the two operations comes after the final displayed term.

Locate the stated number in the count column, then read the group letter from that same row. The size of the number does not tell you its row position.

A number is divisible by a divisor when division leaves no remainder. For 2, the last digit must be even; for 5, it must be 0 or 5; for 10, it must be 0. For 3 or 9, the sum of the digits must be divisible by 3 or 9 respectively. Check each option using the rule for the specified divisor.

Roman numeral values: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000. Add a smaller numeral after a larger one; subtract it when it comes before a larger one. Subtraction pairs are IV = 4, IX = 9, XL = 40, XC = 90, CD = 400 and CM = 900. For example, XIV = 10 + 4 = 14. To write a number, start with its largest parts.

A number is divisible by a divisor when division leaves no remainder. For 2, the last digit must be even; for 5, it must be 0 or 5; for 10, it must be 0. For 3 or 9, the sum of the digits must be divisible by 3 or 9 respectively. Choose the number that fails the specified divisibility rule.

Count the cards whose numbers are divisible by the stated divisor. Divide by the total number of cards and simplify the fraction.

Equivalent fractions are made by multiplying or dividing both numerator and denominator by the same non-zero number. Changing only one, or adding the same number to both, does not preserve the value. Compare the denominators. Multiply the numerator by the same factor used for the denominator.

Work inside brackets first, then multiply and divide, and finally add and subtract. Perform operations of equal priority from left to right. Find the quotient first, then subtract it from the first number.

The label P in the drawing is the perimeter, not the side length. A square has four equal sides, so divide the perimeter by 4 to find one side. Multiply that side length by itself to calculate the area. If lengths are in centimetres, give the area in square centimetres.

Roman numeral values: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000. Add a smaller numeral after a larger one; subtract it when it comes before a larger one. Subtraction pairs are IV = 4, IX = 9, XL = 40, XC = 90, CD = 400 and CM = 900. For example, XIV = 10 + 4 = 14. To write a number, start with its largest parts.

All four square sides have the same length. Multiply one side length by 4 to obtain the perimeter: P = 4 × side.

Count the places where two line segments meet and the line changes direction. Every vertex of a closed polygon forms an angle, including inward corners. Endpoints of an open line do not form angles, and an ellipse has no corners.

Undo the operations in reverse order. For a × x + b = c, first subtract b from c, then divide the difference by a: x = (c − b) ÷ a. Substitute the solution into the original equation to check.

Roman numeral values: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000. Add a smaller numeral after a larger one; subtract it when it comes before a larger one. Subtraction pairs are IV = 4, IX = 9, XL = 40, XC = 90, CD = 400 and CM = 900. For example, XIV = 10 + 4 = 14. To write a number, start with its largest parts.

Work inside brackets first, then multiply and divide, and finally add and subtract. Perform operations of equal priority from left to right. Find the bracketed sum, divide it, then add the final number.

The total difference is the sum of equal interval values. Therefore, one interval equals the difference divided by the number of gaps. Equal gaps mean equal differences, not necessarily a difference of one.