Full Grade 7 test

Alternate interior angles of parallel lines are equal. They lie between the lines on opposite sides of the transversal. The required angle equals the given angle.

Divide both sides of a × x ≤ b by positive a. The direction stays the same: x ≤ b ÷ a. Equality is included in the solution.

Parallelogram area is S = base × height, so base = S ÷ h. Divide the area by the given height. The result is a length in centimetres.

A cone has one circular base and an apex. A cylinder has two equal parallel circular bases and no apex. A prism has two equal parallel bases; a pyramid has one base and an apex.

When dividing powers with the same nonzero base, subtract the second exponent from the first: aᵐ ÷ aⁿ = aᵐ⁻ⁿ. For example, 3⁵ ÷ 3² = 3³.

An equation remains balanced only when the same operation is performed on both sides. A moved term changes sign because the inverse operation is performed on both sides.

A parallelogram has both pairs of opposite sides parallel; opposite sides are also equal. Right angles, all sides equal or equal diagonals are properties of only certain special parallelograms.

Compare the sectors or their labelled percentages. The largest sector has the greatest central angle and represents the largest share. Select its category label.

“At least” means “greater than or equal to”. If the minimum score is a, write x ≥ a; exactly a points also qualifies.

Rectangular prism volume is V = length × width × height. Multiply all three dimensions; centimetre dimensions give cm³.

Opposite parallelogram sides are equal. Perimeter = a + b + a + b = 2 × (a + b). Express the answer in cm.