Full Grade 7 test

For inversely proportional quantities, the product remains constant: x × y = k.

1. Find the table column in which both x and y are known.
2. Multiply them to obtain the constant product k.
3. Divide the constant product by the x-value in the column where y is missing: y = k ÷ x.

The result is the missing value in the table.

Add inside the brackets first, then multiply by the value of x.

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

First add the term subtracted from the x expression to both sides. Then divide by the coefficient of x. Parentheses help keep track of the sign of a negative number.

A square has four equal sides and four right angles. Equal sides alone or parallel opposite sides alone are insufficient; both required properties must hold.

All pie-chart shares total 100%. Add the A, B and C percentages, then subtract their sum from 100: D = 100 − A − B − C.

Cylinder volume = circular base area × height: V = π × r² × h. Use π ≈ 3.14 and square the radius. Express the result in cm³.

First divide both sides by the coefficient outside the brackets. Then subtract the number added to x inside the brackets. Check the complete original equation.

Rectangle diagonals have equal lengths. The second diagonal has the same length as the first; do not double or halve it.

First multiply both sides by the divisor. Once the division is removed, subtract the term added to x from both sides.

The interval (a, b] means a < x ≤ b. The round bracket excludes a, while the square bracket includes b. Check both conditions: the number must exceed a and be at most b.

The median to the base of an isosceles triangle is also an altitude. The intersection of the medians divides each median in the ratio 2 : 1 from the vertex: use GM to find AG. For triangle ABG with AG as the base, the corresponding height is BM. Use the area formula to find BM, then use the fact that M is the midpoint of BC.

With the same base and height, the parallelogram area is a × h and the triangle area is a × h ÷ 2. The parallelogram area is twice the triangle area.

A quarter-circle arc is one quarter of the circumference: l = 2 × π × r ÷ 4. Only the arc is requested, so do not add the lengths of the two radii.

Only like terms can be added. Add their coefficients and keep x.

Add the two given angle measures. Same-side interior angles of parallel lines total 180°; the calculation lets you check that relationship.