Full Grade 7 test

Volume depends on the product of three length dimensions. Multiplying every length by k multiplies the volume by k × k × k = k³. For example, doubling all lengths multiplies volume by 8.

Collect all x terms on one side and constants on the other. For example, subtract cx from both sides and then subtract the constant term. Finally divide by the remaining coefficient of x.

Compare the initial and final coordinates. Reflection in the x-axis changes only the sign of y; reflection in the y-axis changes only x; a 180° rotation about the origin changes both signs.

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

The sample should represent the whole school. Randomly selecting students from every class includes different groups and reduces domination by a single group. One team or one class does not represent all students.

Divide both sides by the coefficient of x. To check, multiply the result by that coefficient and compare with the right side.

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.

Reflection in the x-axis preserves x and reverses the sign of y: (x, y) → (x, −y). The image is the same distance on the other side of the horizontal axis.

Saved amount = target × p ÷ 100. Remaining amount = target − saved amount, or target × (100 − p) ÷ 100.

A negative exponent does not mean that the number itself is negative. When a ≠ 0, use the rule a⁻ⁿ = 1 / aⁿ.

1. Keep the same base a.
2. Move the power to the denominator and make the exponent positive n.
3. Check that the denominator is not zero.

Thus a negative exponent takes the reciprocal of a power; it does not place a minus sign in front of its value.

Student count = total respondents × p ÷ 100. Apply the percentage to the full survey sample.

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

“Interior” means the angles lie between the two lines. “Same-side” means both are on the same side of the transversal. These are therefore same-side interior angles.

Simple interest is calculated from the original deposit each year. Interest = deposit × p ÷ 100 × years. Final balance = original deposit + total interest.

Let x be the number of tickets. The tickets cost kx, so form kx + fee = total. Subtract the fee and divide by the price of one ticket.

The fixed area equals original length × original width. New width = that area ÷ new length. Increasing the length requires a smaller width.

Multiply the point’s x-coordinate by k. If the result equals its y-coordinate, the point lies on the graph.

When x and y are inversely proportional, their product is always the same: x × y = k.

1. Multiply the original x- and y-values to find the constant product k.
2. To find the new y-value, divide k by the new x-value.
3. Choose the result that satisfies y = k ÷ x.

As x increases, y must decrease by the corresponding factor so that their product does not change.

Selecting every nth list member is systematic sampling. The selection interval is fixed; a properly designed sample uses a randomly chosen starting member.

Interior angles on the same side of a transversal, or on the same trapezoid leg between parallel bases, total 180°. Subtract the known angle from 180° to find the other.

Trapezoid area is S = (a + b) × h ÷ 2. Add the two parallel bases, multiply by the perpendicular height and divide by 2.

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.

Substitute x into the formula and multiply by the coefficient of proportionality k.