Full Grade 7 test

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.

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

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

In one complete revolution without slipping, a wheel travels its circumference, 2 × π × r. For n revolutions, distance = n × 2 × π × r. Use π ≈ 3.14.

When subtracting like terms, subtract their coefficients. The variable and exponent stay the same.

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.

Base area = a × b. Volume = base area × height, so h = V ÷ (a × b). Express the height in centimetres.

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

Multiply the original price by (1 + p/100), then multiply the increased price by (1 − p/100). The percentages use different bases, so they do not cancel. For example, increasing €100 by 10% and then decreasing it by 10% gives €99.

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

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

When a transversal crosses parallel lines, corresponding angles are equal. They occupy matching positions at the two intersections, so the required angle has the same measure as the known one.

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.

Divide both sides of −a × x < b by negative −a. Dividing by a negative reverses the inequality: x > b ÷ (−a).

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

The coefficient is the number multiplying x. The constant has no x; its sign matters.

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.

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

Subtract the constant from both sides, then divide by the coefficient of x. Check by substituting the result.

First find the fixed route length: original speed × original time. New time = that distance ÷ new speed. Kilometres divided by km/h give hours.

The coefficient is k = y ÷ x. Divide y by the matching value of x.

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.

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.

Divide the sector angle by 360° and multiply by 100: percentage = angle ÷ 360 × 100. For example, 180° represents 50%.

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

Adjacent parallelogram angles total 180°. Adjacent angle = 180° − given angle. Opposite angles, rather than adjacent ones, are equal.

A 180° rotation about the origin reverses both coordinate signs: (x, y) → (−x, −y). The distance from the origin stays the same.

Circle area is S = π × r². Multiply the radius by itself, then by 3.14. Use cm².

Inversely proportional quantities have a constant product. For a fixed distance, speed × time = distance. Multiplying speed by k divides travel time by k, making it k times shorter.

A cone volume is one third of the volume of a cylinder with the same base and height: V = π × r² × h ÷ 3. Use π ≈ 3.14 and cm³.

Divide the budget by the ticket price and take the whole-number quotient. The ticket count must be an integer and its total price cannot exceed the budget. Check that one more ticket would be unaffordable.

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

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.