Full Grade 8 test

Find neighbouring integers whose squares surround the radicand: a² < n < (a + 1)². Then a < √n < a + 1. For example, 16 < 20 < 25, so 4 < √20 < 5.

Interquartile range IQR = Q3 − Q1. It describes the spread of the middle approximately 50% of the data. A greater IQR means greater spread in this middle portion.

Read the frequencies of both specified intervals from the vertical scale. Subtract the second frequency from the first. Horizontal interval bounds are not frequencies.

Subtract the constant from all three parts, then divide all parts by the positive coefficient. Exclude a strict boundary and include a non-strict one.

Compound interest is calculated on the current balance each period, including earlier interest. Final amount = initial deposit × (1 + p/100)ⁿ. With a positive rate and more than one period, this exceeds the amount from simple interest.

Square of a sum: (x + a)² = x² + 2ax + a². The middle term comes from adding the two cross products ax. Thus the x coefficient is 2a; x² + a² alone is incomplete.

With equal interval widths, the tallest histogram bar gives the greatest frequency. Select the interval beneath that bar.

Let x be the A-ticket count and y the B-ticket count. Write x + y = total and a × x + b × y = revenue. Substitute y = total − x, solve for x, then find y. Give A first.

The square root of a positive integer that is not a perfect square is irrational. It cannot be written as a ratio of integers. I denotes the irrational numbers in the choices.

A finite set has a limited number of elements. The integers from −5 to 5 can all be listed: there are 11. The sets of all natural numbers, rational numbers or points on a line are infinite.

Add vectors coordinate by coordinate: (a, b) + (c, d) = (a + c, b + d). Add first coordinates together and second coordinates together.

The route with a turn is a + b; the direct route is √(a² + b²). When both lengths are positive, the direct route is shorter. If a difference is needed, subtract the direct length from a + b.

In a box plot, the median is the line inside the box. Read its position on the number scale. The box edges mark Q1 and Q3 rather than the median.

A polynomial with one, two or three terms is a monomial, binomial or trinomial respectively. The expression ax² + bx + c has three terms, so it is a trinomial.

Natural numbers belong to the integers Z. Every integer is rational because it can be written n/1. Rational numbers Q belong to the real numbers R: N ⊂ Z ⊂ Q ⊂ R. For a negative integer, Z is the smallest of these sets.

Factor out x. A product is zero when at least one factor is zero. Find both solutions and add them.

Find the lower bound from the first inequality and the upper bound from the second. Both conditions must hold. If the lower bound exceeds the upper bound, the intersection is empty.