Formulas – maths grades 7 to 10

Numbers

Distance from zero · Grade 7

|a|

The absolute value of a number is its distance from zero on the number line. It is never negative.

Examples $|-7| = 7$ $|7| = 7$ $|0| = 0$

Same distance from zero · Grade 7

a \;\to\; -a

Mirror a number across zero and you get its opposite. The sign switches, the distance from zero stays.

Examples $5 \to -5$ $-3 \to 3$ $0 \to 0$

Same signs give plus · Grade 7

(-a) \cdot (-b) = a \cdot b \qquad (-a) \cdot b = -(a \cdot b)

When multiplying, count the minus signs. Two minuses cancel out, a single minus stays.

Examples $(-4) \cdot (-2) = 8$ $(-4) \cdot 2 = -8$

First times and divide · Grade 7

a + b \cdot c = a + (b \cdot c)

Multiply and divide before you add and subtract, as if there were brackets around them. Brackets always come first.

Examples $2 + 3 \cdot 4 = 2 + 12 = 14$ $10 - 6 : 2 = 10 - 3 = 7$

A sum squared · Grade 8

(a + b)^2 = a^2 + 2ab + b^2

The square of a sum has three parts – both squares and twice the product. The middle term is the one people forget.

Examples $(x + 3)^2 = x^2 + 6x + 9$

In a right triangle · Grade 8

a^2 + b^2 = c^2

In a right triangle, the squares of the two legs add up to the square of the hypotenuse. The hypotenuse is opposite the right angle.

Examples $3^2 + 4^2 = 5^2$ $c = \sqrt{a^2 + b^2}$

Base times height · Grade 8

A = g \cdot h

A parallelogram has the same area as a rectangle with the same base and height – cut off a triangle and attach it on the other side.

Examples $A = 6 \cdot 4 = 24$

Average side times height · Grade 8

A = \frac{a + c}{2} \cdot h

For a trapezoid, take the average of the two parallel sides and multiply it by the height.

Examples $A = \frac{8 + 4}{2} \cdot 3 = 18$