What do the Grade 8 Mathematics cards cover?

25 cards across 8 chapters of the national textbook: Numbers rational numbers, Squares, unit, Linear equations, Similarity, Theorems, Circles, Solid figures and 1 more. You can take any chapter one card at a time on the page itself.

Do these help with the Grade 8 national exam?

Yes. Grade 8 sits a national exam, and these are the Mathematics rules and formulas it expects you to know. Past papers with a worked answer behind every question are on the same site, also free.

Where do these cards come from?

They are drafted from Grade 8 Mathematics, the Ministry of Education textbook for this grade. A second pass that cannot see the chapter then re-derives every formula, constant and table row, and anything it cannot confirm is held back instead of published.

Yes. Every card here is free to read and the printable sheet is free to download. Neither needs an account.

When was this last checked?

30 August 2026. Cards arrive chapter by chapter, and the line under each one says when that card was last read through.

Free short notes and revision cards

Grade 8 Mathematics

Grade 8 Mathematics on Temari has 25 revision cards, arranged by the chapters of the Ethiopian national curriculum. Every card says when the rule applies, what each symbol in it stands for, and the mistake students most often make with it. They are free to read and need no account.

25
Cards: 8
Chapters: 16
Formulas: 2
Reference tables: Grade 8 Mathematics
Textbook: Free
Price: 30 August 2026
Last checked

Everything25Formula16Common mistake4Rule3Reference table2

Numbers rational numbers

Absolute Value EquationsRule

When you use it

Use when solving an equation of the form |x| = a for any rational number a.

Watch out

An absolute value cannot be negative. If a is less than 0, there is no solution.

Drafted from Grade 8 Mathematics, pages 2-41, then checked twice before it went up

Cross Product ComparisonRule

When you use it

Use to compare two fractions a/b and c/d with positive denominators by checking if a*d is greater than, less than, or equal to b*c.

Watch out

Ensure both denominators are positive before using cross multiplication.

Drafted from Grade 8 Mathematics, pages 2-41, then checked twice before it went up

Division of Rational NumbersFormula

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a d}{b c}

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a d}{b c}

$a$: numerator of dividend
$b$: denominator of dividend, where b is not 0
$c$: numerator of divisor, where c is not 0
$d$: denominator of divisor, where d is not 0

When you use it

Use when dividing one rational number or fraction by another.

Watch out

Invert only the divisor fraction and change the division sign to multiplication.

Drafted from Grade 8 Mathematics, pages 2-41, then checked twice before it went up

Simple InterestFormula

I = P R T

I = P R T

$I$: simple interest $\text{Birr}$
$P$: principal amount borrowed or invested $\text{Birr}$
$R$: annual rate of interest $\text{year}^{-1}$
$T$: time period $\text{year}$

When you use it

Use to calculate interest, principal, rate, or time for loans and investments.

Watch out

Convert time to years before multiplying. For example, 5 months must be written as 5/12 years.

Drafted from Grade 8 Mathematics, pages 2-41, then checked twice before it went up

Squares, unit

Confusing squaring with doubling and sign rulesCommon mistake

When you use it

Check this when evaluating powers of numbers, especially negative rational numbers.

Watch out

a^2 means a multiplied by a, not a multiplied by 2. Also, (-a)^2 is positive while -a^2 is negative because the exponent applies only to the base.

Drafted from Grade 8 Mathematics, pages 42-67, then checked twice before it went up

Sum of first n odd natural numbersFormula

S_n = n^2

S_n = n^2

$S_n$: Sum of the first n consecutive odd natural numbers $dimensionless$
$n$: Number of consecutive odd terms $dimensionless$

When you use it

Use this to find the sum of consecutive odd natural numbers starting from 1 without adding term by term.

Watch out

The pattern only works if the sum starts at 1 and contains no skipped odd numbers.

Drafted from Grade 8 Mathematics, pages 42-67, then checked twice before it went up

Linear equations

Cartesian Quadrant SignsReference tableI · II · III · +1

Quadrant	x-coordinate	y-coordinate	Signs
$I$	$x > 0$	$y > 0$	$(+, +)$
$II$	$x < 0$	$y > 0$	$(-, +)$
$III$	$x < 0$	$y < 0$	$(-, -)$
$IV$	$x > 0$	$y < 0$	$(+, -)$

When you use it

Use to identify which quadrant an ordered pair lies in based on the signs of its coordinates.

Watch out

Points with a zero coordinate lie on the axes, not in any quadrant.

Drafted from Grade 8 Mathematics, pages 68-103, then checked twice before it went up

Reversing Inequality SignCommon mistake

When you use it

Use when multiplying or dividing both sides of an inequality by a negative number.

Watch out

Failing to reverse the inequality sign when dividing or multiplying by a negative number. For example, -3x < 6 becomes x > -2 upon dividing by -3.

Drafted from Grade 8 Mathematics, pages 68-103, then checked twice before it went up

Similarity

Area Ratio of Similar TrianglesFormula

\frac{A_1}{A_2} = \left(\frac{S_1}{S_2}\right)^2 = k^2

\frac{A_1}{A_2} = \left(\frac{S_1}{S_2}\right)^2 = k^2

$A_1$: Area of the first triangle $\text{m}^2$
$A_2$: Area of the second triangle $\text{m}^2$
$S_1$: Side length of the first triangle $\text{m}$
$S_2$: Corresponding side length of the second triangle $\text{m}$
$k$: Scale factor or constant of proportionality

When you use it

Use when finding the area or side of a similar triangle given the scale factor or side ratio.

Watch out

Always square the scale factor k when setting up the ratio of areas.

Drafted from Grade 8 Mathematics, pages 104-129, then checked twice before it went up

Perimeter Ratio of Similar TrianglesFormula

\frac{P_1}{P_2} = \frac{S_1}{S_2} = k

\frac{P_1}{P_2} = \frac{S_1}{S_2} = k

$P_1$: Perimeter of the first triangle $\text{m}$
$P_2$: Perimeter of the second triangle $\text{m}$
$S_1$: Side length of the first triangle $\text{m}$
$S_2$: Corresponding side length of the second triangle $\text{m}$
$k$: Scale factor or constant of proportionality

When you use it

Use to find an unknown perimeter or side length when two triangles are similar.

Watch out

The ratio of perimeters equals the scale factor k directly, not k^2.

Drafted from Grade 8 Mathematics, pages 104-129, then checked twice before it went up

Scaling Area LinearlyCommon mistake

When you use it

Reach for this reminder when a problem involves changing the dimensions or side lengths of a figure and asking for the new area.

Watch out

Doubling side lengths does not double the area: it quadruples the area because area scales by k^2.

Drafted from Grade 8 Mathematics, pages 104-129, then checked twice before it went up

Theorems

Angle Sum Theorem of a TriangleFormula

m\angle 1 + m\angle 2 + m\angle 3 = 180^\circ

m\angle 1 + m\angle 2 + m\angle 3 = 180^\circ

$m\angle 1$: measure of first interior angle $^\circ$
$m\angle 2$: measure of second interior angle $^\circ$
$m\angle 3$: measure of third interior angle $^\circ$

When you use it

Use to find an unknown interior angle of a triangle when the other two interior angles are given.

Watch out

The sum of the interior angles of any triangle is always 180 degrees, not 360 degrees.

Drafted from Grade 8 Mathematics, pages 130-158, then checked twice before it went up

Euclid TheoremFormula

a^2 = c \cdot c_2, \quad b^2 = c \cdot c_1

a^2 = c \cdot c_2, \quad b^2 = c \cdot c_1

$a$: length of leg BC $\text{m}$
$b$: length of leg AC $\text{m}$
$c$: length of hypotenuse AB $\text{m}$
$c_1$: length of segment AD adjacent to leg b $\text{m}$
$c_2$: length of segment BD adjacent to leg a $\text{m}$

When you use it

Use in a right-angled triangle when an altitude is drawn to the hypotenuse to find side or segment lengths.

Watch out

Multiply the entire hypotenuse by the segment adjacent to that specific leg, never by the segment on the opposite side.

Drafted from Grade 8 Mathematics, pages 130-158, then checked twice before it went up

Exterior Angle TheoremFormula

d = x + y

d = x + y

$d$: measure of the exterior angle $^\circ$
$x$: measure of first remote interior angle $^\circ$
$y$: measure of second remote interior angle $^\circ$

When you use it

Use when finding the measure of an exterior angle or a remote interior angle of a triangle.

Watch out

Do not include the adjacent interior angle. An exterior angle equals the sum of the two opposite remote interior angles only.

Drafted from Grade 8 Mathematics, pages 130-158, then checked twice before it went up

Pythagoras TheoremFormula

a^2 + b^2 = c^2

a^2 + b^2 = c^2

$a$: length of first leg $\text{m}$
$b$: length of second leg $\text{m}$
$c$: length of hypotenuse $\text{m}$

When you use it

Use to find the missing side length of a right-angled triangle given the other two sides.

Watch out

Ensure that c is strictly the hypotenuse opposite the right angle, not one of the legs.

Drafted from Grade 8 Mathematics, pages 130-158, then checked twice before it went up

Circles

Angle of Intersecting ChordsFormula

\theta = \frac{1}{2}(\alpha + \beta)

\theta = \frac{1}{2}(\alpha + \beta)

$\theta$: Angle formed by two intersecting chords inside the circle $^\circ$
$\alpha$: Measure of the first intercepted arc $^\circ$
$\beta$: Measure of the second intercepted arc from vertical angle $^\circ$

When you use it

Use this when two chords intersect inside a circle and you need the angle formed at the intersection point.

Watch out

Remember to add both intercepted arcs before multiplying by half, rather than subtracting them.

Drafted from Grade 8 Mathematics, pages 159-184, then checked twice before it went up

Confusing Arc Measure with Inscribed AngleCommon mistake

When you use it

Use this check when solving angle problems where the vertex is located on the circle boundary.

Watch out

Students often write the inscribed angle equal to the arc measure, forgetting to divide the arc measure by 2.

Drafted from Grade 8 Mathematics, pages 159-184, then checked twice before it went up

Congruent Inscribed Angles and SemicirclesRule

When you use it

Use when finding unknown inscribed angles that intercept the exact same arc or that intercept a diameter.

Watch out

An inscribed angle subtended by a diameter is always a right angle, which equals 90 degrees.

Drafted from Grade 8 Mathematics, pages 159-184, then checked twice before it went up

Solid figures

Classification of Basic Solid FiguresReference tablePrism · Cylinder · Pyramid · +1

Solid Figure	Base Shape	Lateral Faces	Number of Bases
Prism	Congruent polygons	Parallelograms or rectangles	2
Cylinder	Congruent circles	Curved surface	2
Pyramid	Polygon	Triangles meeting at vertex	1
Cone	Circle	Curved surface meeting at vertex	1

When you use it

Use to identify, distinguish, and describe parts of three dimensional geometric solids.

Watch out

Prisms and pyramids have polygonal bases, while cylinders and cones have circular non-polygonal bases.

Drafted from Grade 8 Mathematics, pages 185-220, then checked twice before it went up

Surface Area of a Right Circular CylinderFormula

A_T = 2\pi r(h + r)

A_T = 2\pi r(h + r)

$A_T$: Total surface area $\text{m}^2$
$r$: Base radius $\text{m}$
$h$: Height of the cylinder $\text{m}$

When you use it

Use when finding the total outer surface area of a closed right circular cylinder.

Watch out

If the diameter is given instead of radius, divide the diameter by 2 before substituting into the formula.

Drafted from Grade 8 Mathematics, pages 185-220, then checked twice before it went up

Surface Area of a Right PrismFormula

A_T = ph + 2A_B

A_T = ph + 2A_B

$A_T$: Total surface area $\text{m}^2$
$p$: Base perimeter $\text{m}$
$h$: Height of the prism $\text{m}$
$A_B$: Base area $\text{m}^2$

When you use it

Use this formula to calculate the lateral surface area or total surface area of any right prism.

Watch out

The lateral surface area is only ph. You must add the area of two bases to find the total surface area.

Drafted from Grade 8 Mathematics, pages 185-220, then checked twice before it went up

Volume of Prisms and CylindersFormula

V = A_B h

V = A_B h

$V$: Volume $\text{m}^3$
$A_B$: Base area $\text{m}^2$
$h$: Height $\text{m}$

When you use it

Use this general formula to find the volume of any prism or cylinder by multiplying base area by height.

Watch out

For a circular cylinder, the base area is pi r^2, giving the volume formula V = pi r^2 h.

Drafted from Grade 8 Mathematics, pages 185-220, then checked twice before it went up

Unit 8

Experimental ProbabilityFormula

P(E) = \frac{f}{N}

P(E) = \frac{f}{N}

$P(E)$: Experimental Probability of event E
$f$: Number of times the event occurs
$N$: Total number of trials or observations

When you use it

Use this formula when calculating probability from observed frequency data or repeated trials.

Watch out

Always divide by the total number of all trials, not just the trials where the event failed.

Drafted from Grade 8 Mathematics, page 221 onwards, then checked twice before it went up

Probability BoundsFormula

0 \le P(E) \le 1

0 \le P(E) \le 1

$P(E)$: Probability of event E

When you use it

Use this rule to verify probability values, where 0 represents an impossible event and 1 represents a certain event.

Watch out

A probability can never be negative or greater than 1.

Drafted from Grade 8 Mathematics, page 221 onwards, then checked twice before it went up

Theoretical ProbabilityFormula

P(E) = \frac{n(E)}{n(S)}

P(E) = \frac{n(E)}{n(S)}

$P(E)$: Probability of event E
$n(E)$: Number of favorable outcomes in event E
$n(S)$: Total number of outcomes in sample space S

When you use it

Use this formula when all outcomes in the sample space are equally likely to occur.

Watch out

Do not apply this formula if outcomes do not have equal chances of occurring.

Drafted from Grade 8 Mathematics, page 221 onwards, then checked twice before it went up

The same subject in other years

An exam paper keeps asking for what the year below taught. Those cards are here too.

Your other Grade 8 subjects

Everything else in this year that has cards so far.

Questions students ask

What do the Grade 8 Mathematics cards cover?: 25 cards across 8 chapters of the national textbook: Numbers rational numbers, Squares, unit, Linear equations, Similarity, Theorems, Circles, Solid figures and 1 more. You can take any chapter one card at a time on the page itself.
Do these help with the Grade 8 national exam?: Yes. Grade 8 sits a national exam, and these are the Mathematics rules and formulas it expects you to know. Past papers with a worked answer behind every question are on the same site, also free.
Where do these cards come from?: They are drafted from Grade 8 Mathematics, the Ministry of Education textbook for this grade. A second pass that cannot see the chapter then re-derives every formula, constant and table row, and anything it cannot confirm is held back instead of published.
Is this free?: Yes. Every card here is free to read and the printable sheet is free to download. Neither needs an account.
When was this last checked?: 30 August 2026. Cards arrive chapter by chapter, and the line under each one says when that card was last read through.

Revise, then test yourself

Temari turns these cards into practice questions and marks them as you go, with an AI tutor to explain anything that did not land.

Start free