What do the Grade 7 Mathematics cards cover?

32 cards across 7 chapters of the national textbook: Basic Concepts of Sets, Integers, Linear Equations, Ratio, Proportion and Percentage, Perimeter and Area of Plane Figures, Congruency of Plane Figures and Data Handling. You can take any chapter one card at a time on the page itself.

Is there a national exam in Grade 7?

No. Ethiopia sets national exams in Grade 6, Grade 8 and Grade 12 only. These cards are for your school's own exams, and for the national exam that comes a few years later.

Where do these cards come from?

They are drafted from Grade 7 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?

13 October 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 7 Mathematics

Grade 7 Mathematics on Temari has 32 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.

The Grade 7 Mathematics textbook is on this page as a free PDF, Ministry of Education edition, 252 pages. Go to the download

32
Cards: 7
Chapters: 13
Formulas: 4
Reference tables: Grade 7 Mathematics
Textbook: Free
Price: 13 October 2026
Last checked

Everything32Formula11Common mistake9Method4Rule4Reference table4

Across the whole subject

Sharing a total in a given ratioMethodAdd the numbers of the ratio to find how many parts there are. · Divide the total by the number of parts. · Multiply each number by the value of one part. · +4

What you do	Worked example
Add the numbers of the ratio to find how many parts there are.	3 + 5 = 8 parts
Divide the total by the number of parts.	800 / 8 = 100 Birr for one part
Multiply each number by the value of one part.	3 x 100 = 300 Birr and 5 x 100 = 500 Birr
Add the shares back to check.	300 + 500 = 800, the total you started with
When the question gives one person's share instead of the total, divide that share by its own number.	A receives 300 Birr for the 3, so one part is 100 Birr and B receives 500 Birr
Simplify a ratio by dividing every number in it by their highest common factor.	HCF(12, 18) = 6, so 12 : 18 = 2 : 3
Put both quantities in the same unit before you write the ratio.	50 cm : 2 m becomes 50 : 200, which is 1 : 4

When you use it

Use when a question hands you a total and a ratio and asks for each share, such as splitting 800 Birr between two people in the ratio 3 : 5. Add the numbers of the ratio to get the parts, divide the total by that number to get one part, then multiply each number by one part.

Watch out

Dividing by the wrong number is what costs the marks. Sharing 800 Birr in the ratio 3 : 5, students divide by 2 because there are two people, or by 3 because 3 is the first number. There are 8 parts, so one part is 100 Birr and the shares are 300 and 500. When the question gives one person's share instead of the total, divide by that person's own number: A's 300 Birr stands on the 3, so divide by 3 and not by 8. Add the shares back every time. If they do not give the total, the wrong number was used.

Part to part, part to whole and whole to partRulePart to part · Part to whole · Whole to part · +4

Comparison	Written as	What it says
Part to part	$a : b$	The two parts against each other. 3 boys to 5 girls.
Part to whole	$a : (a + b)$	One part against the whole, when the whole is made of two parts. The boys are 3 : 8 of the class.
Whole to part	$(a + b) : a$	The whole against one part. The class is 8 : 3 of the boys.
Three parts or more	$a : (a + b + c)$	The whole is the sum of every part, so the first part against the whole in a three-part split is a to a + b + c.
Value of a two-term ratio	$\frac{a}{b}$	A ratio of two terms is that fraction, where b is not zero. A ratio such as 2 : 3 : 5 has no single fraction value.
Same unit first	$50 : 200 = 1 : 4$	Put both quantities in one unit before comparing them, and the simplified ratio itself carries no unit.
Order	$3 : 5$	The 3 must be the quantity named first. 5 : 3 answers a different question unless the two are equal.

When you use it

Use when a question compares a ratio with a total, such as a class holding 3 boys for every 5 girls. Decide first whether the second number of your answer is the other part or the whole class, because part to part and part to whole are two different ratios of the same situation.

Watch out

Asked what share of the whole something is, students hand back the part to part ratio. A class with 3 boys to every 5 girls holds 3 + 5 = 8 children, so the boys are 3 : 8 of the class and not 3 : 5. Read the word that follows 'to': if it names the total, add the parts first. The second slip is comparing across units, writing 50 cm to 2 m as 50 : 2 instead of converting first and getting 1 : 4.

Workers and days: inverse proportionMethod

\text{workers} \times \text{days} = \text{total work in worker-days}

\text{workers} \times \text{days} = \text{total work in worker-days}

What you do	5 workers finish in 12 days. How long do 8 workers take?
Decide which way the answer must move before you touch the numbers.	More workers means fewer days, so the answer has to come out below 12.
Multiply first: workers times days is the total work, and it stays constant because every worker is taken to work at the same steady rate.	5 x 12 = 60 worker-days
Divide the total work by the new number of workers.	60 / 8 = 7.5 days, which is seven days and a half day
Check the direction of the answer.	7.5 is below 12, so the set-up was the right way round.
The same answer through rates.	One worker does 1/60 of the job a day, 8 workers do 8/60 = 2/15 a day, and the time is 15/2 = 7.5 days.
The same shape shows up in speed.	Over a fixed distance, speed and time are inversely proportional. At a constant speed, distance and time rise together.
Practice.	6 men finish a work in 15 days. 6 x 15 = 90 man-days, so 9 men take 90 / 9 = 10 days.

When you use it

Use when a job of fixed size is done by a different number of workers and the question asks how long it now takes. Multiply the first pair to get the total work in worker-days, then divide that by the new number of workers.

Watch out

Students set the two pairs up as a direct proportion and cross multiply, so 5 over 12 against 8 over x gives 19.2 days, which says 8 workers need longer than 5 did. Decide which way the answer must move before you touch the numbers: more workers means fewer days, so it has to come out below 12. Multiply first and divide second, and never divide the days by the workers.

Percentage increase and decrease multipliersFormula

\text{New value} = \text{Old value} \times \left(1 \pm \frac{r}{100}\right)

\text{New value} = \text{Old value} \times \left(1 \pm \frac{r}{100}\right)

$r$: the size of the change written as a plain number, so 15 for 15%
$1 + \frac{r}{100}$: the multiplier for an increase: 1.15 for a rise of 15%
$1 - \frac{r}{100}$: the multiplier for a decrease: 0.80 for a fall of 20%

What you are finding	How to write it	Worked example
Percent P of a number N	$\frac{P}{100} \times N$	25% of 80 is 20
What percent one number is of another	$\frac{a}{b} \times 100\%$	15 out of 60 is 25%, and 72 out of 90 is 80%
Increase by r percent	$\text{Old} \times \left(1 + \frac{r}{100}\right)$	200 raised by 15% gives 200 x 1.15 = 230
Decrease by r percent	$\text{Old} \times \left(1 - \frac{r}{100}\right)$	450 lowered by 20% gives 450 x 0.80 = 360
A discount	Multiply by the share of the price you still pay.	A 25% discount means you pay 75%, so multiply by 0.75
Percent, fraction and decimal	$25\% = \frac{25}{100} = 0.25$	Percent to decimal, divide by 100: 37% is 0.37. Decimal to percent, multiply by 100: 0.64 is 64%.

When you use it

Use when a price, a mark or a population changes by a given percent and the question wants the new value. Multiply the original by 1.15 for a rise of 15% or by 0.80 for a fall of 20%, and the number that comes out is already the new value.

Watch out

Two habits cost marks here. The first stops one step short: 200 x 0.15 = 30 is the increase and not the new value, so keep the 1 inside the bracket, multiply by 1.15 and get 230. The second takes the percentage of the wrong number. Decrease 450 by 20% and you get 360, but raising 360 by 20% gives 432 rather than 450, because that 20% is now taken of 360. A percentage change is never undone by the same percentage the other way.

Two percentage changes one after the otherCommon mistake

\text{New value} = \text{Old value} \times \left(1 \pm \frac{r_1}{100}\right) \times \left(1 \pm \frac{r_2}{100}\right)

\text{New value} = \text{Old value} \times \left(1 \pm \frac{r_1}{100}\right) \times \left(1 \pm \frac{r_2}{100}\right)

The case	What students do	What actually happens
80 raised by 10%, then lowered by 5%	Add the rates to a net 5% and compute 80 x 1.05 = 84.	80 x 1.10 = 88, then 88 x 0.95 = 83.6. The true net multiplier is 1.10 x 0.95 = 1.045, a rise of 4.5%.
Which amount the second percent is taken on	Take the 5% of the starting 80.	It is taken on 88, the amount the first change left, so the two changes multiply rather than add.
100 raised by 20%, then lowered by 20%	Assume the two cancel and answer 100.	100 x 1.20 = 120, then 120 x 0.80 = 96, which is 4% below the start.
The order of the two changes	Assume they have to be applied in the order given.	Multiplication is commutative, so 80 x 0.95 x 1.10 = 83.6 as well.

When you use it

Use when a quantity changes twice, such as a price raised by 10% and then cut by 5% in a sale. Multiply the two multipliers onto the original value instead of adding the rates, because the second percent is taken on the amount the first change left.

Watch out

Students add the two rates and treat a 10% rise followed by a 5% fall as one 5% rise, computing 80 x 1.05 = 84 instead of 83.6. The 5% is taken on 88, never on the starting 80. The same slip in reverse costs the most marks: a 20% rise followed by a 20% fall looks like it cancels, but 100 becomes 120 and then 96, which is 4% below where you began.

Basic Concepts of Sets

Counting the elements of a setCommon mistake

When you use it

Use this when a question asks how many elements a set has, or when you compare the sizes of two sets.

Watch out

A repeated element counts once: {1,1,2,2,3} has 3 elements, not 5. The empty set is written { } or ∅ and has 0 elements, so it is not a set containing the number 0.

Drafted from Grade 7 Mathematics, pages 1-10, then checked twice before it went up

Element sign versus subset signCommon mistake

When you use it

Use this when a question asks whether one object or one set lies inside another set.

Watch out

Use ∈ only between an object and a set, for example 6 ∈ N. Use ⊂ only between two sets, for example {2,4} ⊂ N. Writing 2 ⊂ N or {2} ∈ N is wrong. The empty set is a subset of every set, so ∅ ⊂ N is true, but ∅ ∈ N does not follow from that.

Drafted from Grade 7 Mathematics, pages 1-10, then checked twice before it went up

Equal sets versus equivalent setsCommon mistake

When you use it

Use this when a question asks whether two sets are equal or equivalent.

Watch out

Equivalent sets need only the same number of elements. {1,2,3} and {a,b,c} are equivalent but not equal. Equal sets must have exactly the same elements, so every pair of equal sets is equivalent, but not every equivalent pair is equal.

Drafted from Grade 7 Mathematics, pages 1-10, then checked twice before it went up

Listing all subsets and proper subsetsMethod

When you use it

Use this when a question asks you to list all subsets or all proper subsets of a small set.

Watch out

A set is never a proper subset of itself, so A ⊂ A is false even though A is a subset of A. Forgetting the empty set ∅ loses marks, because ∅ is a subset of every set.

Drafted from Grade 7 Mathematics, pages 1-10, then checked twice before it went up

Union and intersection of two setsReference tableA B

Operation	Result for A = {3,4,5,6} and B = {4,6,8,10}
$A \cup B$	$\{3,4,5,6,8,10\}$
$A \cap B$	$\{4,6\}$

When you use it

Use this when two sets are given and you must find their union A ∪ B or their intersection A ∩ B.

Watch out

The union keeps every element of both sets, listing a shared element once. The intersection keeps only the elements that appear in both sets.

Drafted from Grade 7 Mathematics, pages 1-10, then checked twice before it went up

Integers

Division of integers: when the answer is not an integerCommon mistake

When you use it

Reach for this when dividing one integer by another and the result is not a whole number, or when the divisor is zero.

Watch out

The quotient of two integers is not always an integer: 20 ÷ 8 = 2.5. Division by zero is undefined, so 20 ÷ 0 has no answer.

Drafted from Grade 7 Mathematics, pages 11-56, then checked twice before it went up

Sign rule for products and quotientsReference table+ · -

First factor or dividend	Second factor or divisor	Sign of product or quotient
+	+	+
+	-	-
-	+	-
-	-	+

When you use it

Reach for this when multiplying or dividing two integers and you need the sign of the answer before finding its size.

Watch out

Decide the sign first. Two negatives give a positive, as in (-12) x (-13) = 156, and students often write a negative answer instead.

Drafted from Grade 7 Mathematics, pages 11-56, then checked twice before it went up

Subtracting a negative integerFormula

a-(-b)=a+b

a-(-b)=a+b

$a$: any integer from which b is subtracted $dimensionless$
$b$: any integer, whose opposite is subtracted $dimensionless$

When you use it

Reach for this when subtracting a negative integer, such as 4 - (-9), to turn the subtraction into an addition.

Watch out

Two minus signs in a row become a plus sign: 4 - (-9) = 13, not -5. Students often drop the inner minus sign and write 4 - 9 = -5.

Drafted from Grade 7 Mathematics, pages 11-56, then checked twice before it went up

Linear Equations

Balancing and shifting termsRule

When you use it

Use this at every step when you isolate the unknown in a linear equation, whether you add, subtract, multiply or divide.

Watch out

When a term moves to the other side its sign changes. Divide both sides only by a non-zero number, because dividing by 0 is not allowed.

Drafted from Grade 7 Mathematics, pages 57-102, then checked twice before it went up

Clearing fractions with the LCMMethod

When you use it

Use this when a linear equation contains fractions, before you expand brackets or collect terms.

Watch out

Multiply every term on both sides by the LCM, including whole-number terms such as the 5 on the right side of x/4 + ... = 5. Missing one term is the usual lost mark.

Drafted from Grade 7 Mathematics, pages 57-102, then checked twice before it went up

Minus sign in front of a bracketCommon mistake

When you use it

Use this when you remove a bracket that has a minus sign in front of it, or a negative number multiplying it.

Watch out

Every term inside the bracket changes sign. Write -2(x - 4) = -2x + 8, not -2x - 8. Dropping the sign on the second term is the usual lost mark.

Drafted from Grade 7 Mathematics, pages 57-102, then checked twice before it went up

Signs of x and y in each quadrantReference tableI · II · III · +1

Quadrant	Sign of x	Sign of y
I	+	+
II	-	+
III	-	-
IV	+	-

When you use it

Use this when you must say which quadrant a point lies in, from the signs of its coordinates.

Watch out

A point on an axis belongs to no quadrant. For example (-3, 0) lies on the x-axis, not in quadrant II or III.

Drafted from Grade 7 Mathematics, pages 57-102, then checked twice before it went up

Ratio, Proportion and Percentage

Compound interestFormula

A = P(1+R)^{T}

A = P(1+R)^{T}

$A$: amount, principal plus compound interest $Birr$
$P$: principal, the initial amount $Birr$
$R$: interest rate per year as a decimal, e.g. 10% is 0.1 $1 (write the rate per year as a decimal)$
$T$: number of years $year$

When you use it

Use this when interest is added to the principal each year and the next year's interest is calculated on the new total.

Watch out

Use R = 0.1 for 10%, not 10. Also, the question may ask for the interest, which is A - P, not the amount A itself.

Drafted from Grade 7 Mathematics, pages 103-153, then checked twice before it went up

Percentage of a quantityFormula

P = R \times B

P = R \times B

$P$: percentage, the part of the whole $same as B (percentage part)$
$R$: rate, the percent written as a decimal or fraction, e.g. 20% is 0.2 $1 (write the rate as a decimal or fraction)$
$B$: base, the whole quantity, the number after 'of' $same as P (base, the whole)$

When you use it

Use this to find a percent of a number, or to find the whole when a part and its percent are given, by rearranging to B = P / R.

Watch out

The base is the number after 'of', so in '20% of 150' the base is 150. Change the percent to a decimal first, otherwise the answer is wrong by a factor of 100.

Drafted from Grade 7 Mathematics, pages 103-153, then checked twice before it went up

Ratio needs the same unitsCommon mistake

When you use it

Use this before writing any ratio of two measured quantities, such as money, length, mass or time.

Watch out

Change both quantities to the same unit before dividing. For example, 65 cents to 5 Birr is 65 : 500 = 13 : 100, not 65 : 5. A ratio has no unit once both sides match.

Drafted from Grade 7 Mathematics, pages 103-153, then checked twice before it went up

Simple interestFormula

I = PRT

I = PRT

$I$: simple interest earned $Birr$
$P$: principal, the amount borrowed or invested $Birr$
$R$: interest rate per year, e.g. 7% is 0.07 $1 (write the rate per year as a decimal)$
$T$: time in years $year$

When you use it

Use this when money is borrowed or deposited at a fixed rate per year and the interest is paid only on the original principal.

Watch out

Convert the time to years before multiplying: 3 months is 3/12 = 0.25 year. Write 12% as 0.12, not 12, or the answer is 100 times too large.

Drafted from Grade 7 Mathematics, pages 103-153, then checked twice before it went up

Perimeter and Area of Plane Figures

Area of a circleFormula

A=\pi r^2

A=\pi r^2

$A$: area of the circle $\text{cm}^2$
$r$: radius, the distance from the centre to any point on the circle $\text{cm}$
$\pi$: pi, about 3.14 when the textbook asks for a decimal answer $1$

When you use it

Use this when you must find the area of a full circle or a semicircle, and the radius is given or can be found from the diameter.

Watch out

If the diameter is given, divide it by 2 first to get the radius. Putting the diameter straight into r^2 gives an answer four times too large. For a semicircle, halve the final area.

Drafted from Grade 7 Mathematics, pages 154-195, then checked twice before it went up

Area of a rhombus and a kiteFormula

A=\frac{1}{2}\,d_1\,d_2

A=\frac{1}{2}\,d_1\,d_2

$A$: area of the rhombus or kite $\text{cm}^2$
$d_1$: length of the first diagonal $\text{cm}$
$d_2$: length of the second diagonal $\text{cm}$

When you use it

Use this when the figure is a rhombus or a kite and the two diagonals are given or can be found.

Watch out

Area uses the two diagonals, not the side lengths, so do not multiply two sides. Perimeter is different: it needs the sum of all four sides.

Drafted from Grade 7 Mathematics, pages 154-195, then checked twice before it went up

Area of a trapeziumFormula

A=\frac{1}{2}(b_1+b_2)\,h

A=\frac{1}{2}(b_1+b_2)\,h

$A$: area of the trapezium $\text{cm}^2$
$b_1$: length of one parallel base $\text{cm}$
$b_2$: length of the other parallel base $\text{cm}$
$h$: height, the perpendicular distance between the two bases $\text{cm}$

When you use it

Use this when a four-sided figure has exactly one pair of parallel sides and you need its area or a missing base or height.

Watch out

The height is the perpendicular distance between the two parallel bases, not the slanted leg. Use only the bases b_1 and b_2 in the formula, never a leg.

Drafted from Grade 7 Mathematics, pages 154-195, then checked twice before it went up

Area of a triangleFormula

A=\frac{1}{2}\,b\,h

A=\frac{1}{2}\,b\,h

$A$: area of the triangle $\text{cm}^2$
$b$: length of the base $\text{cm}$
$h$: height, the perpendicular from the opposite vertex to the base $\text{cm}$

When you use it

Use this for any triangle when you know one base and the height drawn to that same base.

Watch out

The height must be perpendicular to the base you chose, and both must belong to the same pair. In an obtuse triangle the height falls outside the triangle, so draw it to the extended base. A slanted side is not the height.

Drafted from Grade 7 Mathematics, pages 154-195, then checked twice before it went up

Congruency of Plane Figures

Corresponding parts of congruent trianglesRule

When you use it

Reach for this once two triangles are shown to be congruent and you need a missing side or angle of one of them.

Watch out

Match parts by the letter order of the congruence statement. A side of equal length next to the right one is not the matching side.

Drafted from Grade 7 Mathematics, pages 196-217, then checked twice before it went up

Included side and included angleCommon mistake

When you use it

Reach for this when choosing between SAS and ASA, or when you are given two sides and an angle and must decide whether a test applies.

Watch out

SAS needs the angle between the two given sides, and ASA needs the side between the two given angles. An angle outside the two sides does not complete SAS, and two sides with no included angle do not prove congruence.

Drafted from Grade 7 Mathematics, pages 196-217, then checked twice before it went up

Matching vertices in a congruence statementCommon mistake

When you use it

Reach for this when you write a congruence statement such as triangle ABC congruent to triangle FED, or when you read one to find matching parts.

Watch out

The letter order gives the pairing. If triangle ABC is congruent to triangle FED, then A matches F, B matches E and C matches D. Writing FED as DEF pairs the wrong angles and loses marks.

Drafted from Grade 7 Mathematics, pages 196-217, then checked twice before it went up

The three congruence testsReference tableSSS · SAS · ASA

Test	Parts that must be equal
SSS	Three sides of one triangle equal the three corresponding sides of the other.
SAS	Two sides and the angle between them equal two corresponding sides and the angle between them of the other.
ASA	Two angles and the side between them equal two corresponding angles and the side between them of the other.

When you use it

Reach for this when you must prove two triangles congruent, and pick the test that matches the parts you are given.

Drafted from Grade 7 Mathematics, pages 196-217, then checked twice before it went up

Data Handling

Mean of a data setFormula

\text{mean}=\frac{x_1+x_2+\cdots+x_n}{n}

\text{mean}=\frac{x_1+x_2+\cdots+x_n}{n}

$x_i$: the i-th value in the data set $same as the data$
$n$: the number of values in the data set $count (no unit)$

When you use it

Use when a question asks for the mean or average of a list of values, or when the mean is given and you must find a missing value.

Watch out

Divide by the number of values, not by the largest value. For a missing value, multiply the given mean by the count to get the total sum, then subtract the known values from that total.

Drafted from Grade 7 Mathematics, pages 218-246, then checked twice before it went up

Mode: unimodal, bimodal, trimodal or no modeRule

When you use it

Use when asked for the most frequent value in a list, or when naming a data set as unimodal, bimodal or trimodal.

Watch out

Count how often each value occurs before answering. If every value occurs only once there is no mode. If two or more values tie for the highest count, the data has that many modes.

Drafted from Grade 7 Mathematics, pages 218-246, then checked twice before it went up

Pie chart sector angleFormula

\theta=\frac{V}{T}\times 360^{\circ}

\theta=\frac{V}{T}\times 360^{\circ}

$\theta$: central angle of the sector $^{\circ}$
$V$: value of one category $same as T$
$T$: total value of all categories $same as V$

When you use it

Use when drawing a pie chart from given values or percentages, or when finding the amount a category represents from its sector angle.

Watch out

The sector angles must add up to 360°. When converting a percentage, divide by 100 before multiplying by 360°, so 20% gives 72° and not 7200°.

Drafted from Grade 7 Mathematics, pages 218-246, then checked twice before it went up

The Grade 7 Mathematics textbook

The student textbook for the new curriculum, free as a PDF. The cards on this page follow its chapters.

Ministry of Education edition, English
252 pages
Download the PDF
Oromia Education Bureau edition, Afaan Oromoo
218 pages
Download the PDF

What the book covers

1.Basic Concepts of Sets
2.Integers
3.Linear Equations
4.Ratio, Proportion and Percentage
5.Perimeter and Area of Plane Figures
6.Congruency of Plane Figures
7.Data Handling

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 7 subjects

Everything else in this year that has cards so far.

Questions students ask

What do the Grade 7 Mathematics cards cover?: 32 cards across 7 chapters of the national textbook: Basic Concepts of Sets, Integers, Linear Equations, Ratio, Proportion and Percentage, Perimeter and Area of Plane Figures, Congruency of Plane Figures and Data Handling. You can take any chapter one card at a time on the page itself.
Is there a national exam in Grade 7?: No. Ethiopia sets national exams in Grade 6, Grade 8 and Grade 12 only. These cards are for your school's own exams, and for the national exam that comes a few years later.
Where do these cards come from?: They are drafted from Grade 7 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?: 13 October 2026. Cards arrive chapter by chapter, and the line under each one says when that card was last read through.

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