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 written against the Ministry of Education textbook for Grade 7 Mathematics, and every formula, constant and table row is checked again before a card goes up.

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?

6 September 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 5 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.

5
Cards: 3
Formulas: Free
Price: 6 September 2026
Last checked

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.

The same subject in other years

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Your other Grade 7 subjects

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Questions students ask

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 written against the Ministry of Education textbook for Grade 7 Mathematics, and every formula, constant and table row is checked again before a card goes up.
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?: 6 September 2026. Cards arrive chapter by chapter, and the line under each one says when that card was last read through.

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