- For multiple-choice items, circle the letter of the only correct answer.
- For items with parts a) and b), write complete solutions in your notebook.
A. Natural numbers. Powers. Divisibility
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The result of $56:7 + 3 \cdot (12 - 5)$ is equal to:
- a) $29$
- b) $77$
- c) $35$
- d) $23$
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The result of $2^{5} \cdot 2^{3}:2^{6}$ is equal to:
- a) $2^{2}$
- b) $2^{14}$
- c) $2^{9}$
- d) $2^{8}$
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The result of $37 \cdot 25 + 37 \cdot 75$ is equal to:
- a) $3700$
- b) $2775$
- c) $4625$
- d) $1000$
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Among the numbers $245$, $312$, $540$ and $723$, the number divisible by $2$, by $3$ and by $5$ is:
- a) $245$
- b) $312$
- c) $540$
- d) $723$
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The remainder of dividing $2026$ by $9$ is:
- a) $1$
- b) $2$
- c) $4$
- d) $7$
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Among the numbers $2^{8}$, $3^{5}$, $5^{7}$ and $7^{3}$, the square of a natural number is:
- a) $2^{8}$
- b) $3^{5}$
- c) $5^{7}$
- d) $7^{3}$
B. Common and decimal fractions. Organizing data
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Among the fractions $\frac{7}{9}$, $\frac{9}{9}$, $\frac{11}{8}$ and $\frac{3}{10}$, the improper fraction is:
- a) $\frac{7}{9}$
- b) $\frac{9}{9}$
- c) $\frac{11}{8}$
- d) $\frac{3}{10}$
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The result of $\frac{5}{6} - \frac{1}{4}$ is:
- a) $\frac{7}{12}$
- b) $\frac{4}{2}$
- c) $\frac{1}{3}$
- d) $\frac{4}{10}$
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A book costs $150$ lei. $20\%$ of the price of the book is:
- a) $30$ lei
- b) $75$ lei
- c) $130$ lei
- d) $3$ lei
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The result of $3,75 \cdot 100$ is:
- a) $375$
- b) $0,0375$
- c) $37,5$
- d) $3750$
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The fraction $\frac{7}{20}$, written as a decimal, is:
- a) $0,35$
- b) $0,72$
- c) $3,5$
- d) $0,035$
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The table below shows how many books the pupils of a class read during the holidays. The number of pupils who read at least $3$ books is:
Number of books $0$ $1$ $2$ $3$ $4$ Number of pupils $2$ $5$ $9$ $8$ $4$ - a) $12$
- b) $8$
- c) $21$
- d) $4$
C. Problems
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Consider the natural numbers of the form $\overline{2a4b}$.
a) Write the largest number of this form that is divisible by $5$.
b) Find all numbers of this form that are divisible by both $5$ and $9$.
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I am thinking of a number. I multiply it by $3$, I add $12$ to the result, I divide the sum by $5$ and I get $9$.
a) Check whether the number I thought of can be $10$.
b) Find the number I thought of.
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A cyclist rides a route in three days. On the first day they ride $\frac{2}{5}$ of the route, on the second day $\frac{1}{3}$ of the route, and on the third day they ride the remaining $24\text{ km}$.
a) What fraction of the route did the cyclist ride in the first two days?
b) Find the length of the route.
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In a yard there are hens and rabbits. Together they have $20$ heads and $56$ legs.
a) Show that there cannot be $10$ hens and $10$ rabbits in the yard.
b) Find how many rabbits are in the yard.