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Year 1 test: logic, number sets, fractions and intervals

71 questions in 18 groups: statements and number sets, integers, fractions, decimals, intervals and absolute value.

For multiple-choice questions choose one answer. For the others type the answer: an integer, a fraction such as 3/10 or an interval such as (1,5]. \(\mathbb{I}\) is the set of irrational numbers, \(\top\) means true and \(\bot\) false. When you finish, click Check answers.

1a. Is the statement true? \(\mathbb{Q}\subset\mathbb{N}\)

1b. Is the statement true? \(\mathbb{Z}\subset\mathbb{Q}\)

1c. Is the statement true? \(\mathbb{R}\setminus\mathbb{Q}=\mathbb{Z}\)

1d. Is the statement true? \(\mathbb{Q}\cup \mathbb{I}=\mathbb{R}\)

2a. Is the statement true? \(-5\in\mathbb{Z}\)

2b. Is the statement true? \(0{,}5\in\mathbb{Q}\)

2c. Is the statement true? \(\sqrt2\in\mathbb{Q}\)

2d. Is the statement true? \(3\in \mathbb{I}\)

3a. Calculate: \(-16+(-4)-(-7)\)

3b. Calculate: \(8+(-2)+(-5)+17\)

3c. Calculate: \(5-(2-9)-(4-11)\)

3d. Calculate: \(-16-[2-(-1)]-[2+(-6)]\)

4a. Calculate: \((-5)-(6-3\cdot4)-(-3)\cdot(-2)-2\cdot(-5)\)

4b. Calculate: \((-2)\cdot(+3)+[(-3)\cdot(-4)+(7-9)]\cdot(3-5)\)

4c. Calculate: \((3-6-9)-[2+(-4)-7]\)

4d. Calculate: \([-6:(-2)+15:5-20:(-4)]\cdot3-2\)

5a. Which sign replaces □? \(\frac12\;\square\;\frac54\)

5b. Which sign replaces □? \(\frac83\;\square\;\frac34\)

5c. Which sign replaces □? \(\frac73\;\square\;\frac14\)

5d. Which sign replaces □? \(\frac43\;\square\;\frac{8}{36}\)

6a. Find \(x\) so that the equality holds: \(\frac64=\frac{15}{x}\)

6b. Find \(x\) so that the equality holds: \(\frac26=\frac{x}{18}\)

6c. Find \(x\) so that the equality holds: \(\frac53=\frac{35}{x}\)

6d. Find \(x\) so that the equality holds: \(\frac73=\frac{14}{x}\)

7a. Expand the fraction by 5. Which number replaces □? \(\frac83=\frac{\square}{15}\)

7b. Expand the fraction by 6. Which number replaces □? \(-\frac37=\frac{\square}{42}\)

7c. Expand the fraction by 3. Which number replaces □? \(\frac{6}{11}=\frac{\square}{33}\)

7d. Expand the fraction by 4. Which number replaces □? \(-\frac29=\frac{\square}{36}\)

8a. Bring the fractions to a common denominator. What is the least common denominator? \(\frac{2}{15};\ \frac35;\ \frac83\)

8b. Bring the fractions to a common denominator. What is the least common denominator? \(\frac68;\ \frac56;\ \frac94\)

8c. Bring the fractions to a common denominator. What is the least common denominator? \(\frac{1}{25};\ \frac{8}{35};\ \frac35\)

8d. Bring the fractions to a common denominator. What is the least common denominator? \(\frac27;\ \frac{3}{14};\ \frac{9}{21}\)

9a. Calculate: \(\frac35+\frac23-\frac{4}{15}\)

9b. Calculate: \(\frac29+\frac32-\frac15\)

9c. Calculate: \(\frac34-\frac25-\frac{1}{20}\)

9d. Calculate: \(\frac25+\frac13-\frac{1}{20}\)

10a. Calculate: \(\frac27\cdot\frac35+\frac65\)

10b. Calculate: \(\frac25-\frac37\cdot\frac{14}{5}\)

10c. Calculate: \(\frac57\cdot\frac{21}{8}-\frac14\)

10d. Calculate: \(\frac34\cdot\frac{22}{5}-\frac{7}{10}\)

11a. Calculate: \(\frac53-\frac27:\frac{1}{21}\)

11b. Calculate: \(\frac{4}{11}+\frac35:\frac{9}{10}\)

11c. Calculate: \(\frac79:\frac23+\frac12\)

11d. Calculate: \(\frac47:\frac{8}{21}-\frac45\)

12a. Calculate: \(\left(\frac12-\frac13\right):\left(\frac14-\frac15\right)\)

12b. Calculate: \(\frac{3}{10}-\frac{2}{11}:\frac{4}{35}+\frac45\)

12c. Calculate: \(1\frac{7}{20}:2\frac{7}{20}+2\frac{7}{20}:7\frac{1}{20}\)

12d. Calculate: \(\frac12\cdot1\frac34-2\frac12\cdot2\frac15+5\)

13a. Write the decimal as a fraction in lowest terms: \(0{,}002\)

13b. Write the decimal as a fraction in lowest terms: \(0{,}502\)

13c. Write the decimal as a fraction in lowest terms: \(0{,}013\)

13d. Write the decimal as a fraction in lowest terms: \(0{,}012\)

14a. Which inequality describes the interval \([-1,+\infty)\)?

14b. Which inequality describes the interval \((-\infty,3]\)?

14c. Which inequality describes the interval \([-2,+\infty)\)?

14d. Which inequality describes the interval \((-1,+\infty)\)?

15a. Write the result as an interval, e.g. (1,5]: \((-3,4]\cap(1,2)\)

15b. Write the result as an interval, e.g. (1,5]: \((-1,2]\cap[-3,4]\)

15c. Write the result as an interval, e.g. (1,5]: \((-1,5]\cap[-4,2]\)

15d. Write the result as an interval, e.g. (1,5]: \((-2,2]\cup(-1,4)\)

16a. Calculate: \(|5|-|-7|\)

16b. Calculate: \(|5-(-2)|\)

16c. Calculate: \(|1-3|-|2-(-6)|\)

16d. Calculate: \(|-2-3|-|1-7|\)

17a. Given the statements \(p:\ 2\mid 9\), \(q:\ 3\mid 12\), what is the truth value of \(p\Rightarrow\neg q\)?

17b. Given the statements \(p:\ 2\mid 9\), \(q:\ 3\mid 12\), what is the truth value of \(\neg p\wedge\neg q\)?

17c. Given the statements \(p:\ 2\mid 9\), \(q:\ 3\mid 12\), what is the truth value of \(p\Leftrightarrow\neg q\)?

17d. Given the statements \(p:\ 2\mid 9\), \(q:\ 3\mid 12\), what is the truth value of \(\neg p\wedge q\)?

18a. Given the statements \(p:\ 3>-1\), \(q:\ 2=8\), \(r:\ 3\mid 7\), what is the truth value of \(\neg p\Rightarrow\neg r\)?

18b. Given the statements \(p:\ 3>-1\), \(q:\ 2=8\), \(r:\ 3\mid 7\), what is the truth value of \(\neg q\wedge r\)?

18c. Given the statements \(p:\ 3>-1\), \(q:\ 2=8\), \(r:\ 3\mid 7\), what is the truth value of \(\neg p\Leftrightarrow\neg r\)?