CTJan27 Online Year 7 - Review 15012026

1

Which of the following numbers is NOT a rational number?

$0.333...$ $\frac{1}{4}$ $-5$ $\sqrt{2}$

2

A rational number is defined as a number that can be expressed in the form $\frac{p}{q}$, where $p$ and $q$ are integers, and:

$q \ne 0$ $p$ and $q$ are positive $p$ and $q$ are non-negative $p \ne 0$

3

What is the decimal form of the fraction $\frac{3}{8}$?

$0.375$ $0.425$ $0.35$ $0.38$

4

Convert the terminating decimal $0.65$ into a fraction in simplest form.

$\frac{13}{50}$ $\frac{3}{5}$ $\frac{65}{100}$ $\frac{13}{20}$

5

Which rational number is located exactly halfway between $1.2$ and $1.8$ on the number line?

$1.4$ $1.5$ $1.6$ $1.7$

6

Which of the following rational numbers is the smallest?

$-\frac{1}{2}$ $\frac{1}{4}$ $-\frac{3}{4}$ $\frac{1}{2}$

7

Arrange the following numbers in ascending order: $0.2$, $-\frac{1}{5}$, $0$, $\frac{3}{10}$.

$0, -\frac{1}{5}, 0.2, \frac{3}{10}$ $-\frac{1}{5}, 0.2, 0, \frac{3}{10}$ $0, 0.2, -\frac{1}{5}, \frac{3}{10}$ $-\frac{1}{5}, 0, 0.2, \frac{3}{10}$

8

Calculate: $\frac{1}{3} + \frac{1}{6}$

$\frac{2}{6}$ $\frac{3}{6}$ $\frac{1}{2}$ $\frac{2}{9}$

9

Calculate: $4.5 - (-1.2)$

$-3.3$ $5.7$ $5.3$ $3.3$

10

What is the product of $2.5$ and $-\frac{4}{5}$?

$-1.5$ $1.5$ $-2$ $2$

11

Find the result of the division: $-\frac{5}{6} \div \frac{2}{3}$

$-\frac{5}{9}$ $\frac{5}{4}$ $\frac{5}{9}$ $-\frac{5}{4}$

12

Evaluate: $-0.8 + 1.5 - 0.2$

$1.1$ $0.5$ $-0.5$ $-1.1$

13

The statement $a + (b + c) = (a + b) + c$ illustrates which property of rational number addition?

Associative Property Identity Property Commutative Property Inverse Property

14

Solve for $x$: $x + \frac{1}{4} = \frac{3}{4}$

$\frac{1}{2}$ $1$ $\frac{3}{8}$ $\frac{1}{4}$

15

Solve for $y$: $-3y = 7.5$

$-4.5$ $4.5$ $2.5$ $-2.5$

16

According to the Order of Operations (BIDMAS/PEMDAS), which operation should be performed first in the expression: $18 - 4 \times 2 + 10 \div 5$?

$Multiplication: $4 \times 2$$ $Addition: $4 + 10$$ $Subtraction: $18 - 4$$ $Division: $10 \div 5$$

17

Calculate the value of the following expression using the correct order of operations: $25 - 3 \times (10 - 6) + 7$

$28$ $56$ $14$ $20$

18

Evaluate the following integer expression, paying close attention to the negative signs: $-12 - (-5) + 3 + (-8)$

$-22$ $6$ $-12$ $-2$

19

A diver is $15$ meters below the surface (represented by $-15$). She rises $4$ meters, then dives $3$ times, each dive being $2$ meters. Which expression calculates her final depth, and what is the final depth?

$-15 + 4 - 3 \times 2$; Final depth: $-17$ meters $-15 + 4 - 3 \times 2$; Final depth: $-23$ meters $-15 - 4 + 3 \times 2$; Final depth: $-13$ meters $-15 + 4 - 2 \times 3$; Final depth: $-5$ meters

20

Simplify the following expression: $40 \div [2 \times (6 - 1) + 10]$

$10$ $2$ $4$ $20$

21

Solve the equation using inverse operations: $x - 15 = 32$.

$x = 32 \times 15$ $x = -17$ $x = 47$ $x = 17$

22

Solve for $y$: $6y = 102$.

$y = 96$ $y = 16$ $y = 17$ $y = 612$

23

Which step should be performed first to solve the equation $4x + 9 - x = 30$?

Subtract $x$ from both sides $Combine the like terms $4x$ and $-x$$ $Subtract 9 from both sides$ $Divide both sides by 4$

24

Solve the two-step linear equation: $2x + 7 = 23$.

$x = 10$ $x = 30$ $x = 15$ $x = 8$

25

Solve for $k$: $\frac{k}{5} - 3 = 7$.

$k = 35$ $k = 10$ $k = 50$ $k = 20$

26

Solve the equation involving the distributive property: $4(x - 5) = 16$.

$x = 9$ $x = 11$ $x = 4$ $x = 1$

27

What is the solution to the equation $7x + 12 - 3x = 36$?

$x = 12$ $x = 6$ $x = 8$ $x = 4$

28

Translate the following statement into an algebraic equation: \"Five times a number $n$, decreased by 10, is equal to 45.\"

$5n - 10 = 45$ $5n + 10 = 45$ $5(n - 10) = 45$ $\frac{n}{5} - 10 = 45$

29

A gym membership costs a 25 dollars initial fee plus 15 dollars per month ($m$). If the total cost was 115 dollars, which equation correctly represents this scenario?

$15m + 25 = 115$ $15m - 25 = 115$ $25m + 15 = 115$ $25(m + 15) = 115$

30

A baker sells cookies for 3 dollars each. They spent 12 dollars on ingredients. If their total profit ($P$) was 60 dollars, how many cookies ($c$) did they sell? (Profit = Revenue - Costs)

$c = 24$ $c = 20$ $c = 36$ $c = 16$

31

Solve for $y$: $3(2y + 1) - 5 = 7y + 15$

$-12$ $12$ $-17$ $17$ $15$

32

Find the value of $m$: $6(m - 2) + 4m = 2m + 4 + 4(m + 1)$

$m = 6$ $m = 4$ $m = 3$ $m = 5$

33

Solve for $p$: $12 - 4(p - 6) = 2p - 3(p + 1)$

$p = 18$ $p = 15$ $p = 10$ $p = 13$

34

Solve the equation for $x$: $\frac{2x - 8}{2} + 3(x + 1) = 2x + 11$

$x = 5$ $x = 4$ $x = 7$ $x = 6$

35

What is the value of $z$ that satisfies the equation? $7 + 2[4(z - 1) - 3] = 3z + 1$

$z = \frac{8}{5}$ $z = 1$ $z = \frac{6}{5}$ $z = 2$

36

Which statement correctly describes the hypotenuse ($c$) of a right triangle?

It is the longest side, opposite the right angle. It is represented by $a$ or $b$ in the formula. It is the side adjacent to the right angle. It is always one of the two shortest sides.

37

What is the primary characteristic that identifies a triangle as a right triangle?

All three sides are equal. $The sum of its angles is greater than $180^{\circ}$.$ It has two acute angles and one obtuse angle. $It contains one interior angle that measures $90^{\circ}$.$

38

Which formula correctly states the relationship between the legs ($a$ and $b$) and the hypotenuse ($c$) of a right triangle, according to the Pythagorean Theorem?

$a^2 + b^2 = c^2$ $a^2 + c^2 = b^2$ $a + b = c$ $a^2 \times b^2 = c^2$

39

If the equation $a^2 + b^2 = c^2$ is represented geometrically, what does the term $b^2$ represent?

The length of the leg $b$ squared. The area of a square built on leg $b$. The perimeter of the triangle. The area of a square built on the hypotenuse.

40

What is the value of $\sqrt{144}$?

$14$ $12$ $72$ $288$

41

A right triangle has legs measuring $6$ cm and $8$ cm. Calculate the length of the hypotenuse.

$28$ cm $14$ cm $100$ cm $10$ cm

42

The legs of a right triangle are $5$ meters and $12$ meters long. What is the length of the hypotenuse?

$13$ m $17$ m $\sqrt{119}$ m $169$ m

43

The hypotenuse of a right triangle measures $10$ units, and one leg measures $6$ units. Find the length of the missing leg.

$16$ units $4$ units $8$ units $\sqrt{136}$ units

44

A right triangle has a hypotenuse of $17$ mm and one leg of $15$ mm. Calculate the length of the other leg.

$4$ mm $2$ mm $8$ mm $64$ mm

45

Which set of integers represents a Pythagorean Triple?

$(2, 3, 4)$ $(5, 6, 7)$ $(8, 15, 17)$ $(9, 10, 11)$

46

If the side lengths of a triangle are $7$ cm, $9$ cm, and $12$ cm, is it a right triangle?

$No, because $7^2 + 9^2 \neq 12^2$.$ It is impossible to tell without knowing the angles. $Yes, because $7^2 + 9^2 = 12^2$.$ $Yes, because $7+9>12$.$

47

In the Pythagorean Theorem, the legs are the two sides that:

Are shorter than the hypotenuse combined. Are equal in length. Meet to form the right angle. Are opposite the right angle.

48

A builder needs to find the diagonal length of a rectangular foundation that is $9$ meters long and $12$ meters wide. What is the length of the diagonal?

$15$ m $21$ m $\sqrt{150}$ m $18$ m

49

A cable supporting a flagpole is $25$ feet long. The cable is anchored to the ground $7$ feet away from the base of the pole. How tall is the flagpole?

$32$ ft $18$ ft $24$ ft $\sqrt{576}$ ft

50

If $(3, 4, 5)$ is a known Pythagorean triple, which of the following sets, formed by multiplying the original set by a constant, is also a Pythagorean triple?

$(4, 5, 6)$ $(9, 16, 25)$ $(1, 2, 3)$ $(6, 8, 10)$

51

Which of the following is a statistical question?

D) What time did the school bus arrive today? A) How old is the principal of the school? C) What is the capital of Canada? B) What are the favorite colors of the students in the 7th grade?

52

What is the mode of the data set: $\{4, 7, 3, 7, 5, 4, 7\}$?

C) $5$ B) $4$ A) $3$ D) $7$

53

Calculate the arithmetic mean of the following data set: $\{10, 5, 8, 7\}$.

C) $30$ A) $7.5$ B) $8$ D) $7$

54

Find the median of the data set: $\{12, 15, 8, 18, 10\}$.

D) $15$ C) $12$ B) $10$ A) $8$

55

What is the median of the data set: $\{1, 3, 9, 7\}$?

C) $5$ D) $7$ B) $4$ A) $3$

56

Determine the range of the data set: $\{50, 65, 42, 80, 55\}$.

C) $80$ D) $55$ B) $38$ A) $20$

57

For the data set $\{1, 1, 3, 5, 8, 10, 12\}$, what are the minimum and maximum values for the five-number summary?

C) $3$ and $10$ A) $1$ and $10$ D) $5$ and $8$ B) $1$ and $12$

58

Calculate the first quartile (Q1) for the data set: $\{2, 4, 5, 6, 8, 10, 12\}$.

C) $5$ B) $4$ A) $2$ D) $6$

59

Calculate the third quartile (Q3) for the data set: $\{10, 15, 17, 20, 22, 25\}$.

A) $17$ B) $20$ D) $25$ C) $22$

60

If the first quartile (Q1) of a data set is $15$ and the third quartile (Q3) is $28$, what is the Interquartile Range (IQR)?

B) $13$ C) $6.5$ D) $18.5$ A) $43$

61

Which measure of center is generally least affected by a significant outlier?

B) Mode A) Mean D) Range C) Median

62

What is the mode(s) of the data set $\{1, 2, 2, 3, 5, 5, 6\}$?

A) $3$ D) There is no mode C) $2$ and $5$ B) $2$ only

63

A data set has a mean of $50$. If a high outlier of $100$ is added, how will the mean and median likely change?

D) Both the mean and median will increase by the same amount. A) The mean will increase significantly, and the median will increase slightly or moderately. B) The mean will decrease, and the median will stay the same. C) Both the mean and median will decrease.

64

In a box-and-whisker plot, what does the line segment inside the box represent?

D) The Interquartile Range (IQR) C) The Median ($Q2$) A) The Minimum value B) The Maximum value

65

Data Set A has a range of $15$ and an IQR of $5$. Data Set B has a range of $10$ and an IQR of $8$. Which statement is true regarding the variability of the central $50\%$ of the data?

B) Data Set B has greater variability in its central $50\%$. D) Range must be used to compare central variability. C) Both data sets have the same variability in the central $50\%$. A) Data Set A has greater variability in its central $50\%$.

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CTJan27 Online Year 7 - Review 15012026