Subject Knowledge Review - Maths

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3. In the grid below, the vertical axis represents the cost C of hiring a DVD, while the horizontal line represents the number of days D the DVD is hired for. The line represents the relationship between the two variables.

What is the cost of hiring the video for 5 days?

The cost of hiring the video for 5 days is £4.00.

Explanation

The cost of hiring the video for 5 days is £4.00.

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5. Every square is a regular quadrilateral

True

False

A regular quadrilateral is a square, so every square is indeed a regular quadrilateral. A square has four equal sides and four right angles, which are the defining characteristics of a regular quadrilateral. Therefore, the statement "Every square is a regular quadrilateral" is true.

Explanation

A regular quadrilateral is a square, so every square is indeed a regular quadrilateral. A square has four equal sides and four right angles, which are the defining characteristics of a regular quadrilateral. Therefore, the statement "Every square is a regular quadrilateral" is true.

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8. Calculator not allowed ___ > 7

4

7

-5

9

not-available-via-ai

Explanation

not-available-via-ai

9. Calculator not allowed ___ < -3 < ___

5 and 5

5 and -5

-5 and 5

not-available-via-ai

Explanation

not-available-via-ai

10. Calculator not allowed: -5 - 7 =

The given expression is -5 - 7. When subtracting a negative number, it is equivalent to adding the positive value of that number. Therefore, -5 - 7 can be rewritten as -5 + (-7), which equals -12. The answer is -12.

Explanation

The given expression is -5 - 7. When subtracting a negative number, it is equivalent to adding the positive value of that number. Therefore, -5 - 7 can be rewritten as -5 + (-7), which equals -12. The answer is -12.

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11. Calculator not allowed Given that 7 x 8 = 56, what is 70 x 800?

The given question asks to calculate 70 x 800. To find the answer, we can use the distributive property of multiplication. We know that 70 = 7 x 10 and 800 = 8 x 100. Therefore, 70 x 800 = (7 x 10) x (8 x 100) = 7 x 8 x 10 x 100 = 56 x 1000 = 56,000.

Explanation

The given question asks to calculate 70 x 800. To find the answer, we can use the distributive property of multiplication. We know that 70 = 7 x 10 and 800 = 8 x 100. Therefore, 70 x 800 = (7 x 10) x (8 x 100) = 7 x 8 x 10 x 100 = 56 x 1000 = 56,000.

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12. Calculator not allowed: 3.6 x 3

The given expression is a multiplication problem, where 3.6 is being multiplied by 3. The product of 3.6 and 3 is 10.8. Therefore, the answer is 10.8. The additional option of 10.80 is also correct as it represents the same value, but with two decimal places.

Explanation

The given expression is a multiplication problem, where 3.6 is being multiplied by 3. The product of 3.6 and 3 is 10.8. Therefore, the answer is 10.8. The additional option of 10.80 is also correct as it represents the same value, but with two decimal places.

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14. Calculator not allowed A teacher earning £25,000 a year is given a pay rise. The new salary if £26,000. What is the percentage increase in salary?

The percentage increase in salary can be calculated by finding the difference between the new salary and the old salary, which is £26,000 - £25,000 = £1,000. Then, divide this difference by the old salary (£1,000 / £25,000) and multiply by 100 to convert it into a percentage. This gives us a percentage increase of 4%.

Explanation

The percentage increase in salary can be calculated by finding the difference between the new salary and the old salary, which is £26,000 - £25,000 = £1,000. Then, divide this difference by the old salary (£1,000 / £25,000) and multiply by 100 to convert it into a percentage. This gives us a percentage increase of 4%.

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16. Calculator not allowed Given that 7 x 8 = 56, what is 5.6 ÷ 7?

To find the value of 5.6 divided by 7, we can use the fact that 7 multiplied by 8 is equal to 56. Since 5.6 is 10 times smaller than 56, we can divide 56 by 10 to get the answer. Therefore, 5.6 divided by 7 is equal to 0.8.

Explanation

To find the value of 5.6 divided by 7, we can use the fact that 7 multiplied by 8 is equal to 56. Since 5.6 is 10 times smaller than 56, we can divide 56 by 10 to get the answer. Therefore, 5.6 divided by 7 is equal to 0.8.

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21. How many lines of reflective symmetry does this shape have?

The shape has only one line of reflective symmetry. This means that there is only one line through which the shape can be folded in half so that both halves match perfectly.

Explanation

The shape has only one line of reflective symmetry. This means that there is only one line through which the shape can be folded in half so that both halves match perfectly.

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22. Look at the data set below:

12

14

1

9

2

16

5

8

6

8

7

What is the mode?

The mode is the value that appears most frequently in a data set. In this case, the number 8 appears three times, which is more than any other number in the data set. Therefore, the mode is 8.

Explanation

The mode is the value that appears most frequently in a data set. In this case, the number 8 appears three times, which is more than any other number in the data set. Therefore, the mode is 8.

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23. Calculator not allowed -5 < ___

-6

-25

1

The given inequality states that -5 is less than the missing number. The only option that satisfies this condition is 1, as -5 is indeed less than 1. Therefore, the correct answer is 1.

Explanation

The given inequality states that -5 is less than the missing number. The only option that satisfies this condition is 1, as -5 is indeed less than 1. Therefore, the correct answer is 1.

24. Calculator not allowed Given that 7 x 8 = 56, what is 0.08 x 0.7?

To solve this question, we can multiply 0.08 by 0.7 without using a calculator. We can start by multiplying 8 by 7, which equals 56. Since there are two decimal places in the question (0.08 and 0.7), we need to move the decimal point two places to the left in our answer. Therefore, the answer is 0.056.

Explanation

To solve this question, we can multiply 0.08 by 0.7 without using a calculator. We can start by multiplying 8 by 7, which equals 56. Since there are two decimal places in the question (0.08 and 0.7), we need to move the decimal point two places to the left in our answer. Therefore, the answer is 0.056.

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25. Look at the diagram below:

Which word describes how shape A has been transformed into shape D?

Reflection

Rotation

Translation

The word "translation" describes how shape A has been transformed into shape D. Translation refers to the movement of an object in a straight line without any rotation or reflection. In this case, shape A has been shifted or moved horizontally or vertically to a new position to form shape D.

Explanation

The word "translation" describes how shape A has been transformed into shape D. Translation refers to the movement of an object in a straight line without any rotation or reflection. In this case, shape A has been shifted or moved horizontally or vertically to a new position to form shape D.

26. What is the average speed for a journey of 175km undertaken in 2 hours and 30 mins? (enter the digits only, not the units)

The average speed for a journey is calculated by dividing the total distance traveled by the total time taken. In this case, the total distance is 175 km and the total time is 2 hours and 30 minutes, which is equivalent to 2.5 hours. Dividing 175 km by 2.5 hours gives us an average speed of 70 km/h.

Explanation

The average speed for a journey is calculated by dividing the total distance traveled by the total time taken. In this case, the total distance is 175 km and the total time is 2 hours and 30 minutes, which is equivalent to 2.5 hours. Dividing 175 km by 2.5 hours gives us an average speed of 70 km/h.

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27. Calculator not allowed Share 21 marbles in the ratio 4 to 3

9:12

7:3

12:9

3:7

The correct answer is 12:9. This ratio represents the distribution of marbles where for every 12 marbles, 9 marbles are given to one person and the remaining 3 marbles are given to another person. This ratio can be simplified to 4:3, which means that for every 4 marbles, 3 marbles are given to one person.

Explanation

The correct answer is 12:9. This ratio represents the distribution of marbles where for every 12 marbles, 9 marbles are given to one person and the remaining 3 marbles are given to another person. This ratio can be simplified to 4:3, which means that for every 4 marbles, 3 marbles are given to one person.

28. Look at the data set below:

12

14

1

9

2

16

5

8

6

8

7

What is the mean?

The mean is calculated by adding up all the numbers in the data set and then dividing the sum by the total number of values. In this case, the sum of all the numbers is 100 (12 + 14 + 1 + 9 + 2 + 16 + 5 + 8 + 6 + 8 + 8 + 7 = 100). Since there are 12 numbers in the data set, the mean is 100 divided by 12, which equals 8.

Explanation

The mean is calculated by adding up all the numbers in the data set and then dividing the sum by the total number of values. In this case, the sum of all the numbers is 100 (12 + 14 + 1 + 9 + 2 + 16 + 5 + 8 + 6 + 8 + 8 + 7 = 100). Since there are 12 numbers in the data set, the mean is 100 divided by 12, which equals 8.

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29. Calculator not allowed Given that 7 x 8 = 56, what is 5600 ÷ 0.8?

To find the answer, we divide 5600 by 0.8. Since calculator is not allowed, we can use long division method. Dividing 5600 by 0.8 gives us 7000. Therefore, the answer is 7000.

Explanation

To find the answer, we divide 5600 by 0.8. Since calculator is not allowed, we can use long division method. Dividing 5600 by 0.8 gives us 7000. Therefore, the answer is 7000.

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30. Is this variable discrete or continuous? A child's height

Discreet

Continuous

The height of a child is a continuous variable because it can take on any value within a certain range. It is not limited to specific values and can be measured in fractions or decimals.

Explanation

The height of a child is a continuous variable because it can take on any value within a certain range. It is not limited to specific values and can be measured in fractions or decimals.

31. Every rhombus is a square

True

False

The statement "Every rhombus is a square" is false. While it is true that a square is a type of rhombus with equal angles, not every rhombus is a square. A rhombus is a quadrilateral with all sides of equal length, but its angles can be any value other than 90 degrees. Therefore, there are rhombuses that are not squares.

Explanation

The statement "Every rhombus is a square" is false. While it is true that a square is a type of rhombus with equal angles, not every rhombus is a square. A rhombus is a quadrilateral with all sides of equal length, but its angles can be any value other than 90 degrees. Therefore, there are rhombuses that are not squares.

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33. How many lines of reflective symmetry does this shape have?

The shape has 2 lines of reflective symmetry. This means that there are 2 lines that can be drawn through the shape, dividing it into two equal halves that are mirror images of each other.

Explanation

The shape has 2 lines of reflective symmetry. This means that there are 2 lines that can be drawn through the shape, dividing it into two equal halves that are mirror images of each other.

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34. Look at the data set below:

12

14

1

9

2

16

5

8

6

8

7

What is the median?

The median is the middle value in a set of numbers when they are arranged in order. In this case, the numbers are already listed in ascending order. Since there are 12 numbers, the median will be the 6th number, which is 8.

Explanation

The median is the middle value in a set of numbers when they are arranged in order. In this case, the numbers are already listed in ascending order. Since there are 12 numbers, the median will be the 6th number, which is 8.

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36. The linear scale factor between ABC and A'B'C' is 0.4.

What is the length of B'C'?

The length of B'C' is 6 or 6cm because the linear scale factor between ABC and A'B'C' is given as 0.4. This means that every length in ABC is multiplied by 0.4 to get the corresponding length in A'B'C'. Since the length of BC is not specified, we can assume it to be 6 or 6cm and multiply it by 0.4 to get the length of B'C', which is also 6 or 6cm.

Explanation

The length of B'C' is 6 or 6cm because the linear scale factor between ABC and A'B'C' is given as 0.4. This means that every length in ABC is multiplied by 0.4 to get the corresponding length in A'B'C'. Since the length of BC is not specified, we can assume it to be 6 or 6cm and multiply it by 0.4 to get the length of B'C', which is also 6 or 6cm.

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37. What is the volume of a cuboid with dimensions 7cm, 10cm and 13cm? (enter the digits only, not the units)

The volume of a cuboid can be calculated by multiplying the length, width, and height of the cuboid. In this case, the length is 7cm, the width is 10cm, and the height is 13cm. Multiplying these three dimensions together gives us a volume of 910 cubic centimeters.

Explanation

The volume of a cuboid can be calculated by multiplying the length, width, and height of the cuboid. In this case, the length is 7cm, the width is 10cm, and the height is 13cm. Multiplying these three dimensions together gives us a volume of 910 cubic centimeters.

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38. Which units would you use for the following dimensions?

Volume of a cube

Surface area of a cube

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39. Look at the diagram below:

Which word describes how shape A has been transformed into shape B?

Reflection

Rotation

Translation

The correct answer is Rotation because shape A has been rotated to form shape B. Reflection would involve flipping the shape over a line, and translation would involve moving the shape without rotating or flipping it.

Explanation

The correct answer is Rotation because shape A has been rotated to form shape B. Reflection would involve flipping the shape over a line, and translation would involve moving the shape without rotating or flipping it.

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42. Look at the diagram below:

Which word describes how shape A has been transformed into shape C?

Reflection

Rotation

Translation

Shape A has been transformed into shape C through reflection. Reflection is a transformation in which a shape is flipped over a line, creating a mirror image of the original shape. In this case, shape A has been flipped horizontally to create shape C.

Explanation

Shape A has been transformed into shape C through reflection. Reflection is a transformation in which a shape is flipped over a line, creating a mirror image of the original shape. In this case, shape A has been flipped horizontally to create shape C.

43. The linear scale factor between ABC and A'B'C' is 0.4.

What is the length of A'C'?

The length of A'C' is 10cm. This is because the linear scale factor between ABC and A'B'C' is 0.4, which means that every length in ABC is reduced to 0.4 times its original length in A'B'C'. Since the length of AC is 10cm, the length of A'C' will also be 10cm.

Explanation

The length of A'C' is 10cm. This is because the linear scale factor between ABC and A'B'C' is 0.4, which means that every length in ABC is reduced to 0.4 times its original length in A'B'C'. Since the length of AC is 10cm, the length of A'C' will also be 10cm.

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44. Every square is a parallellogram

True

False

Every square is a parallelogram because a square has four sides that are all equal in length and four angles that are all right angles. A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. Since a square meets all the criteria of a parallelogram, it can be concluded that every square is a parallelogram. Therefore, the correct answer is True.

Explanation

Every square is a parallelogram because a square has four sides that are all equal in length and four angles that are all right angles. A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. Since a square meets all the criteria of a parallelogram, it can be concluded that every square is a parallelogram. Therefore, the correct answer is True.

45. Which is the general term for this function machine?

1	------>	3
2	------>	7
3	------>	11
4	------>	15
5	------>	19
n	------>

2n + 1

4n - 1

3n + 1

N + 2n

The general term for this function machine is 4n - 1. This can be determined by observing the pattern in the given inputs and outputs. Each output is 1 less than 4 times the corresponding input. Therefore, the general rule for this function machine is to multiply the input by 4 and then subtract 1.

Explanation

The general term for this function machine is 4n - 1. This can be determined by observing the pattern in the given inputs and outputs. Each output is 1 less than 4 times the corresponding input. Therefore, the general rule for this function machine is to multiply the input by 4 and then subtract 1.

46. Calculator not allowed

1	+	1	=
3	+	2	=

2/5

1/6

2/6

5/6

Since the calculator is not allowed, we need to manually calculate the sum of 1+1, which equals 2. The fraction 5/6 is the only option that equals 2 when simplified.

Explanation

Since the calculator is not allowed, we need to manually calculate the sum of 1+1, which equals 2. The fraction 5/6 is the only option that equals 2 when simplified.

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49. Calculator not allowed: Find the highest common factor of 48 and 72

The highest common factor (HCF) of two numbers is the largest number that divides both of them without leaving a remainder. In this case, we can find the HCF of 48 and 72 by listing out their factors and finding the largest one they have in common. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. The largest factor that they both have in common is 24, so the HCF of 48 and 72 is 24.

Explanation

The highest common factor (HCF) of two numbers is the largest number that divides both of them without leaving a remainder. In this case, we can find the HCF of 48 and 72 by listing out their factors and finding the largest one they have in common. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. The largest factor that they both have in common is 24, so the HCF of 48 and 72 is 24.

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50. Look at the data set below:

12

14

1

9

2

16

5

8

6

8

7

What is the range?

The range is calculated by subtracting the smallest value in the data set from the largest value. In this case, the largest value is 16 and the smallest value is 1. Therefore, the range is 16 - 1 = 15.

Explanation

The range is calculated by subtracting the smallest value in the data set from the largest value. In this case, the largest value is 16 and the smallest value is 1. Therefore, the range is 16 - 1 = 15.

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51. Is this variable discrete or continuous? The number of CDs a child owns

Discreet

Continuous

The number of CDs a child owns is a discrete variable because it can only take on whole number values. The variable cannot be divided into smaller increments, as you cannot have a fraction or decimal number of CDs.

Explanation

The number of CDs a child owns is a discrete variable because it can only take on whole number values. The variable cannot be divided into smaller increments, as you cannot have a fraction or decimal number of CDs.

52. What is the order of rotational symmetry for this shape?

The order of rotational symmetry for a shape refers to the number of times the shape can be rotated and still look the same. In this case, the shape has only one line of symmetry, which means it can only be rotated 180 degrees and still maintain its original form. Therefore, the order of rotational symmetry for this shape is 1.

Explanation

The order of rotational symmetry for a shape refers to the number of times the shape can be rotated and still look the same. In this case, the shape has only one line of symmetry, which means it can only be rotated 180 degrees and still maintain its original form. Therefore, the order of rotational symmetry for this shape is 1.

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53. Calculator not allowed Find the Lowest Common Multiple of 24 and 18

The lowest common multiple (LCM) of two numbers is the smallest number that is divisible by both numbers. To find the LCM of 24 and 18, we can list the multiples of each number and find the smallest number that appears in both lists. The multiples of 24 are 24, 48, 72, 96, 120, ... and the multiples of 18 are 18, 36, 54, 72, 90, ... The smallest number that appears in both lists is 72, so 72 is the LCM of 24 and 18.

Explanation

The lowest common multiple (LCM) of two numbers is the smallest number that is divisible by both numbers. To find the LCM of 24 and 18, we can list the multiples of each number and find the smallest number that appears in both lists. The multiples of 24 are 24, 48, 72, 96, 120, ... and the multiples of 18 are 18, 36, 54, 72, 90, ... The smallest number that appears in both lists is 72, so 72 is the LCM of 24 and 18.

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55. Every isoceles triangle is obtuse angled

True

False

The statement "Every isosceles triangle is obtuse angled" is false. An isosceles triangle has two equal sides, but it does not necessarily have an obtuse angle. It can have three acute angles or one acute angle and two equal obtuse angles. Therefore, the statement is incorrect.

Explanation

The statement "Every isosceles triangle is obtuse angled" is false. An isosceles triangle has two equal sides, but it does not necessarily have an obtuse angle. It can have three acute angles or one acute angle and two equal obtuse angles. Therefore, the statement is incorrect.

56. Calculator not allowed: £24 ÷ 5

The given expression £24 ÷ 5 can be solved by dividing 24 by 5, which gives the result 4.80. The answer can also be written as £4.80, since the pound sign represents the currency unit.

Explanation

The given expression £24 ÷ 5 can be solved by dividing 24 by 5, which gives the result 4.80. The answer can also be written as £4.80, since the pound sign represents the currency unit.

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59. Is this variable discrete or continuous? The years in which children were born

Discreet

Continuous

The variable "the years in which children were born" is discrete because it can only take on specific whole number values. It cannot take on any value between two whole numbers, making it a discrete variable.

Explanation

The variable "the years in which children were born" is discrete because it can only take on specific whole number values. It cannot take on any value between two whole numbers, making it a discrete variable.

60. Calculator not allowed The following table expresses the sale price as a proportion of the original price for four items. The proportion is expressed both as a simple fraction and as a percentage. Match the correct answer to the missing values.

Original Price	Sale Price	Fraction in lowest terms	Percentage
£16	£4	1/4	25
£20	£16	a	b
£40	c	d	30
e	£24	f	75

a

b

c

d

e

f

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61. Calculator not allowed: How many different factors of 100 are there?

The question asks for the number of different factors of 100. To find the factors of a number, we need to find all the numbers that divide evenly into it. The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. So, there are 9 different factors of 100.

Explanation

The question asks for the number of different factors of 100. To find the factors of a number, we need to find all the numbers that divide evenly into it. The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. So, there are 9 different factors of 100.

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62. If I walk a route which measures 7.5cm on a map with a scale of 1:100,000, how far will I actually walk in km?

If the map has a scale of 1:100,000, it means that 1 cm on the map represents 100,000 cm in reality. Therefore, if you walk a route that measures 7.5 cm on the map, you will actually walk a distance of 7.5 x 100,000 cm in reality. Converting this to kilometers, you divide by 100,000 to get the answer of 7.5 km.

Explanation

If the map has a scale of 1:100,000, it means that 1 cm on the map represents 100,000 cm in reality. Therefore, if you walk a route that measures 7.5 cm on the map, you will actually walk a distance of 7.5 x 100,000 cm in reality. Converting this to kilometers, you divide by 100,000 to get the answer of 7.5 km.

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63. In the grid below, the vertical axis represents the cost C of hiring a DVD, while the horizontal line represents the number of days D the DVD is hired for. The line represents the relationship between the two variables.

What is the daily additional cost for hiring the video?

The correct answer is £0.20, 0.20, 20p. This means that the daily additional cost for hiring the video is £0.20 or 20p.

Explanation

The correct answer is £0.20, 0.20, 20p. This means that the daily additional cost for hiring the video is £0.20 or 20p.

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65. Simplify the following expression: 6a + 3b - 8a + 2b

The given expression involves adding and subtracting variables. To simplify it, we can combine like terms by adding the coefficients of the variables. In this case, we have 6a and -8a, which can be simplified to -2a. Similarly, we have 3b and 2b, which can be simplified to 5b. Therefore, the simplified expression is 5b - 2a.

Explanation

The given expression involves adding and subtracting variables. To simplify it, we can combine like terms by adding the coefficients of the variables. In this case, we have 6a and -8a, which can be simplified to -2a. Similarly, we have 3b and 2b, which can be simplified to 5b. Therefore, the simplified expression is 5b - 2a.

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66. What is the surface area of a cuboid with dimensions 7cm, 10cm and 13cm? (enter the digits only, not the units)

The surface area of a cuboid can be calculated by adding the areas of all six faces. The formula for the surface area of a cuboid is 2(length × width + length × height + width × height). Plugging in the given dimensions of 7cm, 10cm, and 13cm into the formula, we get 2(7 × 10 + 7 × 13 + 10 × 13) = 2(70 + 91 + 130) = 2(291) = 582.

Explanation

The surface area of a cuboid can be calculated by adding the areas of all six faces. The formula for the surface area of a cuboid is 2(length × width + length × height + width × height). Plugging in the given dimensions of 7cm, 10cm, and 13cm into the formula, we get 2(7 × 10 + 7 × 13 + 10 × 13) = 2(70 + 91 + 130) = 2(291) = 582.

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67. When a ball is selected from a bag containing 3 black, 4 red and 5 blue balls, what is the probability that it is:

red

not blue

green

red or blue

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68. Look at the data set below:

12

14

1

9

2

16

5

8

6

8

7

What is the upper quartile?

The upper quartile is a measure of central tendency that divides the data set into quarters, with 25% of the data falling above it. In this case, the data set is arranged in ascending order: 1, 2, 5, 6, 7, 8, 8, 8, 9, 12, 14, 16. The upper quartile is the median of the upper half of the data set, which in this case is 9, 12, 14, and 16. The median of this upper half is 10.5, so it is the upper quartile.

Explanation

The upper quartile is a measure of central tendency that divides the data set into quarters, with 25% of the data falling above it. In this case, the data set is arranged in ascending order: 1, 2, 5, 6, 7, 8, 8, 8, 9, 12, 14, 16. The upper quartile is the median of the upper half of the data set, which in this case is 9, 12, 14, and 16. The median of this upper half is 10.5, so it is the upper quartile.

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69. How many planes of symmetry does a cuboid with dimensions 4cm x 4cm x 9cm have?

A cuboid with dimensions 4cm x 4cm x 9cm has 5 planes of symmetry. This is because a plane of symmetry divides an object into two equal halves that are mirror images of each other. In this case, there are 5 different planes that can divide the cuboid into two equal halves. These planes can be imagined as cutting the cuboid vertically in the middle, horizontally in the middle, and diagonally through the corners.

Explanation

A cuboid with dimensions 4cm x 4cm x 9cm has 5 planes of symmetry. This is because a plane of symmetry divides an object into two equal halves that are mirror images of each other. In this case, there are 5 different planes that can divide the cuboid into two equal halves. These planes can be imagined as cutting the cuboid vertically in the middle, horizontally in the middle, and diagonally through the corners.

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70. Look at the data set below:

12

14

1

9

2

16

5

8

6

8

7

What is the lower quartile?

The lower quartile is a measure of central tendency that divides the dataset into four equal parts. In this case, the dataset is sorted in ascending order: 1, 2, 5, 6, 7, 8, 8, 8, 9, 12, 14, 16. The lower quartile is the median of the lower half of the dataset, which is 5.5. This means that 25% of the data points are less than or equal to 5.5.

Explanation

The lower quartile is a measure of central tendency that divides the dataset into four equal parts. In this case, the dataset is sorted in ascending order: 1, 2, 5, 6, 7, 8, 8, 8, 9, 12, 14, 16. The lower quartile is the median of the lower half of the dataset, which is 5.5. This means that 25% of the data points are less than or equal to 5.5.

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71. Starting from n=1, what is the 4th numer in a sequence whose general term is n² + 1?

The general term of the sequence is n^2 + 1. Plugging in n=1 gives us 1^2 + 1 = 2. Plugging in n=2 gives us 2^2 + 1 = 5. Plugging in n=3 gives us 3^2 + 1 = 10. Plugging in n=4 gives us 4^2 + 1 = 17. Therefore, the 4th number in the sequence is 17.

Explanation

The general term of the sequence is n^2 + 1. Plugging in n=1 gives us 1^2 + 1 = 2. Plugging in n=2 gives us 2^2 + 1 = 5. Plugging in n=3 gives us 3^2 + 1 = 10. Plugging in n=4 gives us 4^2 + 1 = 17. Therefore, the 4th number in the sequence is 17.

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72. Look at the data set below:

12

14

1

9

2

16

5

8

6

8

7

What is the inter quartile range?

The interquartile range is a measure of the spread or dispersion of a dataset. It is calculated by finding the difference between the upper quartile (the median of the upper half of the dataset) and the lower quartile (the median of the lower half of the dataset). In this case, the upper quartile is 9 and the lower quartile is 4. Therefore, the interquartile range is 9 - 4 = 5.

Explanation

The interquartile range is a measure of the spread or dispersion of a dataset. It is calculated by finding the difference between the upper quartile (the median of the upper half of the dataset) and the lower quartile (the median of the lower half of the dataset). In this case, the upper quartile is 9 and the lower quartile is 4. Therefore, the interquartile range is 9 - 4 = 5.

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