The table shows the performance of pupils in a Mathematics test. | Score (%) | Number of Pupils | |---|---| | 0-10 | 2 | | 11-20 | 5 | | 21-30 | 15 | | 31-40 | 20 | | 41-50 | 8 | | 51-60 | 10 | | 61-70 | 15 | | 71-80 | 12 | | 81-90 | 8 | | 91-100 | 5 | (a) Calculate the mean score of the pupils.

1. Listing of the three-dimensional (3D) shapes. (2 mk)
2. Calculating the surface area of a rectangular prism. (3 mk)
3. Refer to criterion (l). A pupil who correctly calculates the square of 95 and 75, but makes errors in calculating the square of 110. How should the pupil be assessed? (1 mk)
4. Describe the pupil's performance in reading points on an x-y co-ordinate system. (0 mk)
5. Uses the division sign appropriately and puts both the dividend and divisor in appropriate positions when performing the long division method. (1 mk)
6. Conducting projects based on buying and selling commodities (0 mk)
7. States how to use Pythagoras’ theorem in real-life situations. (0 mk)
8. Calculate the mean score of the pupils. (10 mk)
9. Reads numbers up to 10,000,000. (1 mk)
10. Applying skills of reasoning and proof in real-life situations (Part Two) (17 mk)
11. Refer to criterion (m). A pupil who calculates 50^2 correctly but makes mistakes in calculating 25^3. How should the pupil be assessed? (1 mk)
12. Explains Pythagoras’ theorem in relation to the sides of a right-angled triangle (0 mk)
13. Drawing 3D Shapes. (2 mk)
14. What are the main difficulties a pupil faces to be classified as 'Below average' in calculating the Highest Common Factor (HCF) of two numbers? (1 mk)
15. Calculating the surface area of a cube. (3 mk)
16. Describe the pupil's performance in writing the co-ordinates of a point on an x-y plane. (0 mk)
17. Writes numbers in numerals up to 10,000,000. (1 mk)
18. Making 3D shapes. (2 mk)
19. Outline the characteristics of a pupil who performs 'Very good' in calculating the Highest Common Factor (HCF) of two numbers. (1 mk)
20. Refer to criterion (n). A pupil struggles to interpret a word problem that requires calculating the exponent of 35^2, and makes errors in computation. How should the pupil be assessed? (1 mk)
21. Writes numbers in words up to 10,000,000. (1 mk)
22. Calculating the surface area of a cylinder. (3 mk)
23. Describe the pupil's performance in drawing plane figures on an x-y co-ordinate plane. (0 mk)
24. Applying Pythagoras’ theorem in real-life, such as crossing roads, playing football, climbing up buildings. (1 mk)
25. Applying skills of reasoning and proof in real-life situations (Part Two) (0 mk)
26. Explains Pythagoras’ theorem has been applied in the real-life situation. (0 mk)
27. Identify the pupil's ability to write whole numbers not exceeding 1 000 000 000 in words. (0 mk)
28. Calculating the volume of a rectangular prism. (3 mk)
29. Identifies place values of numerical digits. (1 mk)
30. Refer to criterion (o). A pupil correctly calculates the square root of 225 but makes minor errors in calculating the square root of 400. How should the pupil be assessed? (1 mk)
31. Calculating the circumference of a circle. (2 mk)
32. Calculating the area of trapeziums. (0 mk)
33. Applying skills of reasoning and proof in real-life situations (Part Two) (0 mk)
34. Simplifies mathematical sentences involving the multiplication and division of exponents. (0 mk)
35. Refer to criterion (p). A pupil correctly solves a word problem involving the square root of 144, but makes a mistake in interpretation and computation in a problem involving the square root of 169. How should the pupil be assessed? (1 mk)
36. What is the performance level of a pupil who divides metric units of length with minor errors? (1 mk)
37. Calculating the area of a circle. (2 mk)
38. What is the number of periods allocated for developing the competency related to using mathematical language to present ideas or arguments (Part One)? (1 mk)
39. Calculating the surface area of a rectangular prism. (2 mk)
40. Explains variations of data from various points on the graph. (0 mk)
41. A pupil divides metric units of length without errors. What is their performance level? (1 mk)
42. Calculating the surface area of a cube. (2 mk)
43. Describe the performance of a pupil who multiplies metric units of weight with errors in computation and units conversion. (1 mk)
44. What is the performance level of a pupil who multiplies metric units of weight with minor errors? (1 mk)
45. Calculating the surface area of a cylinder. (2 mk)
46. Calculating the volume of a rectangular prism. (2 mk)
47. A pupil multiplies metric units of weight without errors. What is their performance level? (1 mk)
48. Describe the performance of a pupil who divides metric units of weight with errors in computation and unit conversion. (1 mk)
49. What is the performance level of a pupil who divides metric units of weight with minor errors? (1 mk)
50. A pupil divides metric units of weight without errors. What is their performance level? (1 mk)
51. Describe the performance of a pupil who multiplies metric units of volume with errors in computation and unit conversion. (1 mk)
52. What is the performance level of a pupil who multiplies metric units of volume with minor errors? (1 mk)
53. Describe the performance of a pupil who struggles to solve word problems involving metric units of measurements with interpretational, conversional and computational errors. (1 mk)
54. What is the performance level of a pupil who solves word problems involving metric units of measurements with minor errors? (1 mk)
55. A pupil solves word problems involving metric units of measurements without errors. What is their performance level? (1 mk)

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The table shows the performance of pupils in a Mathematics test. | Score (%) | Number of Pupils | |---|---| | 0-10 | 2 | | 11-20 | 5 | | 21-30 | 15 | | 31-40 | 20 | | 41-50 | 8 | | 51-60 | 10 | | 61-70 | 15 | | 71-80 | 12 | | 81-90 | 8 | | 91-100 | 5 | (b) Determine the median score of the pupils.

1. Arranges whole numbers based on the place values of the respective digits when multiplying whole numbers to get a product not exceeding 1 000 000 000. (0 mk)
2. Puts the dividend and divisor appropriately to the long division sign. (1 mk)
3. The square root of a number up to six digits has been calculated. (0 mk)
4. Identifying the formula for calculating speed and its three components. (0 mk)
5. Which competency criteria is assessed for a pupil who uses the formula to analyse profit and loss in depositing and loaning money? (1 mk)
6. Simplifying algebraic expressions with terms having whole numbers, fractions, and decimal coefficients have been simplified. (1 mk)
7. Determine the median score of the pupils. (10 mk)
8. Describe the performance of a pupil who solves word problems involving multiplication with mistakes in interpretation and computation. (0 mk)
9. Word problems involving the square root of a number are solved. (0 mk)
10. Applying the concepts of algebra to solve real life problems. (0 mk)
11. Describe the errors made by a pupil who struggles to write numbers in words. (1 mk)
12. Describe the performance criteria for a pupil performing 'Below average' in approximating a whole number to the nearest tens, hundreds and thousands. (2 mk)
13. Converting decimals into percentages. (0 mk)
14. Calculating the volume of the cube. (3 mk)
15. Distinguish between reading and writing whole numbers. (3 mk)
16. Describe the performance of a pupil who is 'Below average' in listing multiples of a number. (1 mk)
17. Describe the errors made by a pupil who writes numbers in words with minor errors. (1 mk)
18. Describe the performance criteria for a pupil performing 'Good' in approximating a decimal number to a given number of decimal places. (2 mk)
19. Calculating the volume of a cylinder. (3 mk)
20. According to the text, what should assessment focus more on than on the end results? (1 mk)
21. How does the performance of a pupil who is 'Average' in listing multiples differ from one who is 'Very good'? (1 mk)
22. Locating a point on x-y co-ordinate plane. (3 mk)
23. Divides a fraction by a fraction with the numerator up to four digits and the denominator up to six digits. (1 mk)
24. Calculates the square root of a number up to six digits. (0 mk)
25. Assess the pupil's ability to add whole numbers with regrouping based on place values of digits. (0 mk)
26. State one thing that pupils' performance has to be assessed based on. (1 mk)
27. Assess the pupil's ability to add whole numbers without regrouping and with regrouping to get a sum not exceeding 1 000 000 000 based on their place values. (0 mk)
28. Multiplying algebraic terms to get a product with not more than exponent 2. (0 mk)
29. Calculating the area of a rectangle. (1 mk)
30. Calculating the area of a triangle. (1 mk)

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The table shows the performance of pupils in a Mathematics test. | Score (%) | Number of Pupils | |---|---| | 0-10 | 2 | | 11-20 | 5 | | 21-30 | 15 | | 31-40 | 20 | | 41-50 | 8 | | 51-60 | 10 | | 61-70 | 15 | | 71-80 | 12 | | 81-90 | 8 | | 91-100 | 5 | (c) Determine the mode score of the pupils.

1. Describe what a pupil would do to be assessed as 'Very good'. (2 mk)
2. Describe the performance of a pupil who is classified as 'Average' in calculating the Lowest Common Multiple (LCM) of two numbers. (1 mk)
3. Applying mathematical operations to solve problems in different contexts. (0 mk)
4. State the 'Average' criterion for reading decimals to three decimal places. (1 mk)
5. Converting fractions into percentages. (0 mk)
6. Applies the division sign appropriately and puts both the dividend and divisor in appropriate positions when performing the long division method without a remainder. (0 mk)
7. Applying the BODMAS pattern skills to solve real-life problems. (5 mk)
8. Fraction with numerators up to three digits and denominators up to four digits have been divided by decimals up to five places. (1 mk)
9. Planning income and expenditure in buying and selling various commodities. (0 mk)
10. Using the concept of speed to identify moving objects that may travel on roads, on water, and in the air. (0 mk)
11. Determine the mode score of the pupils. (10 mk)
12. What are the common mistakes made by a pupil who is 'Below average' in calculating the Lowest Common Multiple (LCM) of two numbers? (1 mk)
13. Applying mathematical operations to solve problems. (0 mk)
14. Changes operations from division to multiplication and reciprocates the divisor. (1 mk)
15. State the 'Average' criterion for writing decimals to three decimal places. (1 mk)
16. Identify one specific competency related to the main competency 3.0. (1 mk)
17. What is the standard of performance for a pupil who achieves 'Very good' in calculating the Lowest Common Multiple (LCM) of two numbers? (1 mk)
18. Divides whole numbers by proper and improper fractions. (0 mk)
19. Writing time in 24-hour format. (1 mk)
20. Adding Tanzanian currency in shillings to get a sum not exceeding 9999. Performs additions involving Tanzanian currency in shillings without errors. (4 mk)
21. Which main competency involves applying measurements? (1 mk)
22. Assess the pupil's ability to subtract whole numbers with regrouping based on the place values of their digits. (0 mk)
23. Changing time from 12-hour to 24-hour format. (1 mk)
24. Assess the pupil's ability to subtract whole numbers up to 1 000 000 000 without regrouping and with regrouping based on their place values. (0 mk)
25. If a Standard III pupil has 12 lessons of mathematics in two weeks, how many periods does each lesson represent? (3 mk)
26. Changing time from 24-hours to 12-hours format. (1 mk)
27. Solving word problems involving time. (1 mk)

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The table describes four performance levels: Below average, Average, Good, Very good. Which of these indicates mastery of the skill?

1. Level of mastery: (1 mk)
2. State the performance level. (1 mk)
3. Identify the next higher performance level after 'Good' for this competency. (1 mk)

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In the context of 'Multiplying algebraic terms', what is the difference in performance between 'Below average' and 'Average'?

1. Difference in performance: (2 mk)
2. Identify the performance level. (1 mk)

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List two criteria from the table that assess a pupil's ability to work with mathematical expressions.

1. Criteria: (2 mk)
2. State the criterion for very good performance. (1 mk)

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Benchmarking of pupil’s performance for subtraction of numbers up to six digits without regrouping.

1. Subtracting numbers up to six digits without regrouping. (1 mk)
2. Subtracting with regrouping of six digit numbers. (1 mk)
3. Solving word problems involving subtraction of numbers with regrouping. (1 mk)

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Benchmarking of pupil’s performance for multiplication and division of numbers.

1. Multiplying numbers to get a product not exceeding six digits. (1 mk)
2. Solving word problems involving multiplication. (1 mk)
3. Dividing numbers up to six digits by a three digit number without a remainder. (1 mk)

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A survey was conducted on the number of hours students spent studying per week. | Hours per week | Number of Students | |---|---| | 0-5 | 10 | | 6-11 | 25 | | 12-17 | 40 | | 18-23 | 30 | | 24-29 | 15 | (a) Draw a histogram to represent the data.

1. Applying mathematics to solve problems in different contexts. (0 mk)
2. What is the lowest level of performance described in the rubric? (1 mk)
3. Describe the performance of a pupil who is classified as 'Below average' in calculating the square of numbers not exceeding 10000. (1 mk)
4. Describe the expected pupil activity for 'Identifying place value of numerical digits'. (1 mk)
5. Applying metric units of length. (0 mk)
6. Describe the performance of a pupil who 'struggles to draw angles using standard measurement tools'. (10 mk)
7. Puts the dividend and divisor appropriately to the long division sign by considering the magnitude of the divisor not exceeding 100 000 with a remainder. (0 mk)
8. Profit and loss in depositing and loaning money have been analysed using an appropriate formula. (0 mk)
9. Draw a histogram to represent the data. (15 mk)
10. Multiplication of metric units of length is performed. Pupil Struggles to multiply metric units of length. Below average: Multiplies metric units of length with errors in computation and units conversion. Average: Multiplies metric units of length with minor errors. Good: Multiplies metric units of length without errors. Very good: Applying metric units of length. (16 mk)
11. What are the characteristics of a pupil whose performance is 'Average' in calculating the square of numbers not exceeding 10000? (1 mk)
12. Mentions the sources of profit and loss in buying and selling commodities. (1 mk)
13. Describe the expected pupil activity for 'Writing whole numbers on a number line'. (1 mk)
14. What is the benchmark for a 'Very good' performance in calculating the square of numbers not exceeding 10000? (1 mk)
15. Provide a reason for the potential difference in difficulty. (1 mk)
16. Analyses with examples the sources of profit and loss in buying and selling commodities. (1 mk)
17. Identifies rectangular shapes without errors. (4 mk)
18. Assess the pupil's ability to use the addition sign in multiplying whole numbers to get a product not exceeding 1 000 000 000. (0 mk)
19. Divides a fraction by a fraction with the numerator up to four digits and the denominator up to six digits. (0 mk)
20. Subtracting Tanzanian shillings not exceeding 9999. Performs subtractions involving Tanzanian shillings without errors. (4 mk)
21. Assess the pupil's ability to multiply whole numbers to get a product not exceeding 1 000 000 000. (0 mk)
22. Multiplication of metric units of volume is performed. Pupil Struggles to multiply metric units of volume. Below average: Multiplies metric units of volume with errors in computation and unit conversion. Average: Multiplies metric units of volume with minor errors. Good: Multiplies metric units of volume without errors. Very good: Multiplication of metric units of volume. (0 mk)

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A survey was conducted on the number of hours students spent studying per week. | Hours per week | Number of Students | |---|---| | 0-5 | 10 | | 6-11 | 25 | | 12-17 | 40 | | 18-23 | 30 | | 24-29 | 15 | (b) Calculate the mean number of hours students spent studying per week.

1. What are activities to be done by the pupil? (2 mk)
2. What does a pupil do if they are assessed as 'Average' in reading and interpreting pictorial statistics? (1 mk)
3. Describe the performance of a pupil who is classified as 'Below average' in calculating the exponent of two digit numbers. (1 mk)
4. Struggles to write time in 12-hour format. (1 mk)
5. How does the performance level 'Below average' differ from 'Average' in criterion (d)? (2 mk)
6. Simplifying algebraic expressions with terms having whole numbers, fractions, and decimal coefficients have been simplified. (17 mk)
7. Calculate the mean number of hours students spent studying per week. (10 mk)
8. What are assessment criteria? (2 mk)
9. What level of performance is considered 'Average' when calculating the exponent of two digit numbers? (1 mk)
10. A student accurately divides 60 minutes by 3 to get 20 minutes. What is their performance level? (1 mk)
11. Solving simple algebraic equations involving whole numbers, fractions, and decimal coefficients have been solved. (0 mk)
12. Outline the performance criteria for a 'Very good' pupil in calculating the exponent of two digit numbers. (1 mk)
13. Writes time in 12-hour format with minor errors. (1 mk)
14. Describe the performance of a pupil who 'identifies perpendicular and parallel lines without mistakes'. (5 mk)
15. Solving word problems of simple algebraic equations involving whole numbers, fractions, and decimal coefficients have been solved. (0 mk)
16. Mentions properties of rectangular shapes without errors. (4 mk)
17. Writes time in 12-hour format without errors. (1 mk)

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A survey was conducted on the number of hours students spent studying per week. | Hours per week | Number of Students | |---|---| | 0-5 | 10 | | 6-11 | 25 | | 12-17 | 40 | | 18-23 | 30 | | 24-29 | 15 | (c) Determine the median number of hours students spent studying per week.

1. Determine the median number of hours students spent studying per week. (10 mk)
2. Identify and describe the benchmark for a 'Good' pupil in criterion (b). (2 mk)
3. Describe the performance of a pupil who 'struggles to calculate angles' and 'calculates angles with loose adherence to the rules and principles'. (10 mk)
4. What is the difference between a pupil assessed as 'Good' and one assessed as 'Very good' in reading and interpreting pictorial statistics? (1 mk)
5. What are the key challenges for a pupil who is 'Below average' in solving word problems involving the exponent of two digit numbers? (1 mk)
6. Refer to Table 1, describe the performance of a pupil who adds integers with errors in manipulation when it comes to negative and positive signs. (2 mk)
7. Reads time in 24-hour format with mistake in reading minutes. (1 mk)
8. Describe the performance of a pupil who is classified as 'Average' in solving word problems involving the exponent of two digit numbers. (1 mk)
9. A pupil writes 100 shillings and 50 cents as '100.50'. What is their performance level? (1 mk)
10. What indicates a 'Very good' performance in solving word problems involving the exponent of two digit numbers? (1 mk)
11. Describe the performance of a pupil who 'calculates angles without errors'. (5 mk)
12. Calculates perimeters of parallelograms and trapeziums without errors. (4 mk)
13. Reads time in 24-hour format without errors. (1 mk)

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Solve the following word problems involving division of decimal numbers: (e) A total of $120.75 is to be divided equally among 5 friends. How much will each friend receive?

1. A total of $120.75 is to be divided equally among 5 friends. How much will each friend receive? (3 mk)
2. Criterion: (1 mk)
3. Identify the performance level. (1 mk)
4. State the 'Average' performance criteria for 'Dividing three digit numbers by two digit numbers without a remainder'. (1 mk)

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Solve the following word problems involving addition of integers: (f) A diver descends 15 meters below sea level and then ascends 7 meters. What is the diver's current depth?

1. A diver descends 15 meters below sea level and then ascends 7 meters. What is the diver's current depth? (3 mk)
2. Description of 'Very good' performance: (2 mk)
3. Describe the performance. (2 mk)
4. Describe the 'Average' performance for solving word problems involving multiplication. (1 mk)

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Examine the criteria for adding numbers up to two decimal places. How is the performance of a pupil who adds numbers up to two decimal places with minor errors described?

1. Describe the performance. (1 mk)

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Refer to the table for subtracting numbers up to two decimal places. A pupil subtracts numbers with up to two decimal places with mistakes in interpreting place values and regrouping. What is this pupil's performance level?

1. Identify the performance level. (1 mk)

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Consider the competency 'Subtraction of fractions with different denominators'. Match the following performance levels with their descriptions: Below average: Average: Good: Very good:

1. Below average description (1 mk)
2. Average description (1 mk)
3. Good description (1 mk)
4. Very good description (1 mk)

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Using the provided table, explain the difference in performance between 'Average' and 'Good' for the competency 'Addition of numbers up to two decimal places'.

1. Describe 'Average' performance. (1 mk)
2. Describe 'Good' performance. (1 mk)

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Consider the competency 'Multiplication of fractions'. List the assessment criteria for 'Below average', 'Average', and 'Good' performance levels.

1. Below average criterion (1 mk)
2. Average criterion (1 mk)
3. Good criterion (1 mk)

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The diagram shows a bar chart representing the favorite colors of students in a class. (a) What is the title of the bar chart? (b) Which color is the most popular? (c) How many students chose blue as their favorite color? (d) How many students are in the class?

1. What is the title of the bar chart? (2 mk)
2. Describe the performance of a pupil who 'struggles to identify rectangular shapes'. (10 mk)
3. What would a pupil struggle to do if they are performing at the lowest level in writing the number of objects from pictorial statistics? (1 mk)
4. A pupil correctly adds 250000 shillings and 300000 shillings to get 550000 shillings. What is their performance level? (1 mk)
5. Which color is the most popular? (2 mk)
6. Describe the performance of a pupil who 'identifies rectangular shapes without errors'. (5 mk)
7. How many students chose blue as their favorite color? (3 mk)
8. Calculates area of parallelograms without errors. (4 mk)
9. How many students are in the class? (3 mk)

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Which of the following is a measure of central tendency?

A line graph is best used to show:

Which statistical measure indicates the spread of data?

The table below shows the benchmarking of pupil's performance on reading and writing coordinates on an x-y co-ordinate plane, and drawing plane figures. Activities to be Done by the Pupil Main Specific Competency Reading of points on x-y co-ordinate system. Writing of co-ordinates of a point on x-y plane. Drawing plane figures on x-y co-ordinate plane. Assessment Benchmarking of pupil’s performance Competency Criteria Below average Struggles to read points on x-y co-ordinate system. Struggles to write the co-ordinates of points on x-y plane. Struggles to draw plane figures on x-y co-ordinate plane. Average Reads points in an x-y co-ordinate system with mistakes in determining the x and y co-ordinates. Writes co-ordinates of points on x-y plane with errors. Draws plane figures on x-y co-ordinate plane with errors. Good Reads points on x-y co-ordinate system with minor mistakes. Writes co-ordinates of points on x-y plane with minor errors. Draws plane figures on x-y co-ordinate plane with minor errors. Very good Reads points on x-y co-ordinate system without mistakes. Writes co-ordinates of points on x-y plane without errors. Draws plane figures on x-y co-ordinate plane without errors. (v) Read the coordinates of the point P shown on the x-y co-ordinate system below. (w) Write the coordinates of the point Q shown on the x-y co-ordinate system below. (x) Draw a square on the x-y co-ordinate plane with vertices at (1,1), (3,1), (3,3), and (1,3).

1. Calculate the volume of a cube with side length 5 cm. (0 mk)
2. Read the coordinates of the point P shown on the x-y co-ordinate system below. (Assume P is at (2, 3)) (0 mk)
3. Write the coordinates of the point Q shown on the x-y co-ordinate system below. (Assume Q is at (-3, -1)) (0 mk)
4. Calculate the volume of a cylinder with radius 3 cm and height 10 cm. (0 mk)
5. Locate the point (4, -2) on an x-y co-ordinate plane. (0 mk)
6. Draw a square on the x-y co-ordinate plane with vertices at (1,1), (3,1), (3,3), and (1,3). (0 mk)

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The table below shows the benchmarking of pupil's performance in solving simple algebraic equations. Activities to be Done by the Pupil Main Specific Competency Applying the concepts of algebra to solve real life problems. Assessment Benchmarking of pupil’s performance Competency Criteria Below average Struggles to solve simple algebraic equations. Average Solves simple algebraic equations with procedural and computational errors. Good Solves simple algebraic equations with minor errors. Very good Solves simple algebraic equations without errors. (a) Solve the equation 3x + 5 = 20 for x.

1. Solve the equation 3x + 5 = 20 for x. (6 mk)

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