UNIT 1



[pic]

GAUTENG DEPARTMENT OF EDUCATION

SCHOOL BASED ASSESSMENT (SBA)

| |

|MATHEMATICS |

GRADE 10

2017

CONTENTS Page

1. Introduction 3

2. Informal or daily assessment 4

3. Formal assessment 5

4. Programme of assessment 6

5. Assessment tasks 8

5.1 Project 8

5.2 Investigation 1 14

5.3 Investigation 2 20

4. Assignment 1 23

5. Assignment 2 28

1. INTRODUCTION

Assessment is a continuous planned process of identifying, gathering and interpreting information about the performance of learners, using various forms of assessment. It involves four steps: generating and collecting evidence of achievement; evaluating this evidence; recording the findings and using this information to understand and assist in the learner’s development to improve the process of learning and teaching. Assessment should be both informal (Assessment for Learning) and formal (Assessment of Learning). In both cases regular feedback should be provided to learners to enhance the learning experience.

Although assessment guidelines are included in the Annual Teaching Plan at the end of each term, the following general principles apply:

• Tests and examinations are assessed using a marking memorandum.

• Assignments are generally extended pieces of work completed at home.

Assignments can be collections of past examination questions, but should focus on the more demanding aspects as any resource material can be used, which is not the case when a task is done in class under strict supervision. At most one project or investigation and an assignment if this is the preferred option should be set in a year. The assessment criteria need to be clearly indicated on the project specification. The focus should be on the mathematics involved and not on duplicated pictures and regurgitation of facts from reference material. The collection and display of real data, followed by deductions that can be substantiated from the data, constitute good projects. A project, in the context of Mathematics, is an extended task where the learner is expected to select appropriate Mathematical content to solve a context-based problem.

Investigations are set to develop the skills of systematic investigation into special cases with a view to observing general trends, making conjectures and proving them. To avoid having to assess work which is copied without understanding, it is recommended that while the initial investigation can be done at home, the final write up should be done in class, under supervision, without access to any notes. Investigations are marked using rubrics which can be specific to the task, or generic, listing the number of marks awarded for each skill:

• 40% for communicating individual ideas and discoveries, assuming the reader has not come across the task before. The appropriate use of diagrams and tables will enhance the investigation.

• 35% for the effective consideration of special cases;

• 20% for generalising, making conjectures and proving or disproving these conjectures; and

• 5% for presentation: neatness and visual impact.

2. INFORMAL OR DAILY ASSESSMENT

The aim of assessment for learning is to collect continually information on a learner’s achievement that can be used to improve individual learning. Informal assessment involves daily monitoring of a learner’s progress. This can be done through observations, discussions, practical demonstrations, learner-teacher conferences, informal classroom interactions, etc., Informal assessment may be as simple as stopping during the lesson to observe learners or to discuss with learners how learning is progressing. Informal assessment should be used to provide feedback to the learners and to inform planning for teaching, it need not be recorded. This should not be seen as separate from learning activities taking place in the classroom. Learners or teachers can evaluate these tasks. Self-assessment and peer assessment actively involve learners in assessment. Both are important as these allow learners to learn from and reflect on their own performance. Results of the informal daily assessment activities are not formally recorded, unless the teacher wishes to do so. The results of daily assessment tasks are not taken into account for promotion and/or certification purposes.

3. FORMAL ASSESSMENT

All assessment tasks that make up a formal programme of assessment for the year are regarded as Formal Assessment. Formal assessment tasks are marked and formally recorded by the teacher for progress and certification purposes. All Formal Assessment tasks are subject to moderation for the purpose of quality assurance. Formal assessments provide teachers with a systematic way of evaluating how well learners are progressing in a grade and/or in a particular subject. Examples of formal assessments include tests, examinations, practical tasks, projects, oral presentations, demonstrations, performances, etc. Formal assessment tasks form part of a year-long formal Programme of Assessment in each grade and subject.

Formal assessments in Mathematics include tests, a June examination, a trial examination (for Grade 12), a project or an investigation. The forms of assessment used should be age- and developmental- level appropriate. The design of these tasks should cover the content of the subject and include a variety of activities designed to achieve the objectives of the subject. Formal assessments need to accommodate a range of cognitive levels and abilities of learners as indicated in the CAPS document.

4. Programme of Assessment:

Learners are expected to have seven (7) formal assessment tasks for their school-based assessment, excluding end of year examinations. The number of tasks and their weighting are listed below:

|TERM |TASK |WEIGHT (%) |DATE |

|Term 1 |Project or Investigation |20 | |

| |Test |10 | |

|Term 2 |Test or Assignment |10 | |

| |Examination |30 | |

|Term 3 |Test |10 | |

| |Test |10 | |

|Term 4 |Test |10 | |

|School-based Assessment | |100 | |

|School-based Assessment mark (as | | | |

|% of promotion mark) | | | |

| | |25% | |

|End-of-year Examinations | |75% | |

|Promotion mark | |100% | |

NB: The school programme of assessment should indicate specific dates when tasks are to be completed during the year. In the event that teachers are not able to abide by the set dates due to unforeseen circumstances, minimal deviations are permissible. Although the project/investigation is indicated in the first term, it could be scheduled in term 2. Only ONE project/investigation should be set per year. Tests should be at least ONE hour long and count at least 50 marks.

In the SBA tasks that follow, you are required to choose only ONE project/investigation and ONE assignment, should you decide to administer an assignment rather than a test in term 2.

5. ASSESSMENT TASKS

5.1 PROJECT: 50 Marks

MAKING A GONIOMETER

In this project you are going to make a simple goniometer and use it to calculate certain heights.

An angle gauge is designed to measure angles of elevation, but can also be used in determining angles of depression.

What do you need?

A carton roll (e.g. toilet paper roll) or a longer carton roll.

What else?

Cut out the protractor below. Paste the protractor onto cardboard or

thick paper.

And then?

Paste the protractor onto stiff cardboard so that the

straight side of the protractor matches up with the length

of the roll.

On the one side, wool or cotton strings are attached

in order to aim at an object.

This wool or cotton must be perpendicular to

each other to help you focus accurately at the highest

or lowest point.

Something else?

Yes. The next step is to attach a string with a small weight to,

the protractor. It is attached to the centre of the protractor.

When the protractor is held horizontally, the weight should

hang vertically along the 90( line.

A drawing pin can be used to fasten the string.

I NOW MADE A GONIOMETER BUT HOW CAN I USE IT?

The angle of elevation is the angle between the horizontal line and the line along which one looks. If you look through the goniometer while it is in a horizontal position and you slowly change the "line of sight" to the top of the building or a pole, then the string with the weight will lie along other diagonal. THE DIFFERENCE BETWEEN THIS ANGLE AND THE 90( ANGLE, WILL BE THE SIZE OF THE ANGLE OF ELEVATION, e.g. angle of elevation is

90( - 60( = 30(.

Consider the following:

1. The "angle of elevation" on the sketch is not the angle

between the horizontal and the "line of sight".

How do you know that the angle is really the same size as?

the angle of elevation?

Use the diagram to answer the question.

2. If the horizontal line is at eye level and not on the ground, what will you consider when you do the calculations?

3. How will you use your goniometer to determine the angle of depression?

DETERMINE THE FOLLOWING:

Use your goniometer, draw neat sketches which represent the following situations and calculate the following as accurately as possible.

1. The height of a rugby post/soccer goalpost.

2. The height of the flag post.

3. How high are you above ground level if you are standing in front of……………..classroom on the first floor and look down at the corridor in front of ………………. class?

4. How high is the roof of the building where the school's name is displayed?

For the educator:

• The given questions can be adjusted in order to be relevant to the

specific school.

• Choose four relevant questions for learners to determine heights.

NB: Learners are expected to complete the application question at the end of the project individually.

MEMORANDUM (Project )

RUBRIC: GONIOMETER

NAME: _____________________________

| |1. |2. |3. |4. |5. |

| |The learner is |The learner has |The learner meets a |The learner performs |The learner performs |

| |unsuccessful |partially complied |large extent to the |well with this project.|very well with this |

| | |with the requirements|requirements of this | |project. |

| | |of this project. |project. | | |

|Make use of the |Have not made ​​a |Made a goniometer |Made a goniometer |Made a reasonably |Make an accurate |

|goniometer to |goniometer. |that is not usable. |that is not 100% |accurate goniometer and|goniometer and is able |

|measure angles. | | |accurate. Is able to |most of the time able |to make correct |

| | | |measure angles, but |to make correct |measurements. |

| | | |with errors. |measurements. | |

| | | | | | |

MARK ALLOCATION: TOTAL MARKS

Sketch : 1 8 x 4 = 32

Dimensions : 2 Goniometer = 5 (use given rubric)

Formula : 2 Application = 13

Substitution : 1 Total: 50

Solution : 2

Total: 8 x 4 = 32

APPLICATION

1. Using the figure, express the following ratios

in terms of a, b, c, d and e.

1.1 [pic]

1.2 [pic]

1.3 [pic]

(3)

2. In the diagram below AB [pic] CD, AD = 3 cm,[pic],

DB = 4 cm and[pic].

2.1 Calculate, to two decimal places, the numerical value of h using ∆CDB. (4)

2.2 Calculate the value of[pic], to one decimal place. (3)

3. The angle of elevation of an elephant of height 2, 6 m from a mouse is [pic]

How far is the mouse from the elephant? (Answer correct to two decimal places) . (3)

[pic] [13]

MEMORANDUM (Application)

| |APPLICATION |13 MARKS | |

| |[pic] | | |

|1.1 | |Answer |( |

| |[pic] | | |

| | | | |

| |[pic] | | |

| | | | |

|1.2 | |Answer |( |

|1.3 | | | |

| | |Answer |( |

| | |[3] | |

|2.1 |In ∆ CDB | | |

| |[pic] = tan 300 |[pic] | |

| |h = 4 tan 300 |[pic] |( |

| |h = 2,31 cm tan 30 |h subject |( |

| | |Answer [4] |( |

| | | |( |

|2.2 |In ∆CDA | | |

| |tan θ = [pic] |tan θ |( |

| |θ = 37,60 |[pic] |( |

| | |Answer | |

| | |[3] |( |

|3 |[pic] |Trig ratio |( |

| |The mouse is 4, 16 m from the elephant. | | |

| | | | |

| | |FM subject |( |

| | | | |

| | |Answer |( |

| | |[3] | |

5.2 INVESTIGATION(S) 1: choose only one investigation in this question

5.2.1 Factors:

What factors does [pic] have for all [pic]?

Investigate whether the following statements are true for all [pic]:

1. [pic]is divisible by 2.

2. [pic] is divisible by 3.

3. [pic]is divisible by 5.

Try to generalise the above statements. Is the general statement true or false?

5.2.2 Surprising results:

What is special about these numbers that gives these surprising results:

1. [pic]. Can you find other numbers whose sum is equal to their product? Can you generalise?

2. Make a conjecture about the following results:

[pic]

Try to prove your conjecture.

3. Calculate the answers to the following and hence make a conjecture:

[pic]

Try to prove your conjecture.

4. And what about this?

[pic]

5.2.2 The painted cube:

Imagine a cube of white wood which is dipped into red paint so that the surface is red, but the inside still white. If one cut is made, parallel to each face of the cube, half way between the parallel faces then there will be 8 smaller cubes. Each of the smaller cubes will have 3 red faces and 3 white faces.

Investigate the number of smaller cubes which will have 3, 2, 1 and 0 red faces if 2/3/4…n equally spaced cuts are made parallel to each face.

Investigate, tabulate your results, make conjectures and justify or prove them.

5.2.3 An interesting sequence:

Consider the sequence [pic]which is generated by the following rule:

[pic] for [pic]

Investigate the sequence formed by choosing any two numbers as [pic] and [pic].

Do the terms ever recur? Try other starting numbers. Make a conjecture and try to prove it.

MEMORANDA: Investigation(s)

Possible solutions:

Factors:

1. When x = 1, [pic] which is divisible by 2

When x = 2, [pic] which is divisible by 2

When x = 3, [pic] which is divisible by 2

When x = 4, [pic] which is divisible by 2

General proof:

[pic]

This is the product of two consecutive numbers.

One of the two consecutive numbers must be a multiple of 2.

So [pic]is always divisible by 2 if [pic]

2. When x = 1, [pic] which is divisible by 3

When x = 2, [pic] which is divisible by 3

When x = 3, [pic] which is divisible by 3

When x = 4, [pic] which is divisible by 3

In fact it seems that for all [pic]is divisible by 6

This can be proved as follows:

[pic]

Rearranging these factors we see that this is a product of 3 consecutive numbers, one of which will have to be a multiple of 3, So [pic] is always divisible by 3 if [pic]

To prove that [pic]is divisible by 6 we can argue that in addition to one of the three consecutive factors being a multiple of 3 at least one must be a multiple of 2 and so the number is always a multiple of 6.

3. When x = 1, [pic] which is divisible by 5

When x = 2, [pic] which is divisible by 5

When x = 3, [pic] which is divisible by 5

When x = 4, [pic] which is divisible by 5

Factorising the expression we get:

[pic]

This is harder! We need to show that one of the 4 factors is always divisible by 5.

So we consider [pic] to be either

• a multiple of 5

• 1 more than a multiple of 5 (leaves a remainder of 1 when divided by 5)

• 2 more than a multiple of 5 (leaves a remainder of 2 when divided by 5)

• 3 more than a multiple of 5 (leaves a remainder of 3 when divided by 5)

or

• 4 more than a multiple of 5 (leaves a remainder of 4 when divided by 5)

But it can be shown that if [pic]leaves a remainder of 1 when divided by 5 then [pic]is a multiple of 5, if it leaves a remainder of 2 or 3, then [pic]is a multiple of 5 and if [pic]leaves a remainder of 4 when divided by 5, then [pic] is a multiple of 5.

Proof that a number that leaves a remainder of 2 or 3 when divided by 5 results in [pic]being a multiple of 5:

Let the number [pic]

Then [pic][pic]

The proof for [pic]is similar!

(Although it is unlikely Grade 10s will get this one, they can conjecture from numerical testing that the statement is true).

The general statement would be that [pic]is divisible by [pic]for all [pic]

It can be shown that this is not true in general by providing a single counter example:

[pic] when [pic] and 14 is not divisible by 4!

Surprising results:

1. Other examples where the sum equals the product are:

[pic]

In general the conjecture is that [pic]

Proof: [pic]

2. Conjecture: [pic]

Proof: [pic]

3. Conjecture: [pic]

Both sides simplify to [pic]

4. Conjecture: [pic]

Proof: [pic]

This can be marked according to the guidelines on page 4 of the SBA document:

40%: for explaining the procedure adopted in investigating each example.

35%: for correct additional examples.

20%: for algebraic conjecture and proof by manipulation of the algebraic conjecture and

5%: for presentation.

The painted cube:

|Number of cuts |3 red faces |2 red faces |1 red face |0 red faces |Total no. of small |

| | | | | |cubelets |

|1 |8 |0 |0 |0 |8 |

|2 |8 |12 |6 |1 |27 |

|3 |8 |24 |24 |8 |64 |

|4 |8 |36 |54 |27 |125 |

|5 |8 |48 |96 |64 |216 |

|N |8 |[pic] |[pic] |[pic] |[pic] |

And by multiplying out we find that [pic]

This can be extended to a rectangular prism [pic]

An interesting sequence:

Let’s start with [pic]. Using the formula we get:

[pic]

The pattern will now repeat as we are back where we started from!

This is true for any terms [pic]and [pic]:

[pic]

5.3 INVESTIGATION 2: 50 Marks

Section A

1. Using a protractor and a ruler, draw ∆ABC, with  = 35°, AC = 6cm and Ĉ = 65°.

Draw a second triangle, ∆GHI, with Ĝ = 80°, GH = 9cm and Ĥ = 35°. Draw these triangles on the same page. (6)

2. Use your two triangles to do the following measurements, again using your protractor and ruler:

1. The sizes of angle A[pic]C and Î. (2)

2. The lengths of AB and BC in ∆ABC. (2)

3. The lengths of GI and HI in ∆GHI. (2)

3. Now make use of all the measurements; both given and your own measurements to do the following calculations and observations:

3.1 GH ; GI ; HI

AB BC AC (3)

3.2 What do you observe about the angles given and measured in (1) and (2.1) for ∆ABC and ∆GHI? (3)

4. Based on your observations, make a conclusion to describe the relationship between

∆ ABC and ∆GHI. (2)

5. Give an alternative property these triangles have in common. (1)

[ 21]

Section B

1. Do similar drawings, on the same page, for the following right angled triangles; ΔKLM and ΔNOP where KL ( LM and NO ( OP. The lengths of the sides given are as follows:

KL = 6cm; LM = 8cm; NO = 9cm and OP = 12cm. (6)

2. Use a protractor to measure all the angles in both triangles and the lengths KM and NP. (6)

3. Do the following calculations:

3.1 KL ; LM ; KM

NO OP NP (3)

3.2 What do you observe from the calculations in (3.1)? (2)

4. What does your answer in (3.2) imply about these triangles? (2)

5. If angle LMK = θ calculate θ by using the lengths of KM and LM. (3)

6. How does θ compare to the measurement in (2)? Which other angle will be equal to θ? Give a reason for your answer. (2)

7. Use the theorem of Pythagoras to calculate the lengths of KM and NP. How does this compare with your measurement in (2)? (5)

[29]

TOTAL: [50]

MEMORANDUM (Investigation)

MEMO: The memo is a guideline and all measurements must be considered as for the learners’ own drawings and the error range for angles: within 2° and lengths: within 2mm.

Section A

1. Accurate measuring and drawing of the two triangles: 4 angles and 2 sides

2. Measurements:

2.1 Angle ABC = 80° and Î = 65° 1 mark each

2.2 AB = 5,5cm and BC = 3,5cm 2 marks

2.3 GI= 6,5cm and HI = 9,8cm 2 marks

3. Ratio’s:

1. All ratios simplified to ± 1,633 1 per ratio 3 marks

3.2 All angles measured are equal. 1 per angle 3 marks

4. GH = GI = HI 2 marks

AB BC AC

5. The angles are equal, equiangular triangles/ similar triangles. 1 mark

Section B

1. Correct measurement of side lengths and right angle:

2 marks for both side lengths in the two triangles: 4 marks

1 mark for each 90° angle: 2 marks

2. Angles measure to ± 37° and ± 53° in each triangle: 2 marks per triangle = 4 marks

Lengths measure: KM = 10cm and NP = 15cm 1 mark each = 2 marks

3. Ratios

1. Each ratio : ⅔ 1 mark per ratio: 3 mark

3.2 KL = LM = KM

NO OP NP 2 marks

4. Similar triangles/ Equiangular triangles 2 marks anyone or both

5. tan θ = LK

LM 1 mark for ratio

= 6

8 1 mark for value

← θ = 36,8° 1 mark for angle

6. The sizes are the same. One is measured and one calculated using the same data.

2 marks

7. KM² = KL² + LM² (Pyth.)

= 6² + 8²

= 36 + 64

= 100

(KM = 10

NP² = ON² + OP² (Pyth.)

= 9² + 12²

= 81 + 144

= 225

(NP = 15 Measurements should be the same as these calculations

5.4 ASSIGNMENT 1: 50 Marks

Question 1

Given the functions: [pic] and [pic]

1.1 Draw [pic]on the same system of axes. Label all intercepts with the axes. (6)

1.2 Use your graph to determine for which values of x; f(x) ( 0 (2)

1.3 Calculate where f(x) = g(x) from your graph, and hence solve the inequality [pic]. (2)

[10]

Question 2

The graphs of [pic]; x > 0 are represented in the diagram below.

The line y = x is also shown in the diagram

2.1 Determine the value of a in the equation [pic]. (2)

2.2 Determine the coordinates of B, the point of intersection of g(x) and the line y = x. (2)

2.3 Determine the coordinates of C, the point of intersection of f(x) and the y-axis. (2)

2.4 Determine the coordinates of D, the reflection of the point A in the y = x line. (2)

2.5 What will the coordinates of A become if the graph of f(x) is moved 2 units down? (2)

2.6 What is the range of f (1)

2.7 Give the domain of g (1) [12]

Question 3

A journey between two towns, Pietermaritzburg and Durban, is exactly 90 km.

1. Use a graph (with at least 5 different speeds in km/h) to model how variation in speed (x) over the journey causes variation in time taken (y) to complete the trip. Hint: time should be given in minutes (8)

3.2 Describe what happens to y (the time) when x ( the speed) increases . (1)

3.3 Is it possible that a vehicle could travel so fast that the trip could be done in no time at all? Give a reason for your answer. (1)

3.4 How does the trend of the graph relate to the question in 3.3? (1)

[11]

Question 4

[pic]

4.1 If A (2; 2) and B (-3:[pic]), determine the equation of AB, in the form y = mx + c. (4)

4.2 f(x) = ax2 is a parabola simmetrical around the Y-axis through the point A and B.

Determine the equation for f . (2)

4.3 What will the equation for the parabola h be if f(x) is shifted down by 2 units? (1)

[7]

Question 5

If f(x) = 2x -7, g(x) = [pic] and k(x) = x² - 2x + 7

Calculate the following:

5.1 f (10) (2)

5.2 k (-2)∙g(1) (4)

5.3 f(g(3)) (4)

[10]

MEMORANDUM (Assignment 1)

Question 1

1.1

(((for parabola (points of intersection with axes)

((( for straight line (6)

1.2 -3 ≤ x ≤ 3 ((one for each correct value (2)

1.3 From the graph: (-1; 8) and (3; 0) (((As on graph: Cont. Accuracy) (2)

[10]

Question 2

2.1 4 = a2(

2 = a( (2)

2.2 B = [pic](( (2)

2.3 C = (0;1) (( (2)

2.4 (4 ; 2) (( (2)

2.5 (2:2) (( (2)

2.6 f : y > 0 ; y [pic][pic]( (1)

2.7 g : x > 0 ; x [pic][pic]( (1)

[12]

Question 3

Distance = 90 km

3.1

Speed (km/h) |20 |30 |40 |50 |60 |90 |100 |120 | |Time in minutes |270 |180 |135 |108 |90 |60 |54 |45 | |

(( table values (at least 4 values correct; 1 mark for at least 1 value correct)

[pic]

((Labelling of axes correctly (x speed and y time)

((Plotting the points as calculated in table

((Creating the curve

2. The time (y) becomes less. (

3. No, unless you travel faster than 100000km/h((Motivation for yes/ no must be sensible)

4. The time (y) becomes less as x increases( [11]

Question 4

4.1 A (2;2) and B (-3:[pic]) y = mx + c

m = [pic]( = [pic] = [pic] = [pic] (

y = [pic] option : y – y1= m(x – x1) 

(2;2) 2 = [pic] (

3 = c (

y = [pic] x + 3 (4)

4.2 y = ax 2 4.3 y = [pic]x 2 - 2 ( (1)

(2;2) 2 = a (2)2 (

2 = 4a 4.4 h(x) = [pic]

a = [pic] ( (2;2) 2 = [pic] (

y = [pic]x2 (2) 4 = a (

h(x) = [pic] (2)

[pic] [9]

Question 5

1. f(10) = 2(10) -7(substitution

= 20 -7

= 13(answer (2)

1. k(-2)∙g(1) = (-2)² -2(-2) + 7

([pic])((Substitution in each function

= 15 x [pic](correct calculation for both [Incorrect substitution: no marks

= 5(answer (4)

2. f(g(3)) = f ( [pic])(substitution into g(x)

= f ([pic])(calculation and answer for g(x)

= 2 ([pic]) – 7(substitution into f(x)

= -6 [pic] or -6.5(answer (4)

[10]

5.5 ASSIGNMENT 2: 50 Marks

Question 1

The diagram shows rectangular tables. Six people can sit at one table, when two tables are placed together ten people can be seated

i) How many people can be seated with three tables? (1)

ii) Write down a formula to calculate how many people can be seated using n tables. (1)

iii) Investigate what happens when the tables are placed side to side as seen. (3)

iv) Write down a formula for the number of people at n tables. (2)

[7]

Question 2

Karabo is training by running for the Comrades Marathon; he starts his training by running 40km per week. Each week he increases the distance covered by 10km.

i) Write down the formula to calculate the distance he runs in the n- th week. (4)

ii) Use the formula to calculate the distance he runs in the 12th week of training (1)

[5]

Question 3

Construction workers resurface parts of the N1 Highway.They complete 2km per day.

i) How many kilometres are completed in total after the first three days? (2)

ii) Write down a formula to find how much road would be repaired after n days? (2)

iii) How many kilometres are repaired after 30 days? (2) [6]

Question 4

For each sequence:

i) Continue the pattern for three more terms [8]

ii) Describe the rule or pattern of the sequence in words [8]

iii) Write a formula for the general term for each sequence [16]

(a) 2 , 4 , 6, , , , , , , , , , ,

(b) 5, 10, 15, , , , , , , , , , , ,

(c) 1, 4, 9,, , , , , , , , , , , , , , ,

(d) 10, 20, 30, , , , , , , , , , , , , , , ,

(e) 2, 5, 10, , , , , , , , , , , , , , , , , ,

(f) 1 , 8, 27, , , , , , , , , , , , , , ,

(g) 2, 9 ,28, , , , , , , , , , , , , , ,

(h ) 4, 7, 10, , , , , , , , , , , , , ,

MEMORANDUM (Assignment 2)

Question 1

i) (4 x 3) + 2 =14( (1)

ii) (4 x n ) + 2 = 4n + 2 ( (1)

iii) The sequence becomes: 6, 8, 10, 12 etc(( (3)

Which implies 4 x number of tables plus 2 seating at the ends of tables ( (1)

iv) Tn = 4n + 2 (where n represent the number of tables) (( (2)

[7]

Question 2

i) Tn = an + c

40 = a(1) + c............1(

50 = 2 a + c.............2(

2 – 1 .....................10 = a(

Tn = 10 n +30(

ii) T12 = 10 (12) + 30 [5]

= 150(

Question 3

i) 6 km (

ii) Tn = 2n ((

iii) Tn = 2 (30) ( [5]

= 60km(

Question 4

(a) 8, 10, 12(

Consecutive even numbers(

Tn = 2n(

(b) 20, 25, 30(

Consecutive multiples of 5(

Tn =5n(

(c ) 16,25,36(

Consecutive square numbers(

Tn = n2

d) 40,50,60(

Multiples of 10(

Tn = 10n(

(e ) 17, 26, 37(

Consecutive square numbers increased by 1(

Tn = n2 + 1(

f) 64, 125, 216(

Consecutive Cubes(

Tn = n3

g) 65, 126, 217(

Consecutive cubes increased by 1(

Tn = n 3+ 1(

h) 13, 16, 19(

Starting from 4 each term increases by 3(

(21)

-----------------------

a

b

c

d

e

[pic]

[pic]

[pic]

cot

bð

C

A

B

4 cm

3 cm

h

[pic]

[pic]

D

cot

b

c

bð

=ð

β

C

A

B

4 cm

3 cm

h

[pic]

[pic]

D

cot

b

c

β

’

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