first number is decreased by 1 and the second number by 2, the three numbers then form a geometric sequence. Find the three numbers.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

SECTION ONE 56 MARKS

Question One

1. If 𝑆𝑛 =3𝑛2− 5 𝑛2

1.1 Determine the sum of the first 10 terms. (2)

1.2 Determine 𝑇10 (3)

Question Two

2. Three numbers form an arithmetic sequence. Their sum is 24.

2.1 If 𝑎 is the first number and 𝑑 the common difference, show that

𝑎 + 𝑑 = 8.

2.2 If the first number is decreased by 1 and the second number by 2, the three numbers then form a geometric sequence. Find the three numbers. (2)

Question Three

3. Consider the number pattern 6; 10; 16; 24; 34; ………..

3.1 If the pattern behaves consistently, determine the next

TWO terms of the pattern. (2)

3.2 Determine the general term of this pattern. (5)

3.3 Calculate 𝑛 if the 𝑛𝑡ℎ term in the pattern is 1264. (4)

Question Four

The diagram below represents a square 𝑃𝐵𝑄𝐴 with side lengths equal to 12 units. A second square is drawn with diagonal 𝐶𝐵 =𝐴𝐵. A third square is drawn with diagonal 𝐷𝐶 = 𝐴𝐶, and a fourth square with diagonal 𝐸𝐷 =2

𝐴𝐷. The pattern continues until 10 Squares are drawn.

Determine the area of the shaded section.

Question 5

5.1 Given the series (2𝑥 + 1) + (2𝑥 + 1)2 + (2𝑥 + 1)3 + (2𝑥 + 1)4 ….

5.1.1 Determine the values of 𝑥 for which the series will converge. (3)

5.1.2 Determine 𝑆∞ if 𝑥 = − 4 (3)

5.2 Calculate the value of 𝑛 if 𝑛∑ 1 (2)𝑘−1 = 5

5.3 Evaluate

Question Six

A quadratic Sequence has the following properties:

𝑇10 = 𝑇14 = 0

𝑇17 = −21

6.1 Which term will have the largest value in the pattern? (1)

6.2 Which other term will have a value of -21? (1)

6.3 Show 𝑇𝑛 = −𝑛2 + 24𝑛 − 140 (4)

6.4 If 𝐹𝑛 is the first difference of this quadratic pattern:

6.4.1 Determine an expression for 𝐹𝑛 (3)

6.4.2 What is the difference between the 91st and 92nd term of the

quadratic pattern? (2)

SECTION 2 64 MARKS

Question One

Consider the function 𝑔(𝑥) = 𝑙𝑜𝑔1𝑥

1.1 Will the graph of 𝑔 be increasing or decreasing? Motivate your answer. (2)

1.2 Find the equation of 𝑔−1(𝑥) and draw a neat sketch of both 𝑔 (𝑥) and 𝑔−1(𝑥)

on the same set of axes. (6)

1.3 Write down the equation of the asymptote of 𝑔(𝑥 + 2). (1)

1.4 Write down the domain of 𝑔−1(𝑥) (1)

Question Two

2.1 Given 𝑓(𝑥) = √4𝑥 and 𝑔(𝑥) = 𝑥2, evaluate 𝑓(𝑔(9)) (3)

2.2 Rewrite 𝑓(𝑥) = 𝑥−1 in the form 𝑓(𝑥) = 𝑎+ 𝑞 and hence give the equations 𝑥−2 𝑥−𝑝 of the asymptotes. (5)

2.3 Given 𝑓(𝑥) = 3𝑥2 − 7

The graph of 𝑓 is shifted 3 units down and 2 units to the left, resulting in the graph of ℎ(𝑥). Determine an expression for ℎ(𝑥) in the form 𝑎𝑥2 + 𝑏𝑥 + 𝑐 (4)

2.4 Given 𝑓(𝑥) = 1 + 2𝑥

2.4.1 Show that 𝑓(𝑥) × 𝑓(−𝑥) = 𝑓(𝑥) + 𝑓(−𝑥) (3)

2.4.2 If 𝑔(𝑥) = 𝑓(𝑥) − 1, determine 𝑔−1(𝑥) in the form 𝑦 = …… (3)

Attachments:

Related Questions

. The fundamental operations of create, read, update, and delete (CRUD) in either Python or Java

CS 340 Milestone One Guidelines and Rubric  Overview: For this assignment, you will implement the fundamental operations of create, read, update,

. Develop a program to emulate a purchase transaction at a retail store. This  program will have two classes, a LineItem class and a Transaction class

Retail Transaction Programming Project  Project Requirements:  Develop a program to emulate a purchase transaction at a retail store. This

. The following program contains five errors. Identify the errors and fix them

7COM1028   Secure Systems Programming   Referral Coursework: Secure

. Accepts the following from a user: Item Name Item Quantity Item Price Allows the user to create a file to store the sales receipt contents

Create a GUI program that:Accepts the following from a user:Item NameItem QuantityItem PriceAllows the user to create a file to store the sales receip

. The final project will encompass developing a web service using a software stack and implementing an industry-standard interface. Regardless of whether you choose to pursue application development goals as a pure developer or as a software engineer

CS 340 Final Project Guidelines and Rubric  Overview The final project will encompass developing a web service using a software stack and impleme