ROOTS INTERNATIONAL SCHOOLS
BRANCH: IGCSE Campus Sialkot
MATHEMATICS (60) Final Exam, Grade,9th,2021 PAPER: 01
TimetAllowed:15 minutes (Objective type) Max Marks:12
Name……………………………………..…………………………….
Q#1 Circle the Correct Option. 1 × 12 = 12 درتسوجابےکرگددارئہاگلںیئ۔ :1وسالربمن
1) Arthur Cayley introduce the “ Theory of Matrices” آررھتےلیک۔۔۔۔۔۔۔ںیماقوبلںیکویھتریاعتمرفرکایئ۔ )1
A 1854 B 1856 C 1858 D 1860
2) 𝑎 𝑏 𝑎 𝑏 )2
𝑖𝑓 𝐴 [ ] 𝑡ℎ𝑒𝑛 |𝐴| = ______ [ = 𝐴 وہوت|𝐴|= ۔۔۔۔۔۔۔۔۔ ]ارگ
𝑐 𝑑 𝑐 𝑑
A 𝑎𝑏 − 𝑐𝑑 B 𝑎𝑐 − 𝑏𝑑 C 𝑏𝑐 − 𝑎𝑑 D 𝑎𝑑 − 𝑏𝑐
3) Which is order of a square matrix وکناسدرہجاکیرمیباقبلاکےہ؟ )3
A 1 − 𝑏𝑦 − 2 B 2 − 𝑏𝑦 − 2 C 2 − 𝑏𝑦 − 1 D 3 − 𝑏𝑦 1
4) 𝑎+3 4 −3 4 𝑎+3 4 −3 4 )4
𝑖𝑓 [ ]=[ ]then the value of 𝑎 is [وہوت 𝑎 یکتمیقولعممرکںی۔ ]=[ ]ارگ
6 0 6 0 6 0 6 0
A -6 B -3 C 3 D 6
5) −1 −2 1 1 −1 −2 1 1 )5
𝑖𝑓 𝑋 + [ ]=[ ] 𝑡ℎ𝑒𝑛 𝑋 = ⋯ 𝑋 = 𝑋 وہوت۔۔۔۔۔۔۔+ [ ]=[ ]ارگ
0 −1 0 1 0 −1 0 1
A 2 2 B 0 2 C 2 0 D 2 2
[ ] [ ] [ ] [ ]
2 0 2 2 0 2 0 2
6) 1 −2 1 −2 )6
𝐴𝑑𝑗 [ ] …? 𝐴𝑑𝑗 [ ] = ۔۔۔۔۔۔۔۔
0 −1 0 −1
A −1 −2 B 1 −2 C −1 2 D −1 0
[ ] [ ] [ ] [ ]
0 1 0 −1 0 −1 2 1
7) {0, ±1, ±2, ±3, … … } 𝑖𝑠 𝑐𝑎𝑙𝑙𝑒𝑑 (7
A Natural Number دقریتادعاد B Whole numberلمکمادعاد C Integers حیحصادعاد D Rational number انقطربمن
1
8) The property of real numbers used in 7 × = 1 𝑖𝑠 (8
7
A Additive inverse یعمجوکعمس B Additive identity یعمج ذایت C Multiplicative inverse رضیب D Additive property یعمج
رصنع وکعمس اختیص
9) The Value of (−𝑖)9 𝑖𝑠 ∶ (9
A 1 B -1 C 𝑖 D −𝑖
10) The value of 𝑖 12 𝑖𝑠 𝑖 یکتمیقولعممرکںی12 (10
A −𝑖 B 𝑖 C -1 D 1
11) If 3√35 𝑖𝑠 𝑟𝑎𝑑𝑖𝑐𝑎𝑛𝑑 𝑖𝑠 … …. ںیمرڈیڈنیک۔۔۔۔۔۔۔ےہ؟3√35 (11
A 3 B 1 C 35 D None
3
12) If 𝑎, 𝑏 ∈ 𝑅 𝑡ℎ𝑒𝑛 𝑜𝑛𝑙𝑦 𝑜𝑛𝑒 𝑜𝑓 𝑎 = 𝑏 𝑜𝑟 𝑎 < 𝑏 𝑜𝑟 𝑎 > 𝑎 = 𝑏 𝑜𝑟 𝑎 < 𝑏 𝑜𝑟 𝑎 > 𝑏 𝑎اوررصفاکی, 𝑏 ∈ 𝑅 ارگ (12
𝑏 which is called
A Tracheotomy property B Transitive property C Additive property یعمجاختیص D multiplicative property
ROOTS INTERNATIONAL SCHOOLS
BRANCH: IGCSE Campus Sialkot
First Term
Maximum Marks:60 Time Allowed: 2:30
Name: Grade:9th
Date: Subject: MATH
INSTRUCTIONS
1: Count the total number of printed pages.
2: Read each question carefully.
3: Read carefully and attempt all questions.
4: A question can consist of two or more parts.
5: No additional page will be given for wring.
6: Students are allowed to use blue/black ink only.
7: Use of lead pencil is strictly not allowed.
8: Check your answer paper before you hand it over. Make sure your name, section and school are filled in.
9: The Marks for each section are shown in the bracket ().
-------------------------------------------------------Do not write below this line-----------------------------
PERCENTAGE
GRADE
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ROOTS INTERNATIONAL SCHOOLS
BRANCH: IGCSE Campus Sialkot
Q#2 Write Short answers Attempt any Eight questions. 2 × 8 = 16 دنمرہجذلیںیمےسوکیئےسآھٹوساالتےکرصتخموجاابتدںی :2وسالربمن
1) What is row matrix? اطقریاقبلیکرعتفیرکںی؟ )1
مستط
2) Define rectangular matrix with an example . یلیاقبلیکرعتفیرکںیہعمباثملدںی )2
3) Define transpose of a matrix. رٹاوپسنزاقبلیکرعتفیرکںی؟ )3
4) Define Diagonals Matrix. رٹمیسکاقبلیکرعتفیرکںی؟ )4
س
5) Define Scalar Matrix. ویکس میٹرکاقبلیکرعتفیرکںی۔ )5
6) Define identity matrix. ودحایناقبلیکرعتفیرکںی )6
7) Find the transpose of the matrix 𝐵 = [5 1 − 6] 𝐵 = [5 1 − 6]اقبلاکرٹاوپسنزاقبلولعممرکںی )7
8) 𝑖𝑓 𝐶 = [5 1 −6] then find 3C ولعممرکںی3C[ = 𝐶وت5 1 −6] ارگ )8
9) 𝑖𝑓 𝐶 = [1 −1 2] 𝑡ℎ𝑒𝑛 𝑓𝑖𝑛𝑑 3𝐶 ولعممرکںی3C[ = 𝐶 وہوت1 −1 2]ارگ (9
10) −1 2 −1 2
Find 2A if 𝐴 = [ ] ولعممرکںی۔2A [ = 𝐴وہوت ]( ارگ10
2 1 2 1
11) 𝑖𝑓 𝐴 = [ 3 0] , 𝐵 = [6] 𝑓𝑖𝑛𝑑 𝐴𝐵 ولعممرکںی۔AB [ = 𝐴وہوت
3 0 6
] , 𝐵 = [ ]( ارگ11
−1 2 5 −1 2 5
Q#3 Write Short answers Attempt any Eight questions. 2 × 8 = 16 دنمرہجذلیںیمےسوکیئےسآھٹوساالتےکرصتخموجاابتدںی۳وسالربمن
1) Define Radical Sign. انقطادعادیکرعتفیرکںی )1
2) Define irrational number and also give an example. ریغانقطادعادیکرعتفیرکںیاوراثملیھبدںی )2
15
3) Represent the numbers and also give an example. دےیئوہےئربمنوکالنئرپاظرہرکںی )3
7
4) Express the recurring decimal as the rational number ≠ 𝑝 حیحصادعادوہں0 اورP,Q ںیماظرہرکںیہکبجp/q رکتاریدعدوکانقطادعاد )4
𝑝
̅̅̅̅
𝑤ℎ𝑒𝑟𝑒 𝑃, 𝑄 𝑎𝑟𝑒 integers and 𝑝 ≠ 0.013 ̅̅̅̅
0. . 13
𝑞
5) Define Closure property of real numbers. یقیقحادعاداختیصدنبشیکرعتفیرکںی )5
6) . Simplify 3√−
8 3 8
√− رصتخمرکںی )6
27 27
7) Find the value of 𝑖 27 اکیاثملےسااسساوروقتامناکوصترواحضرکںی )7
4(3)𝑛
8) Explain the concept of base and exponent with an example. رصتخمرکںی 8)
3𝑛+1 −3𝑛
کمل
یکسادعادیکرعتفیرکںی
4(3)𝑛
9) Simplify 9)
3𝑛+1 −3𝑛
1 1
10) Express in standard form 𝑎 + 𝑏𝑖 𝑎ںیماظرہرکںی+ 𝑏𝑖 ایعمریلکش 10)
2+𝑖 2+𝑖
𝑎کتشکلںیمںیمرصتخمرکںی+ 𝑖𝑏 وک
2+3𝑖
11) 11)
4−𝑖
2+3𝑖
Simplify and write your answer in the form 𝑎 + 𝑏𝑖 ,
4−𝑖
Q#4 Write detailed answers Attempt any Two 8 × 2 = 16 الیصفتََوجاابترحتریرکںی۔
َ دنمرہجذلیںیمےسوکیئےسدووساالتےک ۴وسالربمن
questions.
1) a) Solve the equation by using matrix inverse method 4𝑥 − ؎دییئگاسمواوتںوکاقوبلںےکوکعمسدمدےسلحرکںی a)
2𝑦 = 8, 3𝑥 + 𝑦 = −4 4𝑥 − 2𝑦 − 8, 3𝑥 + 𝑦 = −4
b) Solve the following linear equations by Cramer’s rule 2𝑥 − رکرمیےکاقوننیکدمدےساسمواوتںاکلحرکںی
2𝑦 = 4, 3𝑥 + 2𝑦 = 6 2𝑥 − 2𝑦 = 4, 3𝑥 + 2𝑦 = 6 b)
2) a) Solve by matrix inverse method if اقوبلںےکوکعمسیکدمدےسلحرکںی a)
3𝑥 − 4𝑦 = 4, 𝑥 + 2𝑦 = 8 3𝑥 − 4𝑦 = 4, 𝑥 + 2𝑦 = 8
−3 −3
b) 𝑥 −2 𝑦 −1 𝑧 −4 𝑥 −2 𝑦 −1 𝑧 −4 b)
Simplify [ ] [ ] رصتخمرکںی
𝑥 4 𝑦 −3 𝑧 0 𝑥 4 𝑦 −3 𝑧 0
3) a) 2
(216)3 ×(25)2
1 2
(216)3 ×(25)2
1 a)
Simplify √ 3 √ 3 رصتخمرکںی
(0.4)−2 (0.4)−2
𝑏+𝑐 𝑏+𝑐
(b 𝑥 𝑎 𝑎+𝑏 𝑥𝑏 𝑥 𝑐 𝑐+𝑎 𝑥 𝑎 𝑎+𝑏 𝑥𝑏 𝑥 𝑐 𝑐+𝑎 (b
Prove that ( 𝑏 ) × ( 𝑐) × ( 𝑎) =1 ( 𝑏) × ( 𝑐) × ( 𝑎) = 1اثتبرکںی۔
𝑥 𝑥 𝑥 𝑥 𝑥 𝑥
