1(i) When t = 0, 20 + A = 80, so A must be equal to 60.
1(ii) k = 0.288 (to 3 SF)
1(iii) Since t > 3.82, it is safe to give the food 4 min after removal from the microwave.
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2(i) Remainder = – 12
2 (ii) f(-2) = 0, so (x+2) is a factor of f(x). Solving f(x) = 0, x = -2, 1/2 or 3.
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3(i) Length of rectangle = 9/2 + Sqrt(3)/6
3(ii) c = -1
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4(I) 2.25 4
(ii) 8x^2 + 5x + 64 = 0
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5(a) x^2 – 8x + 32 = 0. No real solution because discriminant is less than 0.
5(b) y = 1/x^2
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6(I) Use the fact that triangle ACE is isosceles and the alternate-segment theorem to state that angle ACE = angle ABC. Angle DEF = angle ECA + angle EAC.
6(ii) angle DFE = 2 x angle ACB.
6(iii) Use the fact that angle BAC = 180 deg – (angle BAF + angle CAE).
So 2 x (angle BAC) = 360 deg – 2(angle BAF + angle CAE).
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7(I) p = 3 and q = 2
7(ii) (a) increasing
7(ii) (b) decreasing
7(iii) It is a maximum point
7(iv) 0
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To be continued
Suggested answers to GCE O Level 2014 A. Math (4047) Paper 1
1. k = -2
2. sqrt(26)/26
3. 1.75
4. -3/x – 2/x^2 + 4/(x-2)
5(i) v = 0.263
5(ii) around v = 0.231
5(iii) around f = 0.120
6. (i) Remember that when there is a mixture of trigo functions which cannot fit into a single trigo identity, convert all the given trigo functions into sine and cosine. Start with the LHS, the more complicated expression. You will reach the key stage where
LHS = 1 / [(1 – sin^2@)/(sin@cos@)] = 1/ (cos^2@/sin@cos@) = 1/(cos@/sin@) = tan@
6(ii) acute angle, so @ = 1.05.
7(i) A = (h, 2h); B = (7h/4, 2h); C = (h, h/2)
7(ii) Area of trapezium = 21 sqr units.
8. Integrate f'(x) to get f(x) with a +c. Use f(pi/2) = 0 to get c = 1/4. Differentiate f'(x) to get f”(x)= 4cos4x + 2sin2x. Proceed to add f”(x) to 4f(x) to get the RHS.
9(i) Pure inequality question. Solve 2x^2 + 5x – 12 > 0 by sketching a quadratic graph. Ans: {x : x < -4 U x > 3/2}
9(ii) Show that the (b^2 – 4ac) of (4x^2 + 4x + 1 = 0) is zero.
9(iii) a = -1.
To be continued ….
O-LEVEL | SEC | A. MATH TUITION
Ad Hoc 1-1 Consultation (for the busiest of students)
Under this scheme, students do not need to register with our centre. If a student needs clarification on a particular topic in E.Math, A.Math, Physics or Chemistry, or needs help solving some questions in these subjects, he can just message the tutor (hp: 97860411, NUS grad, NIE-trained, Ex-RI) to book a 1-hr slot. Fee is $90 per hour and must be paid in advance to confirm the slot (no refund for a no-show whatever the reason). Lessons can be physical in-centre or online via zoom. Fee for home tuition (west area) is $180 per hour.
Weekly Regular Tuition
We have 2 modes of regular weekly tuition for our Math and Science classes (non-IP): Flexible Group Tuition and 1-1 Tuition.
FLEXIBLE HYBRID GROUP TUITION (FHGT) (Proven very effective personalised tuition for the busy student. Try it!)
Features:
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Very small class size (max 4 students)
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Flexible schedule that allows for make-up lessons
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Hybrid Dual Subject system to save on tuition fees.
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Students can ask about their own school work
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Fee Discount on Practical lessons for Science students.
WEEKLY SCHEDULE
MON (5-6.30PM): MATH | A.MATH
TUE (5-6.30PM): PHYSICS | CHEMISTRY
FRI (5-6.30PM): PHYSICS | CHEMISTRY
SAT (5-6.30PM): A.MATH | CHEMISTRY
MON (5-6.30PM): A.MATH | CHEMISTRY
Structure: Once a week, 4 times a month
Registration fee: $30
Monthly fee: $360
1-1 TUITION
Days: To be negotiated and agreed upon
Times: To be negotiated and agreed upon
Registration fee: $30
For further details, click on INDIVIDUAL TUITION.
Note: Our A.Math students also enjoy a 50% discount when they book our science practical sessions (once a month).
Our Tutor is an NIE-trained Ex-MOE Teacher who has been coaching students in A.Math for more than 12 years. An alumnus of Raffles Institution, he holds a a Bachelor of Science degree from the NUS as well as a Master of Education (Curriculum & Teaching) degree from the National Institute of Education.
For enquiries, you may msg the Tutor directly at 97860411.
If you need private 1-1 HEAD START, REVISION or RE-LEARNING of Math, Physics or Chemistry topics, kindly message our tutor directly at 97860411.
TO REGISTER, SMS <STUDENT NAME>, <SUBJECT, DAY> TO 87762711
Administrative Matters:
Location: Blk 644, Bukit Batok Central, #01-68. S(650644).
Our location is just a 3-min walk from either the Bukit Batok MRT station or the Bukit Batok Bus Interchange. Buses that stop along the roads surrounding our location are numbers 157, 178, 66, 506, 173, 174, 176, 187, 985. Buses services which terminate at Bukit Batok Bus Interchange are 61, 77, 106, 173, 177, 189, 852, 941, 945, 947.
O-LEVEL PHYSICS PRACTICAL
O-LEVEL CHEMISTRY PRACTICAL
O-LEVEL BIOLOGY PRACTICAL
TUITION CLASSES:
EDUCATIONAL SERVICES:
O-Level A. MATH Crash Course / Intensive Revision 7 Oct 2014
Dates: 7/10 (Tue) to 10/10 (Fri) , 4 days straight.
Time: 2.00 pm – 5.00 pm
Location: Blk 627, Bukit Batok Central. (It is just a 3-min walk from either the Bukit Batok MRT station or the Bukit Batok bus interchange. Buses that stop along the road in front of Blk 627 are numbers 157, 178, 66, 506, 173, 174, 176, 187, 941, 947, 985)
Fee: $360
Max. no. of students: 8.
Tutor: Mr Ilyasa (ex-sch teacher, M.Ed, PGDE, B.Sc).
A former MOE school teacher, Mr Ilyasa has been coaching students in ‘A’ Level & IB Physics and Mathematics for more than 6 years, as well as ‘O’ Level & IP Physics, Additional Math, E. Math and PSLE Math for more than 10 years. An alumnus of RI and RJC, Mr Ilyasa holds both a Master of Education degree and a Postgraduate Diploma in Education with Credit from the National Institute of Education, as well as a Bachelor of Science degree from the National University of Singapore.
To register, sms <Student Name><AMATH7OCT> to 97860411.
For any queries, you may also talk directly to Mr Ilyasa at 97860411.
SEC 3 ADDITIONAL MATH CONSOLIDATION WORKSHOPS 11 NOV – 14 NOV
Consolidation workshops are for students who have performed poorly in their SA2 exams or in certain topics in their exams. These classes are intended for students to “consolidate” what they have learnt and re-learn if necessary. Such students are encouraged to attend these lessons before attending Headstart lessons.
(1) Indices, Surds & Logarithms: Monday, 11 Nov, 9.30 am – 12.30 pm; Code: S3MC1.
(2) Roots of Quadratic Equations & Inequalities: Monday, 11 Nov, 2 pm – 5 pm; Code: S3MC2.
(3) Polynomials & Partial Fractions: Tuesday, 12 Nov, 9.30 am – 12.30 pm; Code: S3MC3
(4) The Binomial Theorem: Tuesday, 12 Nov, 2 pm – 5 pm; Code: S3MC4.
(5) Trigonometry I: Wednesday, 13 Nov, 9.30 am – 12.30 pm; Code: S3MC5.
(6) Trigonometry II: Thursday, 14 Nov, 9.30 am – 12.30 pm; Code: S3MC6.
Administrative Matters:
Location: Blk 627, Bukit Batok Central
Max Class Size: 6
Fee: $80 for each 3 hr session.
Tutor: Mr Ilyasa (M.Ed., PGDE, B.Sc), former MOE Subject Head with more than 10 years’ experience tutoring students in Math and Physics.
TO REGISTER, SMS <FULL STUDENT NAME>, <CODE> TO 97860411.
For enquiries, kindly call or sms to 9786 0411.
REMINDER: SEC 3 A. MATH, PHYSICS & CHEMISTRY HEADSTART CLASSES COMMENCE THIS SUNDAY 10 NOV
Sec 3 A. Math: Every Sunday, 11.00 am – 12.30 pm (Start Nov 10); Code: S3M1.
Sec 3 Physics: Every Sunday, 9.30 am – 11.00 am (Start Nov 10); Code: S3P1.
Sec 3 Chemistry: Every Sunday, 9.30 am – 11.00 am (Start Nov 10); Code: S3C1.
Location: Blk 627, Bukit Batok Central
Max Class Size: 8
Tutors:
For Math & Physics: Mr Ilyasa (M.Ed, PGDE, B.Sc), former MOE Physics Subject Head with more than 10 years’ experience tutoring students in O-level, IP and A-Level Math & Physics.
For Chemistry: Mr Tan, NTU undergrad with 3 years’ experience tutoring students in O-Level, IP & IB Chemistry.
Monthly fee for each subject or slot is $180, inclusive of materials fee. Discounts apply for multiple subjects or slots.
All of the above courses will end by 15 Dec 2013 and will resume in the week starting 6 Jan 2014.
TO REGISTER, SMS <FULL STUDENT NAME>, <CODE> TO 97860411.
For enquiries, kindly call or sms to 9786 0411.