1) 4 and 5-litre bowls 2) 4 and 3-litre bowls Solution . . . 1) Fill the 5-litre bowl; pour water from it to fill the 4-litre bowl‚ which you empty afterwards. Pour the remaining 1 litre to the 4-litre bowl. Refill the 5-litre bowl and then carefully pour water from it to fill the 4-litre bowl (where there is already 1 litre). This will only need 3 litres. Thus you are left with 2 litres in the 5-litre bowl‚ as requested. 2) Fill the 3-litre bowl and pour all of the water to the 4-litre
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Centre Number For Examiner’s Use Candidate Number Surname Other Names Examiner’s Initials Candidate Signature Pages General Certificate of Secondary Education Foundation Tier November 2013 Mark 2–3 4–5 6–7 Mathematics 43601F Unit 1 Wednesday 6 November 2013 9.00 am to 10.00 am For this paper you must have: l mathematical instruments. 10 – 11 12 – 13 14 – 15 16 – 17 a calculator l F 8–9 TOTAL Time allowed l 1 hour Instructions
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surveys in a superficial way the vast activity of mathematicians around the world‚ it is easy to come away with the impression that mathematics is not actually all that important. The percentage of the world’s population‚ or even of the world’s university-educated population‚ who could accurately state a single mathematical theorem proved in the last fifty years‚ is small‚ and smaller still if Fermat’s last theorem is excluded. If you ask a mathematician to explain what he or she works on‚ you will
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Rock‚ walk x paces to the north‚ and then walk 2x + 4 paces to the east. If they share their information‚ then they can find x and save a lot of digging. What is x? So‚ if you walk x paces north‚ then 2x+4 paces east‚ you have moved roughly east northeast to a distance of 2x+6 paces. This is a right angle‚ with 2x+6 on the hypotenuse or line c‚ so we must solve using the Pythagorean Theorem: a² + b² = c² add in the values (x)² + (2x+4)² = (2x+6)² multiply inside the parenthesis x²
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1. Explain the difference between a “reserve” and a “resource”. What factors influence estimates of reserves and resources for commodities such as minerals or fossil fuels? Resources and reserves are similar in that the both benefit humanity. Resources are materials that can be used to satisfy human needs‚ or used as support. Reserves on the other hand are known deposits with the ability to extract the available material economically; the size of these reserves is not always known or defined
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Simplify 2 1 . − n n +1 2 (d) Solve 4 x − 3 = 7. 2 (e) Expand and simplify ( 3 −1 2 3 + 5 . )( ) 2 (f) Find the sum of the first 21 terms of the arithmetic series 3 + 7 + 11 + ··· . 2 – 3 – Marks Question 2 (12 marks) Use the Question 2 Writing Booklet. (a) Differentiate with respect to x : (i) (ii) (iii) ( x 2 + 3) 9 x 2 loge x sin x . x+4 2 2 2 (b) Let M be the midpoint of (–1‚ 4) and (5‚ 8). 1 Find the equation of the line
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Circle C3 has center A and radius r (therefore circles C1 and C3 are the same size). The point P’ (written P prime) is the intersection of C3 with OP. This is shown in the diagram below. Analytically find OP’ using r=1 and OP=2‚ OP=3‚ and OP=4: First‚ I created a line (see the dashed line in the above figure) between AP’ that creates the ΔAOP’. Because P’ is on the circumference of circle C3 and A is the center of circle C3‚ that means that AP’ is equal to the radius of C3‚ which is 1. We
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other word in a sentence is called “pronoun” Q2. Write any six conjunctions? Ans. Although‚ who‚ and ‚ but ‚ because‚ whom. Q3. Combine the following sentences. Roger hates history. He likes English. He likes Maths. Ans. Roger hates history but he likes English and maths. The day was cold. The day was windy. It was only the first of February. Ans. The day was cold and windy although it was only the first of February. The dog was barking. He was trying to get over the gate.
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insurance‚ the insured agrees to pay a specific premium each year until death. B. whole-life 3. In a health insurance policy‚ a statement that an applicant won’t be covered for a certain pre-existing condition is called a/an C. exclusion. 4. All insurance is based on a principle called D. division of risk. 5. Lorenzo has a checkbook balance of $118.00. He writes two checks‚ one for $9.00 and one for $84.25. He then deposits $95.00. Finally‚ he uses his calculator to determine his
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EUROPEAN SCHOOL Mathematics Higher Level Portfolio Type 1 SHADOW FUNCTIONS Candidate Name: Emil Abrahamyan Candidate Number: 006343-021 Supervisor: Avtandil Gagnidze Session Year: 2013 May Candidate Name: Emil Abrahamyan Candidate Number: 006343-021 Mathematics Higher Level Type 1: Shadow Functions SHADOW FUNCTIONS The Aim of the Investigation: The overall aim of this investigation is to investigate different polynomials with different powers and create shadow function
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