Gce o level maths final
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The document provides information about the format and content of the GCE O-Level Mathematics examination. It consists of two papers, each lasting 2 hours. Paper 1 tests fundamental skills and concepts through 25 short answer questions. Paper 2 tests higher-order thinking through 10-11 longer questions. Calculators and geometrical instruments are allowed. Answers should be given to three decimal places, unless otherwise specified. Various mathematical formulae are provided.
Gce o level maths final
- 1. GCE OLEVEL MATHS MATHEMATICS GCE O Level EXAMINATION FORMAT Paper Duration Description Paper 1 2 hours Paper 2 2 Weighting There will be about 25 short answer questions testing more on the fundamental skills and concepts. Candidates are to answer ALL questions. hours Marks 80 100 Compare the two triangles and identify the common perpendicular height. Then, put as ratio, the length of their bases. 50% There will be about 10 to 11questions of varying marks and lengths testing more on higher order thinking skills. Candidates are to answer ALL questions. B(iv)a 50% 1. 2. Omission of essential working will result in loss of marks. Some questions may integrate ideas from more than one topic of the syllabus where applicable. 3. Relevant mathematical formulae will be provided for candidates. 4. Scienti鐃ic calculators are allowed in both Paper 1 and Paper 2. 5. Candidates should also have geometrical instruments with them for Paper 1 and Paper 2. 6. Unless stated otherwise within a question, three-鐃igure accuracy will be required for answers. This means that four-鐃igure accuracy should be shown throughout the working, including cases where answers are used in subsequent parts of the question. Premature approximation will be penalised, where appropriate. Angles in degrees should be given to one decimal place. 7. SI units will be used in questions involving mass and measures. Both the 12-hour and 24-hour clock may be used for quoting times of the day. In the 24-hour clock, for example, 3.15 a.m. will be denoted by 0315; 3.15 p.m. by 1515, noon by 1200 and midnight by 2400. 8. Candidates are expected to be familiar with the solidus notation for the expression of compound units, e.g. 5 cm/s for 5 centimetres per second, 13.6 g/cm3 for 13.6 grams per cubic centimetre. 9. Unless the question requires the answer in terms of , the calculator value for or = 3.142 should be used. 10. Spaces will be provided on the question paper of Paper 1 for working and answers. B(iv)b 1 = 2 = 3 1 =3 NOTES Mathematical Formulae Observe that OABD is a combination of two triangles, OAB and OBD. Once youcan see, that, identify the common perpendicular height. area of trapezium OABD area of OAB (OD + AB) 1 2 ht AB ht (A) It is given that (C) (D) Simplify Qn A . Arc length = , where Sector area = Worked Solution Trigonometry is in radians Standard deviation = D (A) The coordinates of point A is (3, 4) and point B is (12, 10). If point P lies on the line AB such that . Vectors (B) Express as a column vector. Find . Find the coordinates of P. Trigonometry OABC is a parallelogram and M is the midpoint of BC. OC is produced to D so that OC = CD. OM is produced to meet BD at N. Given that = x and AB= y, express the following vectors in terms of x and y. (i) , (ii) (iv) Given that (iii) area of MDN (a) , area of MDO , 鐃ind the numerical value of Worked Solution = + = = A(ii) = = 10.8 (3sf) A(iii) Tips - It is good to begin with A and ends with B. Meaning, start from point A to O, followed by O to B. In this manner you will always remember where to start and end. Do ensure the answer written is in 3 sf since the actual value is not exact. Same as A(i). = = = Coordinates of P is (6, 6) B(i) B(ii) Same as A(i). =x+y Take note of the . direction of It is in the opposite = =x+y+ = Common Mistakes . Here, students not only change the signs but also swap the position of the numbers. x+y B(iii) =x+y ( x) is factorised wrongly to become . P B Always consider the longer time to be subtracted by the shorter time. Students tend to forget to change 20 minutes to hours. Another mistake is that students tend to subtract the wrong expression as shown: You need to show the expression after substituting the numbers as shown on the left. Do reject an answer that is not applicable to the question. Nil Students use the calculator to solve the equation. Marks will be deducted if the first step is not shown. Students fail to convert the answer to the decimal place(s) as required in the question. Students fail to convert the answer to minutes as required. D Total time taken A sports shop sells two brands of t-shirts, Niki and Adi. Each brand is sold in three different sizes, small, medium and large. The sales in two successive weeks are given in the tables below. First Week Second Week Medium Large 16 28 5 10 36 12 Medium Large 10 20 15 16 32 8 The information for the second week is represented by a matrix Q. (A) Write down the matrix Q. (D) Given that X = (B) Q A(iv) Use sine or cosine rule in questions involving triangles that are not right-angled triangle. For this question, only 2 lengths and an angle are included. Thus, only cosine rule can be used. In part solving calculation, students tend to make an error in calculating Calculate (C) Describe what is represented by the elements of (E) Given that Y = (G) B , calculate S = PX. (P + Q) Describe what is represented by the elements of S. (F) Qn A (P + Q) , calculate V = YS. Describe what is represented by the elements of V. Worked Solution Q= . In cross multiplication, students tend to make this mistake: . (P + Q) Tips Common Mistakes Usually you need to NIL observe how the table is presented, and then write it down as required. Students multiply the Add (P + Q) first before including to the matrix P the . only but not Q. You need to simplify the matrix where possible. Nil C D together, multiplying . Students also have the tendency to forget to to get square root RS. Average sales of each type of t-shirts for each brand. S = PX E Bearing of P from Q Small P= Use the trigonometric ratios for right angled triangle. Angle from North to line PQ . The information for the 鐃irst weeks sales can be represented by the matrix Common Mistakes Students leave the . But, answer as bearing must always be in 3 digits. A(ii) Students do not add the six at the denominator as shown, Adi Tips Do take note of the direction of North. Occasionally, North is not pointed upwards but towards some other direction. Draw the North lines at P and Q. You will see that they are parallel and this will help you in solving the question. Some students do not change the sign for in their working. Same as B(ii). Students do not change . the sign for Worked Solution Bearing of P from R = = hours Niki " (B) A vertical pole of height 7.5m is planted at S. A man walks along the path PR. Find the greatest angle of elevation of the top of the pole when the man viewed from any point along the path. Qn A(i) A(ii) Small N" (A) Calculate (i) the bearing of P from R, (ii) the bearing of P from Q, (iii) PQ, (iv) RS, (v) the shortest distance from S to PR. They will lose marks as the question is asking for coordinates not vector form. In other words, the answer should be in (6, 6) form. . direction of In other words, you are required to change the signs . Take note that is parallel to since it is a parallelogram. And is in the same direction and same magnitude as . R" cm Common Mistakes Nil Matrices A(iii) . Students are confused with the formula of finding the length of the two coordinates. Some students will leave the answer as . = Students often state the positive square rooted answer only, leaving out the negative value. or 36 Tips The answer is most likely in fractions, where the variable, v, will be the denominator. Same as A(i) hours C In the diagram, P, Q, R and S are four markers in a horizontal 鐃ield. Given that PS = 40m, PR = 36m, , , and S is due west of P. (b) area of trapezium OABD area of OAB Qn A(i) s Worked Solution , There are two ways of solving this question. One way is through expanding , followed by solving quadratic equations. The other way is by using the method stated on the left. Always try to see whether the numerator and the denominator can be factorised. Most of the time, they can be factorised. C Sample O Level Maths Questions And Tips , giving both answers to 2 decimal places. Students are not able to follow the order as mentioned in *(Tips). x, followed by a, and lastly 3. Mean = (i) (ii) (iii) Common Mistakes In trying to change to , some students may make mistakes such as missing the negative for or missing x in the negative outside the bracket in . *Bring over to the other side of the equation the terms furthest away from the subject. In this case, you will see that b is the term that is furthest away from is in radians Statistics (B) The 鐃irst part of the journey took 20 minutes more than the second part of the journey. Write down an equation in v, and show that it reduces to Tips In these types of questions, it is almost certain that one or both denominator can be factorised. Once factorised, you will notice that there will be a common factor. B where In pressing the calculator, students tend to mistakenly ) calculate ( followed by the division of 30.6. Qn A(i) Curved surface area of a cone = Area of triangle ABC = The greatest angle of elevation happens when the horizontal distance is the shortest (from part A(v) (D) Calculate, correct to the nearest minutes, the time he took to travel from P to Q. Mensuration Volume of a sphere = B (C) Solve the equation Total amount = Volume of a cone = Wrong usage of cosine and sine ratios. (A) Write down an expression, in terms of v, for (i) the number of hours taken to travel the 鐃irst 100 km, (ii) the number of hours to travel the rest of the journey. . . The shortest distance is the perpendicular line to PR from S. The distance between two towns, P and Q, is 180 km. Mr Lim drove from P to Q at an average speed of v km/h. After traveling for 100 km, he increases his speed by 6 km/h and maintains this speed for the rest of the journey. Express x in terms of y, a and b. Solve A(v) Quadratic Equations Algebra Compound Interest Surface area of a sphere = Students cannot see the relationship of triangle OAB and the trapezium, often resulting in leaving the question blank. Express as a single fraction in its simplest form (B) Students tend to compare the height instead, or they ratio the wrong sides of the triangle. Number of Niki and Adi t-shirts sold in the first week. V = YS F G Total number of t-shirts sold in the first week. Be clear in your explanation. Use the words each effectively. P is a 2x3 matrix and X is a 3x1 matrix. The answer will be a 2x1 matrix. Students are not sure on how to multiply matrices. Or they do not get a 2x1 matrix. Same as (C) Same as (C) Y is a 1x2 matrix and S is a 2x1 matrix. The answer will be a 1x1 matrix. Students multiply wrongly, leaving the answer in a 2x2 matrix. Same as (C) Same as (C) Students are not able to explain in a manner that is acceptable. Lungsuri lelaman www.mendaki.org.sg untuk melihat video Matematik PSLE online dan contoh kertas peperiksaan ini.