tutormansor.wordpress.com Modul Hak Cipta Terpelihara MPSM (Cawangan Kedah)
|
|
- Annis Bradford
- 7 years ago
- Views:
Transcription
1 1 347/ MEI 014 MAJLIS PENGETUA SEKOLAH MALAYSIA NEGERI KEDAH DARUL AMAN MODUL PENINGKATAN PRESTASI TINGKATAN LIMA 014 MATEMATIK TAMBAHAN KERTAS MODUL 1 1 jam 347/ Dua jam tiga puluh minit JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU 1. This question paper consists of three sections : Section A, Section B and Section C.. Answer all questions in Section A, four questions from Section B and two questions from Section C. 3. Give only one answer/solution to each question. 4. Show your working. It may help you to get your marks. 5. The diagrams provided are not drawn according to scale unless stated. 6. The marks allocated for each question and sub - part of a question are shown in brackets. 7. You may use a non-programmable scientific calculator.. A list of formulae is provided in page and 3. This question paper consists of 16 printed pages. 347/ Additional Mathematics Paper [Lihat halaman sebelah Modul Hak Cipta Terpelihara MPSM (Cawangan Kedah)
2 347/ MEI 014 The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. ALGEBRA b b 4ac log c b 1.. log a b a log c a m n m n. a a a 9. T n a ( n 1) d m n m n 3. a a a n 10. S n [ a ( n 1) d ] m n mn 4. ( a ) a n T n ar 5. log a mn log a m log a n n a ( r 1) a (1 1. S n r 1 1 m 6. log a log a m log a n n 13. a S, r < 1 1 r n 7. log m nlog m a a CALCULUS r r n ), r 1 1. y = uv, dy d dv u d du v d 4 Area under a curve = b a y d or du dv v u u dy. y =, d d v d v 3. dy d dy du du d = b dy a 5. Volume of revolution = b y d or a = b dy a GEOMETRY 1. Distance = ( 1 ) ( y y1 ). Mid point (, y ) = 1 y, 1 y 3. Division of line segment by a point n (, y ) = 1 m ny my, 1 m n m n 4. Area of triangle = 1 ( ) ( ) y y y y y y 5. r 6. rˆ y i yj y 347/ Additional Mathematics Paper [Lihat halaman sebelah Modul Hak Cipta Terpelihara MPSM (Cawangan Kedah)
3 3 347/ MEI 014 STATISTICS 1. Wi Ii 7 I N Wi. f n n! P r f ( n r )! 3. ( ) = n n! 9 C r N N ( n r )! r! 4. f ( ) f 10 P(AB) = P(A) + P(B) P(AB) = f f n r n r 11 P ( X = r ) = C r p q, p + q = 1 N F 5. m = L + C fm 13 npq 6. Q 1 X I Z = Q 0 TRIGONOMETRY 1. Arc length, s = r. sin ( A B ) = sin A cos B cos A sin B 1. Area of sector, A = 9. cos ( A B ) = cos A cos B sin A sin B r 3. sin ² A + cos² A = 1 tan A tan B 10 tan ( A B ) = 1 tan A tan B 4. sec ² A = 1 + tan ² A tan A 11 tan A = 1 tan A 5. cosec ² A = 1 + cot ² A a b c 1 sin A sin B sin C 6. sin A = sin A cos A 13 a² = b² + c² bc cos A 7. cos A = cos ² A sin ² A = cos ² A 1 14 Area of triangle = 1 sin ab C = 1 sin ² A 347/ Additional Mathematics Paper [Lihat halaman sebelah Modul Hak Cipta Terpelihara MPSM (Cawangan Kedah)
4 4 347/ MEI 014 Section A Bahagian A [ 40 marks ] [ 40 markah ] Answer all questions. Jawab semua soalan. 1 Solve the simultaneous equations y 4 and Selesaikan persamaan serentak y 4 dan y 10. y 10. [5 marks] [5 markah] (a) Given that g : 4 and gf ( ) 6 5. Find the function of f( ) (b) Given that k : 3 4, find the value of (i) k 1 (5) [3 marks] (ii) p if k 1 ( p) [3 marks] (a) Diberi bahawa g : 4 dan gf ( ) 6 5. Cari fungsi f( ). [3 markah] (b) Diberi bahawa k : 3 4, cari nilai bagi (i) k 1 (5) (ii) p jika k 1 ( p). [3 markah] 3 (a) The quadratic function can be epressed in the form of f ( ) 10 1 ( ), find the value of m and n. [ marks] y m n (b) If and are the roots of quadratic equation with roots 3 and , form the equation [4 marks] (a) Persamaan kuadratik boleh dinyatakan dalam bentuk f ( ) 10 1 ( ), cari nilai m dan n. y m n [ markah] (b) Jika and adalah punca-punca bagi persamaan kuadratik 9 0, terbitkan satu persamaan kuadratik yang mempunyai punca-punca 3 dan 3. [4 markah] 347/ Additional Mathematics Paper [Lihat halaman sebelah Modul Hak Cipta Terpelihara MPSM (Cawangan Kedah)
5 5 347/ MEI B R Q O Diagram 4 / Rajah 4 C In Diagram 4, point Q lies on the straight line OR such that OQ : QR 3:. Point Q also is the midpoint of the straight line BC. Given that OC 6, CR 3y and OB 4y. (a) Epress in terms of and y (i) OR, (ii) QR, (iii) BR. (b) Hence, determine whether BR is parallel to OC. [6 marks] [ marks] Dalam Rajah 4, titik Q terletak pada garis OR dengan keadaan OQ : QR 3:. Titik Q juga adalah titik tengah bagi garis lurus BC. Diberi bahawa OC 6, CR 3y dan OB 4y (a) Ungkapan dalam sebutan dan y, (i) OR, (ii) QR, (iii) BR. (b) Seterusnya, tentukan samada BR adalah selari dengan OC. [6 markah] [ markah] 347/ Additional Mathematics Paper [Lihat halaman sebelah Modul Hak Cipta Terpelihara MPSM (Cawangan Kedah)
6 347/ MEI (a) A set of eight numbers, 1,, 3,..., has a mean of 5 and variance of 9. Find (i) (ii), 6 [3 marks] (b) If each of the numbers is multiplied by 3 and then increased by 5, find the new value for the (i) mean, (ii) standard deviation. [4 marks] (a) Suatu set yang terdiri daripada lapan nombor, 1,, 3,..., mempunyai min 5 dan varians 9. Cari (i), (ii) [3 markah] (b) Jika setiap nombor didarab dengan 3 dan ditambah dengan 5, cari nilai yang baru untuk (i) min, (ii) sisihan piawai. [4 markah] 347/ Additional Mathematics Paper [Lihat halaman sebelah Modul Hak Cipta Terpelihara MPSM (Cawangan Kedah)
7 7 347/ MEI B E G I A D F H O Diagram 6 / Rajah 6 Diagram 6 shows part of the arrangement of an infinite series of right angle triangles. It is given OA = OB, OD = OE, OF = OG, OH = OI and so on. The length of OA is p cm. D is the midpoint of AO, F is the midpoint of DO, H is the midpoint of FO and so on. (a) Show that the areas of the triangle AOB, DOE, FOG,... form a geometric progression and hence, state the common ratio of the progression. (b) Given OA 0 cm, (i) determine which triangle has an area of 5 1 cm, (ii) find the sum to infinity of the areas, in cm, of the triangles. [3 marks] [5 marks] Rajah 6 menunjukkan sebahagian daripada susunan tak terhingga bagi siri segitiga tepat. Diberi OA = OB, OD = OE, OF = OG, OH = OI dan seterusnya. Panjang OA ialah p cm. D ialah titik tengah bagi AO, F ialah titik tengah bagi DO, H ialah titik tengah bagi FO dan seterusnya. (a) Tunjukkan luas bagi segitiga tepat AOB, DOE, FOG,...membentuk satu janjang geometri dan seterusnya, nyatakan nisbah sepunya bagi janjang ini. (b) Diberi OA 0 cm, (i) tentukan segitiga yang keberapa mempunyai luas 5 1 cm. (ii) cari hasil tambah hingga tak terhinggaan, dalam cm, bagi siri segitiga itu. [3 markah] [5 markah] 347/ Additional Mathematics Paper [Lihat halaman sebelah Modul Hak Cipta Terpelihara MPSM (Cawangan Kedah)
8 347/ MEI Use graph paper to answer this question. Section B Bahagian B [ 40 marks ] [ 40 markah ] Answer four questions from this section. Jawab empat soalan daripada bahagian ini. Gunakan kertas graf untuk menjawab soalan ini y Table 7 / Jadual 7 Table 7 shows the values of two variables, and y, obtained from an eperiment. Variables and y are related by the equation y hk, where h and k are constants. (a) Plot log10 y against, using a scale of cm to 1 unit on the ais and cm to 01 unit on the log10 y ais. Hence, draw the line of best fit. (b) Use your graph in 7 (a) to find the value of (i) h, (ii) k, (iii) y when = 35. [4 marks] [6 marks] Jadual 7 menunjukkan nilai-nilai bagi dua pembolehubah, dan y, yang diperoleh daripada satu eksperimen. Pembolehubah dan y dihubungkan oleh persamaan y hk (a) Plot log10, dengan keadaan h dan k ialah pemalar. y melawan, dengan menggunakan skala cm kepada 1 unit pada paksi dan cm kepada 01 unit pada paksi log10 y. Seterusnya, lukis garis lurus penyuaian terbaik. [4 markah] (b) Gunakan graf di 7(a) untuk mencari nilai (i) h, (ii) k, (iii) y apabila = 3 5. [6 markah] 347/ Additional Mathematics Paper [Lihat halaman sebelah Modul Hak Cipta Terpelihara MPSM (Cawangan Kedah)
9 9 347/ MEI 014 A O D E F B Diagram / Rajah C Diagram shows a sector OEF with centre O and radius 6 cm. ABCD is a rectangle and the straight line BC is a tangent to the curve EF. It is given that AD cm. [ Use 3 14 ] Calculate (a) the value of, in radians, (b) the perimeter, in cm, of the shaded region, [ marks] [4 marks] (c) the area, in cm of the shaded region. [4 marks] Rajah menunjukkan sebuah sektor OEF dengan pusat O dan jejari 6 cm. ABCD adalah sebuah segi empat tepat dan garis lurus BC adalah tangen kepada lengkung EF. Diberi AD cm. [ Guna 3 14 ] Hitung (a) nilai bagi, dalam radian, (b) perimeter, dalam cm, kawasan berlorek, (c) luas, dalam cm, kawasan berlorek. [ markah] [4 markah] [4 markah] 347/ Additional Mathematics Paper [Lihat halaman sebelah Modul Hak Cipta Terpelihara MPSM (Cawangan Kedah)
10 10 347/ MEI y y = y = + Q P A B O Diagram 9/Rajah 9 Diagram 9 shows the straight line y = + intersecting the curve y = P and Q. at the points Find (a) the coordinates of P and Q, [3 marks] (b) the area of the shaded region A, [4 marks] (c) the volume generated, in terms of π, when the shaded region B is revolved through 360 o about the -ais. [3 marks] Rajah 9 menunjukkan garis lurus y = + yang menyilang lengkung y = titik P dan Q. Cari (a) koordinat P dan Q, [3 markah] (b) luas rantau berlorek A, [4 markah] (c) pada isipadu janaan, dalam sebutan π, apabila rantau berlorek B dikisarkan melalui 360 o pada paksi-. [3 markah] 347/ Additional Mathematics Paper [Lihat halaman sebelah Modul Hak Cipta Terpelihara MPSM (Cawangan Kedah)
11 11 347/ MEI Solution by scale drawing is not accepted. Penyelesaian secara lukisan berskala tidak diterima. y Q T (0, ) Diagram 10 / Rajah 10 S 0 R Diagram 10 shows a triangle QRS. The straight line RS is perpendicular to the straight line QS. Point S lies on the -ais and point R lies on the y-ais. The equation of y straight RS is 1. 4 (a) Find (i) the coordinates of S, [1 mark ] (ii) the equation of the straight line QS. [ marks] (b) Given that ST : TQ = : 1, find the coordinates of Q, [ marks] (c) Calculate the area of triangle QRS, [ marks] (d) Point P(,y) moves such that its distance from S is always twice its distance from R. Find the equation of locus P. [3 marks] Rajah 10 menunjukkan sebuah segi tiga QRS. Garis RS adalah berserenjang dengan garis QS. Titik S terletak pada paksi- dan titik R terletak pada paksi-y. Persamaan y garislurus RS adalah 1. 4 (a) Cari (i) koordinat S, [1 markah] (ii) persamaan garis lurus QS. [ markah] (b) Diberi ST : TQ = : 1, cari koordinat Q, [ markah] (c) Hitung luas segi tiga QRS, [ markah] (d) Titik P(, y) bergerak dengan keadaan jaraknya dari S adalah sentiasa dua kali jaraknya dari R. Cari persamaan lokus bagi P. [3 markah] 347/ Additional Mathematics Paper [Lihat halaman sebelah Modul Hak Cipta Terpelihara MPSM (Cawangan Kedah)
12 1 347/ MEI 014 Section C Bahagian C [ 0 marks ] [ 0 markah ] Answer any two questions from this section. Jawab mana-mana dua soalan daripada bahagian ini. 11 Diagram 11 shows a quadrilateral PQRS, QS = cm, QR = 9 cm, SP = 1 cm, PQS 106, SQR 39 P 1 cm SS cm 106 Q 39 9 cm R R Diagram 11/Rajah 11 (a) Calculate (i) the angle of QSP [3 marks] (ii) area of triangle QSP [ marks] (iii) the length, in cm, of RS [ marks] (b) Given S lies on the straight-line SQ which further epanded, and S P = SP (i) sketch triangle SPS [1 mark] (ii) find the length of QS [ marks] Rajah 11 menunjukkan sebuah sisiempat PQRS. QS = cm, QR = 9 cm, SP = 1 cm, PQS 106, SQR 39 (a) Hitungkan (i) sudut QPS [3 markah] (ii) luas bagi segitiga PQS [ markah] (iii) panjang, dalam cm, RS [ markah] ( b) Diberi bahawa titik S berada di atas garis lurus SQ yang diperpanjangkan dan S P = SP (i) lakar kan segitiga SPS [1 markah ] (ii) cari panjang QS [ markah] 347/ Additional Mathematics Paper [Lihat halaman sebelah Modul Hak Cipta Terpelihara MPSM (Cawangan Kedah)
13 13 347/ MEI Table 1 shows the price indices of three types of fuel for the year 010 based on the year 00. The pie chart represents the proportion of the fuel used in a factory FUEL BAHAN API Year 010 based on the year Price indes for the year 00 Indeks harga pada tahun 010 berasaskan tahun 00 A 135 B 10 C 105 Table 1 / Jadual 1 A 7 % C B 46 % (a) If the factory spends RM6 000 per week for fuel A in the year 010, find the corresponding ependiture for fuel A in the year 00. [ marks] (b) Calculate the composite inde for fuel ependiture of the factory in the year 010 based on the year 00. [3 marks] (c) The fuel ependiture of the factory is RM per week in the year 00. Calculate its corresponding ependiture in the year 010. [ marks] (d) The price of fuel A remains unchanged, while the price of fuel B increases 35%, the price of fuel C increases 30% from 010 to the year 013. Calculate the composite inde for the fuel ependiture of the factory in the year 013 based on the year 00. [3 marks] Jadual 1 menunjukkan indeks harga bagi tiga jenis bahan api pada tahun 010 berasaskan tahun 00. Carta pai mewakili pembahagian bahan api itu yang digunakan di sebuah kilang. (a) Jika kilang itu membelanjakan RM6 000 seminggu untuk bahan api A pada tahun 010, cari perbelanjaan yang sepadan untuk bahan api A pada tahun 00. [ markah] (b) Hitungkan indeks gubahan bagi perbelanjaan bahan api kilang itu pada tahun 010 berasaskan tahun 00. [3 markah] (c) Perbelanjaan bahan api bagi kilang itu pada tahun 00 ialah RM seminggu. Hitungkan perbelanjaan bahanapi yang sepadan pada tahun 010. [ markah] (d) Harga bahan api A tidak berubah, manakala harga bahan api B meningkat 35%, harga bahan api C meningkat 30% dari tahun 010 ke tahun 013. Hitungkan indeks gubahan bagi perbelanjaan bahan api kilang itu pada tahun 013 berasaskan tahun 00. [3 markah] 347/ Additional Mathematics Paper [Lihat halaman sebelah Modul Hak Cipta Terpelihara MPSM (Cawangan Kedah)
14 14 347/ MEI A hardware store wants to load boes of nail and y boes of screw into a lorry to be delivered to a project site. The constraints that the hardware store has are as follows: I The lorry cannot carry more than 60 boes. II The number of boes of nail must not eceed twice the number of boes of screw. III At least 15 boes of nail are delivered. (a) Write down three inequalities, other than and, that satisfy the above constraints. [3 marks] (b) Using scale of cm to 10 boes for both aes, construct and shade the region R satisfy all the constraints. [3 marks] (c) Using the graph constructed in (b), find (i) The maimum numbers of screw boes that can be delivered if the lorry has 35 boes of nail. (ii) The maimum profit of the hardware store if the profit from the sale of every bo of nail and screw are RM30 and RM35 respectively. [4 marks] Sebuah kedai ingin memuatkan kotak paku dan y kotak skrew ke sebuah lori untuk dihantar ke suatu tapak projek. Kekangan kedai itu adalah seperti berikut. I Lori itu tidak boleh membawa lebih daripada 60 kotak. II Bilangan kotak paku hendaklah tidak melebihi dua kali bilangan kotak skrew. III Sekurang-kurangnya 15 kotak paku dihantar. (a) Tulis tiga ketaksamaan, selain daripada dan, yang memenuhi kekangan di atas. [3 markah] (b)dengan menggunakan skala cm kepada 10 kotak pada kedua-dua paksi, bina dan lorek rantau R yang memenuhi semua kekangan. [3 markah] (c) Guna graf yang dibina di (b), cari (i) Bilangan maksimum kotak skrew yang boleh dihantar jika lori itu telah dimuatkan dengan 35 kotak paku. (ii) Keuntungan maksimum kedai itu jika keuntungan daripada jualan setiap kotak paku dan kotak skrew masing-masing RM30 dan RM35. [4 markah] END OF QUESTION PAPER KERTAS SOALAN TAMAT 347/ Additional Mathematics Paper [Lihat halaman sebelah Modul Hak Cipta Terpelihara MPSM (Cawangan Kedah)
15 Nama Pelajar : 347/ Additional Mathematics Tingkatan 5 :. Mei 014 PROGRAM PENINGKATAN PRESTASI AKADEMIK SPM 014 MODUL 1 ADDITIONAL MATHEMATICS Paper. MARKING SCHEME 1
16 MARKING SCHEME ADDITIONAL MATHEMATICS PAPER N0. SOLUTION MARKS 1 y 4 or y 4 P1 ( y 4) y 10 ( 4) 10 y y ( y1)( y 3) 0 ( 3)( 1) 0 1 and 3 (both) y 3 and y 1 (both Eliminate /y Solve quadratic equation (a) g f [ ( )] 6 5 [ f ( )] [ f ( )] ( 3) f ( ) 3 (find composite function) 5 (b) (i) (ii) k k 1 1 k 4 ( ) (5) p 4 ( p) 3 p (find inverse function) 3 (a) (b) f ( ) ( 5) sor 3 3 por (4) 7 36 P1 P1 P1 7 6
17 4 (a) (i) (ii) OR OC CR 63y QR OR 5 (6 3 y ) y 5 5 (iii) BR BQ QR 6 y (b) BR hoc cannot find h. not parallel find h 5 (a) (i) 5 40 P1 (ii) (b) new mean 3(5) 5 0 new standard deviation 3(3) 9 7 3
18 6 (a) p, p, p, p p p p 1 r 4 (b) (i) 1 n ( ) 4 1 n (ii) 300 S
19 7 (a) (b) log10 y log10 y 6 correct values of log y Plot log10 y vs. Correct aes & uniform scale points plotted correctly Line of best-fit (c) (i) log y log k log h log h = 1.40 k = *gradient P1 (ii) log10 h = *y-intercept h =.09 (iii) y =
20 N0. SOLUTION MARKS (a) 1 4 sin 6 = 1.46 rad (b) S 6(1.46) EF Use s r =.76 cm Perimeter =.76 + (6) + (6) + () = 4.76 cm (c) Area of sector OEF = 1 (6) (1.46) =6. Area of rectangle = 4 Area of the shaded region = 4 6. = 1.7 cm 10 6
21 N0. SOLUTION MARKS 9 (a), 4 P (, 4 ), Q ( 4,16 ) for solving quad.eqn. (b) A = 4 ( ) d use ( y y1 ) d = = = (4) ( ) (4) (4) ( ) ( ) 3 3 Note : If use area of trapezium and y d, give marks accordingly. integrate correctly Sub. the limit correctly (c) V = 4 ( ) 0 d correct limit = integrate correctly = or 04.π 10 7
22 N0. SOLUTION MARKS 10 (a) (i) ( 4, 0 ) (ii) m y (b) 4 y0 0 or 3 3 (,1 ) (c) Area of = = = 30 unit use area formula correctly (d) PS PR P1 ( 4) y ( y ) 3 3y 16y 0 10
23 9 N0. SOLUTION MARKS sin106 sin ) QSP QPS QPS i sin 1 1 ) cm PQS Luas ii cm cos ) ( ) RS RS iii b)i) ii) o o Sin Sin QS ' QS = 11.6 cm 10 P S Q S
24 N0. SOLUTION MARKS a)perbelanjaan bahanapi A tahun RM can be seen 135(7) 10(46) 105(7) b) Indeks gubahan 100 P1 10 c) 10 Perbelanjaan bahanapi d) Indeks harga bahan api 013 I A I B IC Indeks gubahan pada tahun 013 berasaskan tahun (7) 16(46) 136.5(7) P1 (I A =135 OR I B = 16 OR I C =136.5) 10 10
25 N0. SOLUTION MARKS 13 a) Tiga ketaksamaan : i. ii. iii. y y At least one straight line is drawn correctly from inequalities involving and y. All the three straight lines are drawn correctly. Region is correctly shaded. y = 15 (15, 45) 5 y = 17 + y = 60 c) i.) Bilangan maksimum skrew 5 kotak (ii) Titik maksimum (15,45) Keuntungan maksimum; 30 35y k 30(15) 35 (45) k k RM 05 P1 10 END OF MARKING SCHEME 11
SULIT 2 1449/2 MATHEMATICAL FORMULAE RUMUS MATEMATIK
SULIT 2 1449/2 MATHEMATICAL FORMULAE RUMUS MATEMATIK The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. Rumus-rumus berikut boleh membantu anda
More informationNAMA:... Tingkatan :... BAHAGIAN PENGURUSAN SEKOLAH BERASRAMA PENUH DAN SEKOLAH KECEMERLANGAN KEMENTERIAN PELAJARAN MALAYSIA
SULIT 4531/3 NAMA:... Tingkatan :... 4531/3 Fizik Kertas 3 Ogos 2012 1 ½ jam BAHAGIAN PENGURUSAN SEKOLAH BERASRAMA PENUH DAN SEKOLAH KECEMERLANGAN KEMENTERIAN PELAJARAN MALAYSIA PEPERIKSAAN PERCUBAAN SPM
More informationStraight Line. Paper 1 Section A. O xy
PSf Straight Line Paper 1 Section A Each correct answer in this section is worth two marks. 1. The line with equation = a + 4 is perpendicular to the line with equation 3 + + 1 = 0. What is the value of
More informationSTRESS EFFECT STUDY ON 6 DIFFERENT PATTERN OF TYRES FOR SIZE 175/70 R13 SYAHRIL AZEEM ONG BIN HAJI MALIKI ONG. for the award of the degree of
STRESS EFFECT STUDY ON 6 DIFFERENT PATTERN OF TYRES FOR SIZE 175/70 R13 SYAHRIL AZEEM ONG BIN HAJI MALIKI ONG A report submitted in partial fulfilment of the requirements for the award of the degree of
More informationSEKTOR SEKOLAH BERASRAMA PENUH BAHAGIAN SEKOLAH KEMENTERIAN PELAJARAN MALAYSIA PEPERIKSAAN AKHIR TAHUN TINGKATAN 4 2006 MATEMATIK.
Matematik Kertas Oktober 006 ¼ jam SEKTOR SEKOLH ERSRM ENUH HGIN SEKOLH KEMENTERIN ELJRN MLYSI EERIKSN KHIR THUN TINGKTN 4 006 MTEMTIK Kertas Satu jam lima belas minit JNGN UK KERTS SOLN INI SEHINGG IERITHU.
More informationKalkulus Fungsi Dua Peubah atau Lebih
Kalkulus Fungsi Dua Peubah atau Lebih Warsoma Djohan Prodi Matematika, FMIPA - ITB March 6, 00 Kalkulus / MA-ITB / W.D. / 00 (ITB) Kalkulus Fungsi Dua Peubah atau Lebih March 6, 00 / 9 Fungsi Dua Peubah
More informationsekolahsultanalamshahkoleksisoalansi jilpelajaranmalaysiasekolahsultanala mshahkoleksisoalansijilpelajaranmala ysiasekolahsultanalamshahkoleksisoal
sekolahsultanalamshahkoleksisoalansi jilpelajaranmalaysiasekolahsultanala mshahkoleksisoalansijilpelajaranmala ysiasekolahsultanalamshahkoleksisoal KOLEKSI SOALAN SPM ansijilpelajaranmalaysiasekolahsultan
More informationCIRCLE COORDINATE GEOMETRY
CIRCLE COORDINATE GEOMETRY (EXAM QUESTIONS) Question 1 (**) A circle has equation x + y = 2x + 8 Determine the radius and the coordinates of the centre of the circle. r = 3, ( 1,0 ) Question 2 (**) A circle
More informationCore Maths C2. Revision Notes
Core Maths C Revision Notes November 0 Core Maths C Algebra... Polnomials: +,,,.... Factorising... Long division... Remainder theorem... Factor theorem... 4 Choosing a suitable factor... 5 Cubic equations...
More informationJOB AGENT MANAGEMENT SYSTEM LU CHUN LING. A thesis submitted in partial fulfillment of. the requirements for the award of the degree of
JOB AGENT MANAGEMENT SYSTEM LU CHUN LING A thesis submitted in partial fulfillment of the requirements for the award of the degree of Bachelor of Computer Sciences (Software Engineering) FACULTY OF COMPUTER
More informationEquation of a Line. Chapter H2. The Gradient of a Line. m AB = Exercise H2 1
Chapter H2 Equation of a Line The Gradient of a Line The gradient of a line is simpl a measure of how steep the line is. It is defined as follows :- gradient = vertical horizontal horizontal A B vertical
More informationChapter 17 COMPLETION. 1. Receipt of notice from Contractor. 2. Final Inspection. PT
Flowchart Description Action By Reference 1 1. Receipt of notice from Contractor - 2 2. Final Inspection. PT 3 Yes No 3. Works (or Section) is practically completed for all purposes of the Contract? -
More informationKRITERIA BORANG NYATA CUKAI PENDAPATAN (BNCP) TIDAK LENGKAP CRITERIA ON INCOMPLETE INCOME TAX RETURN FORM (ITRF) PEMBERITAHUAN
KRITERIA BORANG NYATA CUKAI PENDAPATAN (BNCP) TIDAK LENGKAP CRITERIA ON INCOMPLETE INCOME TAX RETURN FORM (ITRF) PEMBERITAHUAN (Pin. 1/2014) MULAI 1 JANUARI 2012, BNCP YANG TIDAK LENGKAP AKAN DIPULANGKAN
More informationwww.mathsbox.org.uk ab = c a If the coefficients a,b and c are real then either α and β are real or α and β are complex conjugates
Further Pure Summary Notes. Roots of Quadratic Equations For a quadratic equation ax + bx + c = 0 with roots α and β Sum of the roots Product of roots a + b = b a ab = c a If the coefficients a,b and c
More informationBiggar High School Mathematics Department. National 5 Learning Intentions & Success Criteria: Assessing My Progress
Biggar High School Mathematics Department National 5 Learning Intentions & Success Criteria: Assessing My Progress Expressions & Formulae Topic Learning Intention Success Criteria I understand this Approximation
More informationAdditional Topics in Math
Chapter Additional Topics in Math In addition to the questions in Heart of Algebra, Problem Solving and Data Analysis, and Passport to Advanced Math, the SAT Math Test includes several questions that are
More informationSPAM FILTERING USING BAYESIAN TECHNIQUE BASED ON INDEPENDENT FEATURE SELECTION MASURAH BINTI MOHAMAD
SPAM FILTERING USING BAYESIAN TECHNIQUE BASED ON INDEPENDENT FEATURE SELECTION MASURAH BINTI MOHAMAD A project report submitted in partial fulfillment of the requirements for the award of the degree of
More informationPRODUCTIVITY IMPROVEMENT VIA SIMULATION METHOD (MANUFACTURING INDUSTRY) HASBULLAH BIN MAT ISA
PRODUCTIVITY IMPROVEMENT VIA SIMULATION METHOD (MANUFACTURING INDUSTRY) HASBULLAH BIN MAT ISA Thesis submitted in fulfillment of the requirements for the award of the degree of Bachelor of Mechanical Engineering
More informationDEVELOP AND DESIGN SHEMATIC DIAGRAM AND MECHANISM ON ONE SEATER DRAG BUGGY MUHAMMAD IBRAHIM B MD NUJID
DEVELOP AND DESIGN SHEMATIC DIAGRAM AND MECHANISM ON ONE SEATER DRAG BUGGY MUHAMMAD IBRAHIM B MD NUJID A report in partial fulfillment of the requirements For award of the Diploma of Mechanical Engineering
More informationGEOMETRIC MENSURATION
GEOMETRI MENSURTION Question 1 (**) 8 cm 6 cm θ 6 cm O The figure above shows a circular sector O, subtending an angle of θ radians at its centre O. The radius of the sector is 6 cm and the length of the
More informationGARIS PANDUAN PENGENDALIAN DIVIDEN SATU PERINGKAT DALAM LEBIHAN AKTUARI YANG DIPINDAHKAN KEPADA DANA PEMEGANG SAHAM
LHDN.01/35/(S)/42/51/84 GARIS PANDUAN PENGENDALIAN DIVIDEN SATU PERINGKAT DALAM LEBIHAN AKTUARI YANG DIPINDAHKAN KEPADA DANA PEMEGANG SAHAM 1. PENDAHULUAN 1.1 Lebihan Aktuari adalah lebihan baki pada akhir
More informationSTRAND: ALGEBRA Unit 3 Solving Equations
CMM Subject Support Strand: ALGEBRA Unit Solving Equations: Tet STRAND: ALGEBRA Unit Solving Equations TEXT Contents Section. Algebraic Fractions. Algebraic Fractions and Quadratic Equations. Algebraic
More informationSection 9-1. Basic Terms: Tangents, Arcs and Chords Homework Pages 330-331: 1-18
Chapter 9 Circles Objectives A. Recognize and apply terms relating to circles. B. Properly use and interpret the symbols for the terms and concepts in this chapter. C. Appropriately apply the postulates,
More informationLIGHTNING AS A NEW RENEWABLE ENERGY SOURCE SARAVANA KUMAR A/L ARPUTHASAMY UNIVERSITI TEKNOLOGI MALAYSIA
LIGHTNING AS A NEW RENEWABLE ENERGY SOURCE SARAVANA KUMAR A/L ARPUTHASAMY UNIVERSITI TEKNOLOGI MALAYSIA LIGHTNING AS A NEW RENEWABLE ENERGY SOURCE SARAVANA KUMAR A/L ARPUTHASAMY A project report submitted
More informationQUADRILATERALS CHAPTER 8. (A) Main Concepts and Results
CHAPTER 8 QUADRILATERALS (A) Main Concepts and Results Sides, Angles and diagonals of a quadrilateral; Different types of quadrilaterals: Trapezium, parallelogram, rectangle, rhombus and square. Sum of
More informationWEDNESDAY, 2 MAY 1.30 PM 2.25 PM. 3 Full credit will be given only where the solution contains appropriate working.
C 500/1/01 NATIONAL QUALIFICATIONS 01 WEDNESDAY, MAY 1.0 PM.5 PM MATHEMATICS STANDARD GRADE Credit Level Paper 1 (Non-calculator) 1 You may NOT use a calculator. Answer as many questions as you can. Full
More informationMASTER S PROJECT REPORT SUMMARY
MASTER S PROJECT REPORT SUMMARY LEVEL OF SERVICE (LOS) FOR MULTILANE HIGHWAY AND ROAD ACCIDENT INFORMATION SYSTEM DEVELOPMENT OF BATU PAHAT AREA (LORIS) Prepared by: Mohd Ezree Bin Abdullah Master of Engineering
More informationGUIDELINES ON THE STAMPING OF SHARE TRANSFER INSTRUMENTS FOR SHARES THAT ARE NOT QUOTED ON THE KUALA LUMPUR STOCK EXCHANGE.
KETUA EKSEKUTIF/KETUA PENGARAH, LEMBAGA HASIL DALAM NEGERI, BAHAGIAN DUTI SETEM, JABATAN TEKNIKAL, TINGKAT 11(KANAN), BLOK 9, KOMPLEKS KERAJAAN JALAN DUTA 50600 KUALA LUMPUR. MALAYSIA. No. Ruj: LHDN. 01/34/42/68-100-032(T)
More informationOCBC GREAT EASTERN CO-BRAND CARD FREQUENTLY ASKED QUESTIONS (FAQ) REBATE FEATURES, INTEREST FREE AUTO INSTALMENT PAYMENT PLAN (AUTO-IPP) AND BENEFITS
OCBC GREAT EASTERN CO-BRAND CARD FREQUENTLY ASKED QUESTIONS (FAQ) REBATE FEATURES, INTEREST FREE AUTO INSTALMENT PAYMENT PLAN (AUTO-IPP) AND BENEFITS 1. What benefits can I get when I use the OCBC Great
More informationTOPIK 1 Konsep Pengukuran dan Skala Pengukuran
HBEF3203 Pengukuran dan Penilaian dalam Pendidikan TOPIK 1 Konsep Pengukuran dan Skala Pengukuran Azman Fadzil Galton dan Binet membuat kajian mengukur kebolehan individu. Bermula dengan kajian tersebut,
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, August 18, 2010 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of
More informationCo-ordinate Geometry THE EQUATION OF STRAIGHT LINES
Co-ordinate Geometry THE EQUATION OF STRAIGHT LINES This section refers to the properties of straight lines and curves using rules found by the use of cartesian co-ordinates. The Gradient of a Line. As
More informationwww.sakshieducation.com
LENGTH OF THE PERPENDICULAR FROM A POINT TO A STRAIGHT LINE AND DISTANCE BETWEEN TWO PAPALLEL LINES THEOREM The perpendicular distance from a point P(x 1, y 1 ) to the line ax + by + c 0 is ax1+ by1+ c
More informationVersion 1.0. General Certificate of Education (A-level) January 2012. Mathematics MPC4. (Specification 6360) Pure Core 4. Final.
Version.0 General Certificate of Education (A-level) January 0 Mathematics MPC (Specification 660) Pure Core Final Mark Scheme Mark schemes are prepared by the Principal Eaminer and considered, together
More informationMATHEMATICS Unit Pure Core 2
General Certificate of Education January 2008 Advanced Subsidiary Examination MATHEMATICS Unit Pure Core 2 MPC2 Wednesday 9 January 2008 1.30 pm to 3.00 pm For this paper you must have: an 8-page answer
More informationPROFITABILITY ANALYSIS
PROFITABILITY ANALYSIS Ekonomi Teknik Kimia By Dr. Istadi 2007 Schedule Time Value of Money (Interest Rate) & Cash Flow Depreciation & Salvage Value Profitability Analysis Selection of Alternatif Investment
More informationAnalytical Geometry (4)
Analytical Geometry (4) Learning Outcomes and Assessment Standards Learning Outcome 3: Space, shape and measurement Assessment Standard As 3(c) and AS 3(a) The gradient and inclination of a straight line
More informationCircle Name: Radius: Diameter: Chord: Secant:
12.1: Tangent Lines Congruent Circles: circles that have the same radius length Diagram of Examples Center of Circle: Circle Name: Radius: Diameter: Chord: Secant: Tangent to A Circle: a line in the plane
More informationCIRCUMFERENCE AND AREA OF A CIRCLE
CIRCUMFERENCE AND AREA OF A CIRCLE 1. AC and BD are two perpendicular diameters of a circle with centre O. If AC = 16 cm, calculate the area and perimeter of the shaded part. (Take = 3.14) 2. In the given
More informationBISKUT RAYA INVENTORY MANAGEMENT SYSTEM (BRIMS) NURUL AMIRAH BINTI ROSLAN THESIS SUBMITTED IN FULFILLMENT OF THE DEGREE OF COMPUTER SCIENCE
BISKUT RAYA INVENTORY MANAGEMENT SYSTEM (BRIMS) NURUL AMIRAH BINTI ROSLAN THESIS SUBMITTED IN FULFILLMENT OF THE DEGREE OF COMPUTER SCIENCE FACULTY OF COMPUTER SYSTEM & SOFTWARE ENGINEERING UNIVERSITI
More informationii) 9 months Plan - Interest Rate at 0.75% per month The minimum transfer amount is RM1,000 and maximum is subject to Cardmember
BALANCE TRANSFER - TERMS & CONDITIONS 1. Holders of Maybank Credit Card Card(s) ( Cardmember ) may apply to transfer outstanding balances including principal, accrued profit, profit and other charges as
More informationUNIT 1: ANALYTICAL METHODS FOR ENGINEERS
UNIT : ANALYTICAL METHODS FOR ENGINEERS Unit code: A/60/40 QCF Level: 4 Credit value: 5 OUTCOME 3 - CALCULUS TUTORIAL DIFFERENTIATION 3 Be able to analyse and model engineering situations and solve problems
More informationPage 1 of 1. Page 2 of 2 % &! " '! ( ' ( $) * +, - % -. !" # $
Argosoft Pos Server Panduan Page 1 of 1 Isi Mulai... 3 Menguasai... 5 Pilihan... 7 Menentukan catatan... 10 Menentukan Linkungan... 11 Linkungan betul... 12 Menentukan linkungan berganda... 13 Menambahkan
More informationTAHAP KOLESTEROL HDL DALAM KALANGAN PELAJAR OBES DI SEKOLAH MENENGAH
TAHAP KOLESTEROL HDL DALAM KALANGAN PELAJAR OBES DI SEKOLAH MENENGAH Syed Kamaruzaman Syed Ali, Prof. Madya Dr. Rosnah Ismail, Dr. Raji Subramaniam Universiti Malaya Abstract This research was done to
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Tuesday, August 13, 2013 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Tuesday, August 13, 2013 8:30 to 11:30 a.m., only Student Name: School Name: The possession or use of any communications
More informationBENGKEL INOVASI PEDAGOGI. Penyelesaian Masalah Matematik Sekolah Rendah dengan Menggunakan Strategi Melukis Gambar Rajah. oleh
1 BENGKEL INOVASI PEDAGOGI Penyelesaian Masalah Matematik Sekolah Rendah dengan Menggunakan Strategi Melukis Gambar Rajah oleh Lai Kim Leong Institut Perguruan Batu Lintang kimleonglai@yahoo.com ABSTRAK
More informationShape, Space and Measure
Name: Shape, Space and Measure Prep for Paper 2 Including Pythagoras Trigonometry: SOHCAHTOA Sine Rule Cosine Rule Area using 1-2 ab sin C Transforming Trig Graphs 3D Pythag-Trig Plans and Elevations Area
More informationPaper Reference. Edexcel GCSE Mathematics (Linear) 1380 Paper 4 (Calculator) Monday 5 March 2012 Afternoon Time: 1 hour 45 minutes
Centre No. Candidate No. Paper Reference 1 3 8 0 4 H Paper Reference(s) 1380/4H Edexcel GCSE Mathematics (Linear) 1380 Paper 4 (Calculator) Higher Tier Monday 5 March 2012 Afternoon Time: 1 hour 45 minutes
More informationAdvanced Math Study Guide
Advanced Math Study Guide Topic Finding Triangle Area (Ls. 96) using A=½ bc sin A (uses Law of Sines, Law of Cosines) Law of Cosines, Law of Cosines (Ls. 81, Ls. 72) Finding Area & Perimeters of Regular
More informationINTEGRATING CONSUMER TRUST IN BUILDING AN E-COMMERCE WEBSITE NUR ZAILAN BIN OTHMAN
i INTEGRATING CONSUMER TRUST IN BUILDING AN E-COMMERCE WEBSITE NUR ZAILAN BIN OTHMAN A project report submitted in partial fulfillment of the requirements for the award of the degree of Master of Science
More informationWednesday 5 November 2014 Morning
H Wednesday 5 November 2014 Morning GCSE MATHEMATICS B J567/03 Paper 3 (Higher Tier) * 1 1 8 3 2 9 5 6 3 5 * Candidates answer on the Question Paper. OCR supplied materials: None Other materials required:
More informationExample Practice Papers for Cambridge IGCSE Mathematics Extended Practice Book. Example Practice Paper 4 17
Eample Practice Papers for Cambridge IGCSE Mathematics Etended Practice Book Eample Practice Paper Mark scheme for Paper 13 Eample Practice Paper 4 17 Mark scheme for Paper 4 36 NAME Cambridge IGCSE Mathematics
More informationCHAPTER 8 QUADRILATERALS. 8.1 Introduction
CHAPTER 8 QUADRILATERALS 8.1 Introduction You have studied many properties of a triangle in Chapters 6 and 7 and you know that on joining three non-collinear points in pairs, the figure so obtained is
More informationSQA Higher Mathematics Unit 3
SCHOLAR Study Guide SQA Higher Mathematics Unit 3 Jane Paterson Heriot-Watt University Dorothy Watson Balerno High School Heriot-Watt University Edinburgh EH14 4AS, United Kingdom. First published 2001
More informationCore Maths C1. Revision Notes
Core Maths C Revision Notes November 0 Core Maths C Algebra... Indices... Rules of indices... Surds... 4 Simplifying surds... 4 Rationalising the denominator... 4 Quadratic functions... 4 Completing the
More informationALGEBRA 2/TRIGONOMETRY
ALGEBRA /TRIGONOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA /TRIGONOMETRY Tuesday, January 8, 014 1:15 to 4:15 p.m., only Student Name: School Name: The possession
More informationYou must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
Write your name here Surname Other names Pearson Edexcel Certificate Pearson Edexcel International GCSE Mathematics A Paper 4H Centre Number Monday 1 January 015 Afternoon Time: hours Candidate Number
More informationGeometry Unit 5: Circles Part 1 Chords, Secants, and Tangents
Geometry Unit 5: Circles Part 1 Chords, Secants, and Tangents Name Chords and Circles: A chord is a segment that joins two points of the circle. A diameter is a chord that contains the center of the circle.
More informationYou must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
Write your name here Surname Other names Edexcel IGCSE Centre Number Mathematics A Paper 3H Monday 6 June 2011 Afternoon Time: 2 hours Candidate Number Higher Tier Paper Reference 4MA0/3H You must have:
More information*X100/12/02* X100/12/02. MATHEMATICS HIGHER Paper 1 (Non-calculator) NATIONAL QUALIFICATIONS 2014 TUESDAY, 6 MAY 1.00 PM 2.30 PM
X00//0 NTIONL QULIFITIONS 0 TUESY, 6 MY.00 PM.0 PM MTHEMTIS HIGHER Paper (Non-calculator) Read carefully alculators may NOT be used in this paper. Section Questions 0 (0 marks) Instructions for completion
More informationA STUDY ON MOTIVATION TO START UP A BUSINESS AMONG CHINESE ENTREPRENEURS
A STUDY ON MOTIVATION TO START UP A BUSINESS AMONG CHINESE ENTREPRENEURS A master project submitted to the Graduate School in partial fulfillment of the requirements for the degree Master of Business Administration,
More informationTSI College Level Math Practice Test
TSI College Level Math Practice Test Tutorial Services Mission del Paso Campus. Factor the Following Polynomials 4 a. 6 8 b. c. 7 d. ab + a + b + 6 e. 9 f. 6 9. Perform the indicated operation a. ( +7y)
More informationGARISPANDUAN MENGENAI DUTI SETEM KE ATAS SURATCARA PINDAHMILIK SYER BAGI SYER YANG TIDAK TERSENARAI DI BURSA SAHAM KUALA LUMPUR.
KETUA EKSEKUTIF/KETUA PENGARAH, LEMBAGA HASIL DALAM NEGERI, BAHAGIAN DUTI SETEM, JABATAN TEKNIKAL, TINGKAT 11(KANAN), BLOK 9, KOMPLEKS KERAJAAN JALAN DUTA 50600 KUALA LUMPUR. MALAYSIA. No. Ruj: LHDN. 01/34/42/68-100-032(T)
More informationDEFINITIONS. Perpendicular Two lines are called perpendicular if they form a right angle.
DEFINITIONS Degree A degree is the 1 th part of a straight angle. 180 Right Angle A 90 angle is called a right angle. Perpendicular Two lines are called perpendicular if they form a right angle. Congruent
More informationIMPROVING SERVICE REUSABILITY USING ENTERPRISE SERVICE BUS AND BUSINESS PROCESS EXECUTION LANGUAGE AKO ABUBAKR JAAFAR
IMPROVING SERVICE REUSABILITY USING ENTERPRISE SERVICE BUS AND BUSINESS PROCESS EXECUTION LANGUAGE AKO ABUBAKR JAAFAR A project report submitted in partial fulfillment of the requirements for the award
More informationYou must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
Write your name here Surname Other names Pearson Edexcel International GCSE Mathematics A Paper 1FR Centre Number Wednesday 14 May 2014 Morning Time: 2 hours Candidate Number Foundation Tier Paper Reference
More informationCLIENT SERVER APPLICATION FOR SERVER FARM PERFORMANCE MONITORING ABDIRASHID HASSAN ABDI
ii CLIENT SERVER APPLICATION FOR SERVER FARM PERFORMANCE MONITORING ABDIRASHID HASSAN ABDI A project submitted in partial fulfillment of the requirements for the award of the degree of Master of Computer
More informationMathematics Placement Examination (MPE)
Practice Problems for Mathematics Placement Eamination (MPE) Revised August, 04 When you come to New Meico State University, you may be asked to take the Mathematics Placement Eamination (MPE) Your inital
More informationCircles - Past Edexcel Exam Questions
ircles - Past Edecel Eam Questions 1. The points A and B have coordinates (5,-1) and (13,11) respectivel. (a) find the coordinates of the mid-point of AB. [2] Given that AB is a diameter of the circle,
More informationMODELING AND SIMULATION OF SINGLE PHASE INVERTER WITH PWM USING MATLAB/SIMULINK AZUAN BIN ALIAS
MODELING AND SIMULATION OF SINGLE PHASE INVERTER WITH PWM USING MATLAB/SIMULINK AZUAN BIN ALIAS This thesis is submitted as partial fulfillment of the requirement for the award of the Bachelor Degree Electrical
More information2014 2015 Geometry B Exam Review
Semester Eam Review 014 015 Geometr B Eam Review Notes to the student: This review prepares ou for the semester B Geometr Eam. The eam will cover units 3, 4, and 5 of the Geometr curriculum. The eam consists
More informationTuesday 6 November 2012 Morning
H Tuesday 6 November 2012 Morning GCSE MATHEMATICS A A502/02 Unit B (Higher Tier) *A516821112* Candidates answer on the Question Paper. OCR supplied materials: None Other materials required: Geometrical
More informationANSWER SHEET INFORMATION AND COMUNICATION TECHNOLOGY (1CT)
Name IC No. Question No 2 4 9 2 3 4 5 6 8 20 25 ANSWER SHEET INFORMATION AND COMUNICATION TECHNOLOGY (CT) Candidate s Answer Class Index No. MARKS C (i) Y 2 (ii) X 3 3 False/Palsu 4 (a) Theft 5 malicious
More informationTrigonometric Functions and Triangles
Trigonometric Functions and Triangles Dr. Philippe B. Laval Kennesaw STate University August 27, 2010 Abstract This handout defines the trigonometric function of angles and discusses the relationship between
More informationWednesday 6 November 2013 Morning
H Wednesday 6 November 2013 Morning GCSE MATHEMATICS B J567/03 Paper 3 (Higher Tier) *J540550313* Candidates answer on the Question Paper. OCR supplied materials: None Other materials required: Geometrical
More informationD.3. Angles and Degree Measure. Review of Trigonometric Functions
APPENDIX D Precalculus Review D7 SECTION D. Review of Trigonometric Functions Angles and Degree Measure Radian Measure The Trigonometric Functions Evaluating Trigonometric Functions Solving Trigonometric
More informationMATHS LEVEL DESCRIPTORS
MATHS LEVEL DESCRIPTORS Number Level 3 Understand the place value of numbers up to thousands. Order numbers up to 9999. Round numbers to the nearest 10 or 100. Understand the number line below zero, and
More informationFriday, January 29, 2016 9:15 a.m. to 12:15 p.m., only
ALGEBRA /TRIGONOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA /TRIGONOMETRY Friday, January 9, 016 9:15 a.m. to 1:15 p.m., only Student Name: School Name: The possession
More informationHigher Education Math Placement
Higher Education Math Placement Placement Assessment Problem Types 1. Whole Numbers, Fractions, and Decimals 1.1 Operations with Whole Numbers Addition with carry Subtraction with borrowing Multiplication
More informationAlgebra. Exponents. Absolute Value. Simplify each of the following as much as possible. 2x y x + y y. xxx 3. x x x xx x. 1. Evaluate 5 and 123
Algebra Eponents Simplify each of the following as much as possible. 1 4 9 4 y + y y. 1 5. 1 5 4. y + y 4 5 6 5. + 1 4 9 10 1 7 9 0 Absolute Value Evaluate 5 and 1. Eliminate the absolute value bars from
More informationQuadrilateral Geometry. Varignon s Theorem I. Proof 10/21/2011 S C. MA 341 Topics in Geometry Lecture 19
Quadrilateral Geometry MA 341 Topics in Geometry Lecture 19 Varignon s Theorem I The quadrilateral formed by joining the midpoints of consecutive sides of any quadrilateral is a parallelogram. PQRS is
More information6.1 Basic Right Triangle Trigonometry
6.1 Basic Right Triangle Trigonometry MEASURING ANGLES IN RADIANS First, let s introduce the units you will be using to measure angles, radians. A radian is a unit of measurement defined as the angle at
More informationMath Placement Test Practice Problems
Math Placement Test Practice Problems The following problems cover material that is used on the math placement test to place students into Math 1111 College Algebra, Math 1113 Precalculus, and Math 2211
More informationSan Jose Math Circle April 25 - May 2, 2009 ANGLE BISECTORS
San Jose Math Circle April 25 - May 2, 2009 ANGLE BISECTORS Recall that the bisector of an angle is the ray that divides the angle into two congruent angles. The most important results about angle bisectors
More informationMath Placement Test Study Guide. 2. The test consists entirely of multiple choice questions, each with five choices.
Math Placement Test Study Guide General Characteristics of the Test 1. All items are to be completed by all students. The items are roughly ordered from elementary to advanced. The expectation is that
More informationPractical Geometry CHAPTER. 4.1 Introduction DO THIS
PRACTICAL GEOMETRY 57 Practical Geometry CHAPTER 4 4.1 Introduction You have learnt how to draw triangles in Class VII. We require three measurements (of sides and angles) to draw a unique triangle. Since
More informationColegio del mundo IB. Programa Diploma REPASO 2. 1. The mass m kg of a radio-active substance at time t hours is given by. m = 4e 0.2t.
REPASO. The mass m kg of a radio-active substance at time t hours is given b m = 4e 0.t. Write down the initial mass. The mass is reduced to.5 kg. How long does this take?. The function f is given b f()
More informationMath 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.
Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used
More informationPERATURAN-PERATURAN LEMBAGA PEMBANGUNAN INDUSTRI PEMBINAAN MALAYSIA (PENYAMPAIAN NOTIS) 2015
WARTA KERAJAAN PERSEKUTUAN 29 Mei 2015 29 May 2015 P.U. (A) 102 FEDERAL GOVERNMENT GAZETTE PERATURAN-PERATURAN LEMBAGA PEMBANGUNAN INDUSTRI PEMBINAAN MALAYSIA (PENYAMPAIAN NOTIS) 2015 LEMBAGA PEMBANGUNAN
More informationTHE RELATIONSHIP BETWEEN HUMAN RESOURCE INFORMATION SYSTEM (HRIS) AND HUMAN RESOURCE MANAGEMENT (HRM) ALFRED PUN KHEE SEONG
THE RELATIONSHIP BETWEEN HUMAN RESOURCE INFORMATION SYSTEM (HRIS) AND HUMAN RESOURCE MANAGEMENT (HRM) ALFRED PUN KHEE SEONG UNIVERSITI TEKNIKAL MALAYSIA MELAKA I / We * hereby declare that have read For
More informationy intercept Gradient Facts Lines that have the same gradient are PARALLEL
CORE Summar Notes Linear Graphs and Equations = m + c gradient = increase in increase in intercept Gradient Facts Lines that have the same gradient are PARALLEL If lines are PERPENDICULAR then m m = or
More informationMake sure you get the grade you deserve!
How to Throw Away Marks in Maths GCSE One tragedy that only people who have marked eternal eamination papers such as GCSE will have any real idea about is the number of marks that candidates just throw
More informationAlgebra and Geometry Review (61 topics, no due date)
Course Name: Math 112 Credit Exam LA Tech University Course Code: ALEKS Course: Trigonometry Instructor: Course Dates: Course Content: 159 topics Algebra and Geometry Review (61 topics, no due date) Properties
More information1. Find the length of BC in the following triangles. It will help to first find the length of the segment marked X.
1 Find the length of BC in the following triangles It will help to first find the length of the segment marked X a: b: Given: the diagonals of parallelogram ABCD meet at point O The altitude OE divides
More informationClick here for answers.
CHALLENGE PROBLEMS: CHALLENGE PROBLEMS 1 CHAPTER A Click here for answers S Click here for solutions A 1 Find points P and Q on the parabola 1 so that the triangle ABC formed b the -ais and the tangent
More informationWednesday 15 January 2014 Morning Time: 2 hours
Write your name here Surname Other names Pearson Edexcel Certificate Pearson Edexcel International GCSE Mathematics A Paper 4H Centre Number Wednesday 15 January 2014 Morning Time: 2 hours Candidate Number
More informationChapter 8 Geometry We will discuss following concepts in this chapter.
Mat College Mathematics Updated on Nov 5, 009 Chapter 8 Geometry We will discuss following concepts in this chapter. Two Dimensional Geometry: Straight lines (parallel and perpendicular), Rays, Angles
More informationPaper Reference. Edexcel GCSE Mathematics (Linear) 1380 Paper 3 (Non-Calculator) Monday 6 June 2011 Afternoon Time: 1 hour 45 minutes
Centre No. Candidate No. Paper Reference 1 3 8 0 3 H Paper Reference(s) 1380/3H Edexcel GCSE Mathematics (Linear) 1380 Paper 3 (Non-Calculator) Higher Tier Monday 6 June 2011 Afternoon Time: 1 hour 45
More information