NOTA PETA MINDA VISUAL™ © PNI Neuron (M) Sdn. Bhd. I Nota Peta Minda Visual Tingkatan 5 KSSM The diagram shows a sector OPQR with centre O. Given that PQ = 2.4 cm, QR = 1.5 cm and POQ = 1.2 rad. (iii) Find the perimeter of the above diagram. Perimeter of OPQR = OP + PQ + QR + OR = 2 + 2.4 + 1.5 + 2 = 7.9 cm Length of arc PQ, s = x 2πr s = r θ θ 2π 2 θ 2π 1 2 2 Area of sector POQ, A = x πr A = r θ (θ in radians) θ P O Q s A (i) Find the value of the radius. s = rθ r = r = r = 2 cm Given that s = 2.4 cm and θ = 1.2 rad. s θ 2.4 1.2 (ii) Find the value of QOR in radians. s = rθ θ = = = 0.75 rad. Given that s = 1.5 cm s r 1.5 cm 2 cm P R Q 1.5 cm 2.4 cm 1.2 rad. O r cm LENGTH OF AN ARC OF A CIRCLE The diagram shows a sector OPQR with centre O. Given that PQ = 2.4 cm, QR = 1.5 cm and POQ = 1.2 rad. (iii) Find the perimeter of the above diagram. Perimeter of OPQR = OP + PQ + QR + OR = 2 + 2.4 + 1.5 + 2 = 7.9 cm Length of arc PQ, s = x 2πr s = r θ θ 2π 2 θ 2π 1 2 2 Area of sector POQ, A = x πr A = r θ (θ in radians) θ P O Q s A (i) Find the value of the radius. s = rθ r = r = r = 2 cm Given that s = 2.4 cm and θ = 1.2 rad. s θ 2.4 1.2 (ii) Find the value of QOR in radians. s = rθ θ = = = 0.75 rad. Given that s = 1.5 cm s r 1.5 cm 2 cm P R Q 1.5 cm 2.4 cm 1.2 rad. O r cm SUKATAN MEMBULAT CIRCULAR MEASURES Example Riang Belajar KSSM Add Math F5-biV-14PP-.indd 1 06-08-20 1:24:13 PM
NOTA PETA MINDA VISUAL™ © PNI Neuron (M) Sdn. Bhd. II Nota Peta Minda Visual Tingkatan 5 KSSM Determine the coordinates of the turning points of a curve - At the turning point of the curve, the gradient is zero. - Turning points maximum and minimum points where the graph turns. Find the turning point of the curve y = 4x - x 2. Then, determine whether the turning point is a maximum or a minimum point. Solution Given that y = 4x - x , 2 = 4 - 2x When = 0, 4 - 2x = 0 x = 2 so, y = 4(2) - 2 2 = 4 ∴ The turning point is (2, 4). Value of x Value of dy dx x = 1 (< 2) 4 - 2 (1) = 2 (>0) x = 2 4 - 2 (2) = 0 x = 3 (> 2) 4 - 2 (3) = -2 (<0) dy dx = 2 dy dx = -2 dy dx = 0 maximum point minimum point dy dx = 0 dy dx = 0 dy dx > 0 dy dx < 0 dy dx > 0 dy dx < 0 (2, 4) is a maximum point. y x y x y 0 0 x dy dx dy dx 0 x x x 1 2 3 x x x x x x Steps to find the maximum and minimum points: Solve = 0 to find the v alue(s) of x. Substitute the value(s) of x into the expression for y. Check whether the obtained value is a maximum value or a minimum value. dy dx 1 2 3 PEMBEZAAN DIFFERENTIATION Example Riang Belajar KSSM Add Math F5-biV-14PP-.indd 2 06-08-20 1:24:14 PM
NOTA PETA MINDA VISUAL™ © PNI Neuron (M) Sdn. Bhd. III Nota Peta Minda Visual Tingkatan 5 KSSM AREA OF THE REGION BETWEEN A CURVE AND A STRAIGHT LINE Solution INTEGRATION AS A SUMMATION OF AREAS │ │ │ │ PEngamiran integration Example Riang Belajar KSSM Add Math F5-biV-14PP-.indd 3 06-08-20 1:24:14 PM
NOTA PETA MINDA VISUAL™ © PNI Neuron (M) Sdn. Bhd. IV Nota Peta Minda Visual Tingkatan 5 KSSM Rotation of Rotation of Solution Solution The is revolved V VOLUME PEngamiran integration Example 1 Example 2 Riang Belajar KSSM Add Math F5-biV-14PP-.indd 4 06-08-20 1:24:14 PM
NOTA PETA MINDA VISUAL™ © PNI Neuron (M) Sdn. Bhd. V Nota Peta Minda Visual Tingkatan 5 KSSM Solution Solution last letter. as the Total number of ways to arrange the 5 letters choices available for the last letter. - - - Answer : 6 numbers Permutations Example 1 Example 2 PILIH ATUR DAN GABUNGAN PERMUTATIONS AND COMBINATIONS Riang Belajar KSSM Add Math F5-biV-14PP-.indd 5 06-08-20 1:24:15 PM
NOTA PETA MINDA VISUAL™ © PNI Neuron (M) Sdn. Bhd. VI Nota Peta Minda Visual Tingkatan 5 KSSM Solution from N N T The application of either the need of ordering the arrangement from from ways of choosing time COMBINATIONS PILIH ATUR DAN GABUNGAN PERMUTATIONS AND COMBINATIONS Example Riang Belajar KSSM Add Math F5-biV-14PP-.indd 6 06-08-20 1:24:15 PM
NOTA PETA MINDA VISUAL™ © PNI Neuron (M) Sdn. Bhd. VII Nota Peta Minda Visual Tingkatan 5 KSSM Solution N represent the event that with rain without rain not raining in January have wilted. have wilted. survived. represent the event that M P with rain without rain without rain the probability that rain Solution BINOMIAL DISTRIBUTION TABURAN KEBARANGKALIAN PROBABILITY DISTRIBUTIONS Example Riang Belajar KSSM Add Math F5-biV-14PP-.indd 7 06-08-20 1:24:16 PM
NOTA PETA MINDA VISUAL™ © PNI Neuron (M) Sdn. Bhd. VIII Nota Peta Minda Visual Tingkatan 5 KSSM - like so: z x z x z x Z NORMAL DISTRIBUTION TABURAN KEBARANGKALIAN PROBABILITY DISTRIBUTIONS Example Riang Belajar KSSM Add Math F5-biV-14PP-.indd 8 06-08-20 1:24:16 PM
NOTA PETA MINDA VISUAL™ © PNI Neuron (M) Sdn. Bhd. IX Nota Peta Minda Visual Tingkatan 5 KSSM FUNGSI TRIGONOMETRI trigonometric functions Example Trigonometric ratios for any angle in 0º θ 360º Riang Belajar KSSM Add Math F5-biV-14PP-.indd 9 06-08-20 1:24:16 PM
NOTA PETA MINDA VISUAL™ © PNI Neuron (M) Sdn. Bhd. X Nota Peta Minda Visual Tingkatan 5 KSSM Let Example 1 Example 2 Example BASIC IDENTITIES COMPOUND-ANGLE AND DOUBLE-ANGLE FORMULAE FUNGSI TRIGONOMETRI trigonometric functions Riang Belajar KSSM Add Math F5-biV-14PP-.indd 10 06-08-20 1:24:17 PM
NOTA PETA MINDA VISUAL™ © PNI Neuron (M) Sdn. Bhd. XI Nota Peta Minda Visual Tingkatan 5 KSSM MODELS OF LINEAR PROGRAMMING possible C When When When When Example PENGATURCARAAN LINEAR Linear programming Riang Belajar KSSM Add Math F5-biV-14PP-.indd 11 06-08-20 1:24:17 PM
NOTA PETA MINDA VISUAL™ © PNI Neuron (M) Sdn. Bhd. XII Nota Peta Minda Visual Tingkatan 5 KSSM DISPLACEMENT, VELOCITY AND ACCELERATION AS A FUNCTION OF TIME Find the distance Recall the formula for progression: to change any possible negative values to positive DISPLACEMENT (s) The O 4 KINEMATIK GERAKAN LINEAR Kinematics of linear motion Example Riang Belajar KSSM Add Math F5-biV-14PP-.indd 12 06-08-20 1:24:17 PM
NOTA PETA MINDA VISUAL™ © PNI Neuron (M) Sdn. Bhd. XIII Nota Peta Minda Visual Tingkatan 5 KSSM As time cannot take on negative values, the bowling ball first stop, w Given that the bowling bowl moves from a fixed point O at time t = 0. Substitute VELOCITY (v) KINEMATIK GERAKAN LINEAR Kinematics of linear motion Example Riang Belajar KSSM Add Math F5-biV-14PP-.indd 13 06-08-20 1:24:18 PM
NOTA PETA MINDA VISUAL™ © PNI Neuron (M) Sdn. Bhd. XIV Nota Peta Minda Visual Tingkatan 5 KSSM the particle accelerates about O the particle starts accelerating, ACCELERATION (a) V DIFFERENTIATION AND INTEGRATION IN THE KINEMATICS OF LINEAR MOTION KINEMATIK GERAKAN LINEAR Kinematics of linear motion Example Riang Belajar KSSM Add Math F5-biV-14PP-.indd 14 06-08-20 1:24:18 PM