SUEC �� Adv Maths (Line Segment)

Mar 6, 2022Download as PPTX, PDF0 likes108 views

Sources: Visual - various maths sites (credits to original creator) Questions - Dong Zong's Textbook suitable for SUEC (Maths), SPM (Maths and Add Maths) too

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The document discusses writing linear equations in slope-intercept form. It reviews that the slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept. It provides examples of writing equations given the slope and y-intercept, given a point and the slope, and finding the equation of a line passing through two given points by first calculating the slope and then using one of the points to find the y-intercept.

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��ѦϦԦ�?��Ҧ� �̦� ��Ҧ�?�ҦŦ�? �ҦӦ�? �Ӧ��˦��ͦ�?�ҦŦ�? �æɦ� �Ħɦ��ĦɦʦӦԦ��? ��?�ȦǦ̦� ��ԦҦɦ�?? ��ѦϦҦ��ͦ��ӦϦ˦ɦҦ̦�? ��? ��Ԧʦ�?�Ϧ� �� ԦĦѦɦ�? ��ŦԦ�?�Ħ�? ��ϦԦѦ�?? ��?�Ȧ�? - ��ԦҦɦ�?? �� 2020 - 2021

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This document provides a comprehensive reference of important algebraic, trigonometric, logarithmic, and derivative formulae for the Higher Secondary Certificate (HSC) board exam. It includes over 100 formulae across various mathematical domains to assist exam preparation. Key formulae covered include trigonometric identities, logarithmic properties, derivatives of basic functions, and algebraic manipulations of exponents and radicals.

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1. There are 6 math books and 5 language books on different shelves. The number of ways to choose 1 of each is 6 �� 5 = 30. 2. There are 5 colors of tops and 4 colors of skirts. The total number of dress combinations is 5 �� 4 = 20. There are 3 styles of shoes, so the total number of styles is 3. 3. The number of 3-digit numbers that can be formed without repeating digits is 100 �� 99 �� 98 = 9,702. The number of ways for 2 boys to sit in 5 chairs is 5 �� 4 = 20.

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(1) The document discusses finding equations of tangent lines to circles and the intersections of those tangent lines. It provides examples of finding the slopes and equations of tangent lines given the circle's center and a point on the circle. (2) Methods are described for finding the angles between two tangent lines to a circle based on their slopes. Examples are given of solving systems of equations to find the points where tangent lines intersect. (3) One example determines the equation of a circle given that it passes through two known points and is tangent to another circle at a third point.

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The document contains calculations of distances between various geographic points using latitude and longitude coordinates. It includes the distances between points Q and A, which is 319.2 km, and the distance from a point at 42��N 33��27'E or 42��N 6��33'W to 40��N 33��47'E, which is calculated as 8,895.35 km or 4,800 nautical miles. It also contains a calculation using trigonometric functions that finds the distance between two points is 6,560 km or 3,540 nautical miles.

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SUEC �� Adv Maths (Line Segment)

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Editor's Notes

#2: https://www.onlinemathlearning.com/line-segment.html
#3: https://brilliant.org/wiki/section-formula/
#6: 2. The three points P, Q, and R are the three quarter points on the line segment AB, respectively, and find the value of the ratio �� between them divided into AB.
#10: https://www.allmath.com/points-coordinates.php 4. ratio = 2:1 5. ratio = 2:3
#11: 7. lambda = - 2
#12: 13. lambda = - 3/2 14. (b) y = 0 15. D = (x1 + l/k x2)/1+(l/k) 16. m=n=1

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SUEC �� Adv Maths (Line Segment)

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