RS-AV: Matematik Lektioner

Exponents Exponents are used to express very large numbers in a simplified form. ___ seconds = 1 minute 60 ___ minutes = 1 hour 60 ___ seconds = 1 hour 60*60=3,600 ___ hours = 1 day 24 ___ minutes = 1 day 24*60=1,440 ___ seconds = 1 day 24*60*60=86,400 ___ days = 1 week 7 ___ seconds = 1 week 7*86,400=604,800 ___ days = 1 month 30 ___ seconds = 1 month 30*86,400=2,592,000 ___ days = 1 year 365 ___ seconds = 1 year 365*86,400=31,536,000 Speed: On foot: 6 kilometers in 1 hour Running: 12 km/hour Bicycle: 20 km/hour Scooter: 60 km/hour Train: 100 km/hour Car: 140 km/hour High-end car: 250 km/hour Sports car: 350 km/hour Airplane: 700 km/hour Supersonic airplane: 1200 km/hour LIGHT 300,000 km in 1 second 300,000*60 km in 1 minute 300,000*60*60 km in 1 hour 300,000*60*60*24 km in 1 day 300,000*60*60*24*365 km in 1 year 94,608,000,000,000 Ninety-four thousand six hundred and eight billion kilometers in a ...

(x/3) + (4/5) = 1/4 x/3 = (1/4) - (4/5) [While performing addition or subtraction on fractions, the key is to make the denominators the same.] x/3 = (5/20) - (16/20) x/3 = -11/20 x = (-11/20) * 3 x= -33/20 F+F+F=15 3F=15 F=15/3=5 R-4(F)=-5 R-4(5)=-5 R-20=-5 R=-5+20 [5 steps left, 20 steps right] R=15 Bob's Age = x Matt's Age = x+4 Lana's Age = 2(x+4)-5 =2x+2*4-5 =2x+8-5 =2x+3 Multiplication is distributive over addition. a(b+c) = ab+ac This is known as DISTRIBUTIVE PROPERTY. (2/3)(5+3x-11) =(2/3)*5 + (2/3)*3x - (2/3)*11 =(10/3) + 2x - (22/3) =2x-(12/3) =2x-4 Let's say length is l and breadth is b. Perimeter = 2l + 2b Area = lb Perimeter is equal to thrice the area. 2l+2b = 3lb b=1 cm 2l+2*1 = 3l*1 2l+2=3l 3l=2l+2 3l-2l=2 l=2 cm -9-8 9 steps left, again 8 steps left -17 No. of questions faced=20 Let's say, x answers were correct and y answers were wrong. x+y=20..............(1) For x correct answers, he gets 5x points, and, for y wrong answers, he gets -3y points. 5x...

How far is the point (5,10) from Origin? Suppose x is the distance from Origin to (5,10). Here, we can imagine a right triangle with the vertices at (0,0), (5,0) and (5,10). That is, the floor distance is 5 and the wall height is 10. 5 and 10 are the arms of the right triangle here. We want to find the hypotenuse. According to Pythagoras Theorem, we can write x^2=5^2+10^2 x^2=25+100 x^2=125 x= √125 √

What is the slope of (x/2) + (y/3) = 1? 3/2 Does this line make an acute angle with the X-Axis or obtuse? Obtuse Does the point (1,3/2) lie on this line? (x/2)+(y/3)=1 (1/2)+(3/2 divided by 3)=1 (1/2)+(1/2)=1 1=1 LHS=RHS Yes, the point lies on the line.

SOLVING LINEAR EQUATIONS IN TWO VARIABLES Example 1: x+y=5 x-y=1 Where do these two lines intersect? Let's add the two equations. (x+y)+(x-y)=5+1 x+y+x-y=6 2x=6 x=6/2=3 x+y=5 3+y=5 y=5-3=2 (3,2) is the point of intersection of the given lines. Example 2: 2x+3y=14 5x-y=1 Where do the two lines cut? 2x+3y+5x-y=14+1 7x+2y=15 This isn't working. Again, let's try differently. 2x+3y=14 5x-y=1 Let's multiply both sides of this equation by 3. 15x-3y=3 Adding the two equations, 2x+3y+15x-3y=14+3 17x=17 x=17/17=1 5x-y=1 5(1)-y=1 5-y=1 -y=1-5 -y=-4 y=4 (1,4) is the point of intersection of the given lines. Example 3: 2x+5y+29=0 3x+2y+16=0 Let's multiply the first equation by 2 and the second equation by 5. 4x+10y+58=0 15x+10y+80=0 Subtracting the second equation from the first one, (4x+10y+58)-(15x+10y+80)=0 4x+10y+58-15x-10y-80=0 4x-15x+58-80=0 -11x-22=0 -11x=22 x==22/-11=-22/11=-2 2x+5y+29=0 2(-2)+5y+29=0 -4+5y+29=0 5y+25=0 5y=-25 y=-25/5=-5 (-2,-5) is the point of intersect...

Ax+By+C=0 Does this represent a straight line? Yes, it does because it is a "LINEAR" equation in x and y. (The power of x is 1 and the power of y is 1.) What is the slope of this line? What is the y-intercept of this line? And what is the x-intercept? By = -Ax-C y = (-Ax-C)/B y = (-Ax/B) - (C/B) y = (-A/B)x - (C/B) Compare this to y = mx+c m = -A/B c = C/B Therefore, Ax+By+C=0 has a slope of -A/B. Its y-intercept is -C/B. It cuts the Y-Axis at the point (0, -C/B). To find the x-intercept, we have to substitute 0 for y. Ax+By+C=0 Ax+B(0)+C=0 Ax+C=0 Ax=-C x = -C/A So the x-intercept is -C/A. That is, Ax+By+C=0 cuts the X-Axis at the point (-C/A,0). Summary: Ax+By+C=0, Slope=-A/B, y-intercept=-C/B, x-intercept=-C/A What is the slope of any line parallel to Ax+By+C=0? -A/B What is the slope of any line perpendicular to Ax+By+C=0? Let us say the slope of the perpendicular line is p. (-A/B)p=-1 p=(-1)(-B/A) p=B/A Analyse 2x+3y+4=0. [Comparing with Ax+By+C=0, A=2, B=3 and C=4.] 01) ...