# Maths Chapters 13-18

Flashcards by scudf001, updated more than 1 year ago Created by scudf001 almost 8 years ago
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Maths Flashcards on Maths Chapters 13-18, created by scudf001 on 06/12/2013.

## Resource summary

 Question Answer To solve normal linear equations you use BIDMAS EXAMPLE QUESTION: SOLVE 8+5y=18 -8 5y=10 /5 y=10 EXAMPLE QUESTION: SOLVE 4(y-5)=24 4y-20=24 +20 4y=44 /4 y=11 What do you do when you have a question like this: 12/(p+2) = 3 You move the denominator to the other side: 12 = 3(p+2) Then work it out normally: 12 = 3p+6 6 = 3p 2 = p What do you do when you have a question like this: x+1/2 - 4x-1/3 = 5/12 You firstly find the LCM: 12 12(x+1)/2 - 12(4x-1)/3 = 12x5/12 Then divide it through: 6(x+1) - 4(4x-1) = 5 Then work it out normally: 6x+6-16x+4 = 5 -10x+10 = 5 -10x = -5 x = 2 What do you do if you are given a question like this: p/5 + 3 = 7 You move the whole number first: p/5 = 4 And then move the denominator: p = 4x5 p = 20 When you need to set up a linear equation from a word problem, you have to work backwards and check it to make sure you have used the right numbers. You always put halfs into wholes when setting up your own linear equations. What is: Formula Expression Equation Identity A formula has 2 or more unknowns An expression has no equal signs An equation is where you are able to find what the letter is. An identity is always true What do you do when you are asked to increase £200 by 40%? You do 100%+40%=140% 140%/100%=1.4 (multiplier) 1.4x200=280 ANSWER = £280 What happens when you are asked to decrease £200 by 5%? You do 100%-5%=95% 100%/95%=0.95 0.95x200=190 ANSWER = £190 (always minus when decreasing) How do you work out Percentage Profit? How do you work out Percentage Loss? profit/origional amount x 100 loss/origional amount x 100 If you are asked to work out simple interest you work out the muliplier and add it on year by year If you are asked to work out compound interest you find the muliplier but add it on all at once. EXAMPLE QUESTION: The balance is £1000 and there is a 10% compound interest per year. Work out the balance after 3 years. 10%+100%=110% 110%/100%=1.1 1000 x 1.1^3 = £1331 What is the general equation of a straight line? y=mx+c EXAMPLE QUESTION: Your given the equation y=2x+3, both y and x are unknown, work out what y and x are if x goes from 0 to 5. x = 1 2 3 4 5 y = 3 5 7 9 11 When x is 3 y is 7 If you are given the equation 2x+y=6 you have to change the equation so that y is the subject (y=) by -2x so its y=6-2x and then you make a table x = 1 2 3 4 5 y = 6 4 2 0 2 If you are given the equation 2x+3y=12 you use the cover up method. If x is zero you cver up x (0, ) so you have the equatio 3y=12 so y=4 the coordinates would then be (0,4) and then do the same for if y was 0 To find the mid-point of a line you find the coordinates of both ends of the line and the add the x coordinats and the y coordinates together seperately and divide by two. EXAMPLE: (1,7) + (3,1) 1+3/2 = 2 7+1/2=4 so the mid-point would be (2,4) The gradient is the change in y for every 1 x To work out the gradient you do the change in y divided by the change in x If you are asked to find the y-intercept if you are given two or more coordinates and the gradient you insert the information you have got into the equation y=mx+c and then work it out from that Any line that has an equation with the same gradient is parrallel If the equation of a line is y=3x, the perpendicukar line would be y=-1/3x (because if its origionally a posative you out a negative and if its origionally a negative you out a positive) If the ratio is in the same units you dont have to write the units EXAMPLE QUESTION: If you are given the ratio of green paint as B:Y - 2:5 and you know that they use 140ml of yellow paint. How much blue paint would they use? 140/5=28 28x2=60ml Inverse Proportion is where one increases at the same rate as the other decreases How do you describe a transformation? You write the vector and the word transfromation. How do you describe a reflection? You write the word reflection adn the equation of the line that it was reflected on. How do you describe a rotation? You have to write the direction (anti-clockwise/clockwise), the degree of turn, the center of rotation and the word rotation How do you describe an enlargement? You need to write the word enlargement, write the scale factor and the center of the enlargement. The scale factor forn an enlargement is the length of a side of the image / the length of the corresponding side. Fractions or decimals as a scale factor make the enlargement smaller If the scale factor is a negative, you draw the enlargement on the other side of the center of enlargement. What is the difference between discrete and continuous data on histograms? When drawing a histogram, the discrete data have gaps between the bars whereas continuous data have no gaps When there are unequal class intervals in a bar you asjust the height of the bar by using a scale of frequency density. What ar the equations for Frequency Density Frequency Class Width Frequency Density = frequency/class width Frequency = frequency density x class width Class Width = frequency density x frequency A frequency polygon... joins up the middle of each histogram bar What happens when you draw a histogram/polygon for cumulative frequency? The cross for the polygon goes at the end of each bar. the Y-Axis is the cumulative frequency. How do you find the angles and the radius for Pie Charts? To work out an angle you use the equation: number/total x 360 To work out the radius you square root the total and then divide both the totals by the same number

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