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| 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 |