Mock Flashcards

Question

Fractional indices using the fourth rule?

Answer 1

1. Carry out the rule 2. The root of the number is what you multiple itself root to get itself 3. The extra square you add on 4. Work it out= answer

Answer 2

Hence= use the other question to help

Answer 3

Combining rule 4 and 5!

Answer 4

1. The minus in fraction means it’s 1/ number +power 2. Change to a square root with no minus on the power 3. Figure out the square root Extra steps: (if needed) 1. Figure out the root ether cube or squared 2. Then figure out the power

Answer 5

Harder exam question: 1. Find a link between 32 and 16 to do with powers both in power of 2 2. Multiply powers and change the fraction to a number with a minus on the power 3. Powers are 5x=-4 4. X= -4/5

Answer 6

Area of a circle= π r²

Answer 7

Circumference= whole circle (2πr) Diameter= x 2 radius

Answer 8

1. Use the frequency from the first diagram, the first one stays the same e.g 2 then the second one you add 2 and the next frequency number 6= 8 2. Drawing the graph: always plot the end points (0

Answer 9

1. Find 42 on the minutes axis 2. Then draw up until you reach the line and draw across to the other axis 3. Then read the value on that axis e.g 28, total pupils 30, 30-28=2 Answer= 2

Answer 10

multiplying numerators (top numbers) and denominators (bottom numbers) then simplify . you can cancel before you multiply you can cancel any top number with any bottom number can be diagonal

Answer 11

1. Turn the mixed number into a top heavy fraction (bottom number stays the same, then mixed numbers bottom number + top number= new top number) 2. Check for cancellations 3. Then multiply 4. Change back into a mixed number (bottom number/ top= whole number, bottom stays the same, top number is what is left over from dividing to get the mixed number)

Answer 12

1. Ignore decimal points the multiply the numbers 2. Count the number of decimal places in question in both numbers then you will have same in the answer 3. Check by rounding the question

Answer 13

.Can be written with a dot on the numbers recurring, and if there is 3+ recurring numbers put a dot on first recurring number and on the end one to say all the ones in between also are recurring Writing a recurring decimal as an exact fraction .put a digit over the correct number of 9s, after you can simplify

Answer 14

Proving recurring decimals 1. Say let x=the decimal 2. If it’s 1 recurring number you times by 10 if it’s 2 recurring numbers you times 100 ect… 3. You then subtract the 1st line from the second line 4. Turn into a fraction, simpfly if you can

Answer 15

.If you do all the steps and get a decimal you must multiply it out

Answer 16

a solid geometric figure whose two ends are similar, equal, and parallel rectilinear figures, and whose sides are parallelograms. (Not circular)

Answer 17

A prism has the same cross section all the way through. E.g cuboid, triangular prism 1. Shade in the cross section 2. Find the are of the cross section e.g triangle A= bxh/2 3. Multiply the area by the length Volume of a prism= cross section x length

Answer 18

1. Area of each individual surface (draw dotted lines onto the shape) 2. The sides are Rectangles: LxW 3. Layout: Bottom, top, right, left, front, back 4. Units: cm^2

Answer 19

Volume of a cuboid: Volume: length x width x height Volume of a cube: Volume= area^3

Answer 20

.Direct= as one increase the other also increase

Answer 21

.Inverse= as one increases the other decreases

Answer 22

If it says proportional= direct proportional

Answer 23

1. y ∝ x 2. y=kx k= (constant) 3. Swap the letters for the numbers given 4. To figure out k (constant) 5. Then you write an equation connecting y and x using y=kx then swap k for the figured out constant Extra steps when it’s asks you find another value of a letter e.g find value y when x=8 1. Substitute the the new value, then work out the value

Answer 24

1. y ∝ 1/x 2. y= k/x 3. Swap the letters for the numbers given 4. To figure out k (constant) 5. Then you write an equation connecting y and x using y=k/x then swap k for the figured out constant Extra steps when it’s asks you find another value of a letter e.g find value y when x=4 1. Substitute the the new value, then work out the value

Answer 25

(can be decimals or fractions) 1. Draw the options 2. Probability must add up to 1 so spilt between options (on each branch) 3. Then repeat the options 4. Then you can work out the probability, by going along a branch and multiplying 5. For the total probability is to add the two probability’s together

Answer 26

(You can work out what happens if she wins both then take away from 1 to get probability of not winning both)

Answer 27

Using fractions: Denominator= total options Top number= chance of happening to a particular option

Answer 28

1. Work out the probability that they get the same 2. Then take it away from 1 (total probability) answer if they not the same chocolate

Answer 29

What can you work out from a velocity time graph: 1. Acceleration at any given time 2. Total distance travelled at any given time

Answer 30

.measured in= m/s^2 .horizontal= 0 acceleration (constant) .Find Gradient (acceleration) m= change in y/change in x

Answer 31

Separate graph into shapes then find the area of each shape the add it up Or If it’s parallel (top and bottom line) you can use the formula for the area of a trapezium

Answer 32

Estimate for acceraltion at a certain time: 1. Find the point 2. Draw a tangent (where the point is touched by a line but the rest isn’t) 3. Draw a right angled triangle using the line to find gradient 4. Work out the scale on graph 5. Find the gradient change in y/ change in x

Answer 33

1. Speed= distance/time 2. Distance travelled under the graph (cut up Into shapes) (Trapezium parrel lines are a and b) 3. Add up the areas 4. Time is last number on the time axis 5. The divided them Speed= distance/time

Answer 34

(straight lines are constant) 1. Use the words to create a graph 2. Work out the areas of each shape then add them together

Answer 35

.The people who has nothing go on the outside of the circle (the take away the people from total). .to figure out who has both you add up the ones that say they have the items then take away away from the actual total of people = the ones that have both. .to find who goes in the individual ones you minus the total you are told from the ones that have both. (To check you add them up to check they match the total)

Answer 36

(In probability you don’t need to cancel down fractions.)

Answer 37

You can multiply out the fractions

Answer 38

Multiply both sides by the fractions recipcaol e.g 2/3 (3/2) Fractions of a number e.g 3/2 8 (8/2=4x3) divide by the bottom number times by the top

Answer 39

Multiply both sides by the common (same) denominator (use the least) to each thing the equation

Answer 40

.Two signs next to each other are different you take away .two signs are the same you add

Answer 41

.two signs are different answer will be negative .two signs are the same the answer will be positive

Answer 42

.C and d you swap around the numbers then add a minus on to the answer

Answer 43

1. Two brackets 2. X^2= two xs in each bracket 3. The second number, needs the two numbers in the brackets to add up to it 4. The third number, need the two numbers in the brackets to multiply up to it You can check my expanding it by doing the moon shape: the first bracket each thing in it multiplied by the other bracket

Answer 44

1. Start in the same way 2 brackets that both have an x in it. 2. If it is minus when multiplying you need one minus 3. If both are you still need one minus just make sure they add and multiply to the correct numbers

Answer 45

Sometimes you can make both minuses if you need a negative adding number but a positive multiplication number, because multiplying two minuses makes a positive but add to a minus.

Answer 46

The rights hand equals 0. If you have two things that multiply to equal 0, then one of them is 0. 1. Put the equation out brackets (separate) 2. Then solve the linear equations, the answers will be the solutions You can check by substituting each answers to the solutions.

Answer 47

Make it equal zero by subtracting or adding it to both sides.

Answer 48

The the coefficient of x^2 is larger then 1. Take the coefficient of x^2 and multiply it by the end number in the equation (constant) 2. Then you have to find two numbers that multiply to make the answer to the first step and also need to add to make the middle number. 3. You the spilt the middle number into the answer to the second step also including x to each of the answers 4. Then put the first number and the last number next to the spilt number. 5. You then factorises (normally) the two terms each (two total) 6. You get the same bracket from the two factorisation, this is the first bracket of the factorisation of the difficult quadratic 7. The second bracket of the factorisation of the difficult quadratic, is from the left overs.

Answer 49

Larger number multiplication: e.g 168 you half the number as you go up faster (1 and 168, 2 and 84)…

Answer 50

1. Factorising as normal with quadratics coefficient of x^2, so you have brackets 2. Then get rid of the brackets and just have the two linear equation that equal 0 3. Then solve the two linear equations to find the two values of x (can be in fractions)

Answer 51

You can check by putting the value of x into the diagram.

Answer 52

You can’t move terms from one side of the equation to the other To show it’s true: Make the left hand side look exactly like the right hand side 1. Simplify the left side, getting rid of brackets(expanding) and collecting alike terms 2. And do any thing else needed to make it the same e.g factorising

Answer 53

1. Expand and simplify in any way 2. Look at all the x terms on both sides and form an equation 3. Then solve the equation for the values of a 4. Then use the number terms and the d terms and form an equation 5. Then solve the equation for the value of d You can check by putting the values of a and d into the smaller equations to see if it equals the same.

Answer 54

You add the the two past numbers together to get the next two terms e.g 1+1=2 1+2=3

Answer 55

X1= means the first number in the pattern X2= means the second number in the pattern Xn>300 = what is it’s number (n) in sequence when the value first goes over 300.

Answer 56

Xn+Xn+1=21= means the 21 (value) in sequence

Answer 57

A term to term rule= means how do get from one number to the next

Answer 58

Times a number by the same number e.g 2x2=4 is a square number The nth terms is n (which is a placement in the sequence) then what you do to get the next number.

Answer 59

You can check by implementing this into one of the patterns.

Answer 60

X^2= a curved graph not a straight line Completing the table for the equation Non calculator- 1. Substitute the letter x e,g 0 2. 2x0^2-4x0-2 = 0-0-2= -2 3. Now 2: 2x2^2-4x2-2 (BIDMAS) 8-8-2=-2 4. Check for patterns then complete the rest After completing the table you can plot the points on to the graph, and join the points with a smooth curve. Important: The bottom of the graph must be curved.

Answer 61

E.g use your graph to find the value of y when x=1.5 1. Draw on the graph a line straight through 1.5 x 2. Where the line crosses the graph and read the value on the y axis with another drawn line 3. Answer: y=-3.5 Important: You can get multiple values on these questions

Answer 62

E.g Using your graph, solve 2x^2-4x-2=0 1. The question on matches the graph drawn 2. y=2x^2-4x-2 3. 2x^2-4x-2=0 4. Y must equal 0, so on the graph draw a line y=0 on the graph (a line across on the 0) 5. Where the graph and line crosses is the answers 6. X=-0.4, 2.4

Answer 63

1. To solve this because it is different to the graph because of the -3 you must prove it true 2. y= x^2-2x 3. X^2-2x-3=1 4. To make it equal and the same as the graph you need to move the -3 so it is on the equals side 5. X^2-2x=4 6. y=4 draw this line on the graph 7. Then draw down from where it crosses the line to the get the x values 8. X=1.25, 3.25

Answer 64

Positive: U Negative: n

Answer 65

Y intercept is the consent e.g -3 can also be called the value of something

Answer 66

Y= line across X= line down <>= bigger than signs mean to draw a broken line <> (with a line underneath) =equals a unbroken lines Method: 1. Shade in the area that’s is not going to be discard(when doing multiple) 2. When having an inequality like y

Answer 67

Y=f(x) is the normal graph without change

Answer 68

Cubic y=x^3 Graphs are a wiggle To be cubic the highest power of x needs to be cubed. Turing point= where the graph turn and changes direction If it -x^3 it switches side

Answer 69

1. Complete the table as usual (start with 0 it’s easier) 2. The turning point is the curve (change in direction) only put the x axis point down not y axis

Answer 70

reciprocal y= 1/x They are asymptote to the curve= this means the curve will get closer and closer to them but never touch them

Answer 71

A vector is something with both magnitude and direction. On diagrams they are denoted by an arrow, where the length tells us the magnitude and the arrow tells us direction.

Answer 72

.Length of vector is the magnitude and the direction is where it is pointing .If you have two vectors a and b draw another line next to them to create a triangular shape saying a+b, if it’s subtraction it goes in the other direction

Answer 73

.vector 2(a+b)= 2a+2b draw the two a lines separate and then the two b lines separate then a line to join them like a triangle saying 2a+2b 2(a+b) is a scalar multiple of a +b: meaning it has the same direction

Answer 74

.express a line e.g x and y you put a arrow over head of xy going in the same direction .underline your vectors (a vector is the letter given for one the notions) .if you want to change it so it’s goes in opposite direction yx then the vector will change to be negative .combing vectors going the long way round go from xz to zy which means your at xy, to show this you minus the vector of xz and zy then put = to the vector of xy

Answer 75

.find a path to get to the vector .the ratio add them to get denominator of the other part of of the vector line e.g BD= 1/4 BC .get to BC by going the opposite way to reach the edges of BC to get the expression .subsuite expression of BC .expand any brackets .the original path way at the start to find AD subsuite the values for AB and BD then work it out to get AD

Answer 76

Vectors are often split up into two parts, which we call components: An x component, which moves left or right, and a y component, which moves up or down.

Answer 77

To add/subtract column vectors, we add/subtract the x and y values separately.

Answer 78

.Prisms: have the same cross-section all the way through E.g cylinder, triangular prism, cuboid, cube Cross section: the shape it looks like at the front e.g circle, triangle

Answer 79

.if one side gives a really bad decimal change your working out to the other side to get an easier number to work with .remember if a time and the number of people increase the time will decrease so one side you multiply the other you divide

Answer 80

.check through (do not add them for the denominator for this question) the last number is the denominator the first is numerator

Answer 81

.Ratio and graphs, plot the ratio as if it’s x,y

Answer 82

.do the opposite of the to move it to the other side Opposites: Cubbed to cubbed root Squared to square root Add to subtract Multiply to divide

Answer 83

.Move the easy terms first .if you multiply an side by a term you must put the other terms in brackets

Answer 84

.if the term you want is in brackets you must multiply it out

Answer 85

.if it’s in a fraction multiply out the fraction

Answer 86

.get all the ones with the desired terms on one side and all the others on the other side (Put the desired one with side with more on) . terms with multiple desired terms without numbers you can factorise it

Answer 87

.subtract powers and divide numbers

Answer 88

.can be quadratics so factorise, you can tell if it’s a quadratic by the x^2 .or if it’s not a quadratic you can factorise normally .if it’s difference of two squares you can factorise again: (must have a minus in between)

Answer 89

.the denominator must be the same, and do what you do to the bottom to the top 1. Must have a common denominator (what you do to bottom you do to the top) 2. Join the fractions an if minus symbol you must put it on the second top fraction (if there is already a minus on a number it’s turns to a plus 3. Multiply out the brackets then join add/subtract like terms (simplify) 4. Then if you can’t do anything else that should be the answer

Answer 90

.the denominators are letters so times each denominator by the other letter then the same to the top (you have to use brackets if there is more then one term when multiplying) .don’t multiply out brackets if it won’t simplify even more

Answer 91

.Factorise it if you can (difference of two squares), then you can make both denominators the quadratic .whether you have a quadratic you must factorise it

Answer 92

1. Write the other side as a singular fraction 2. The solve how you normally solve to get the value of x e.g multiplying, adding, subtracting 3. Solving linear equations

Answer 93

Solving, quadratics when it = 0 1. Make the one side one hole fraction 2. Then multiply the bottom the fraction the singular number on the other side 3. Expand the brackets (quadratic) 4. Then move all terms to the left so the other side is worth 0 5. You then have a quadratic solving question 6. Factorise the quadratic 7. Then separate each bracket saying it =0 to make 2 linear equations 8. Then continue to solve as normal to get what x equals (two answers)

Answer 94

If we can’t simplify a number to remove the root sign it is a surd, e.g a square number is not a surd because you can simplify it.

Answer 95

.multiply the same root number will equal taht number without the root

Answer 96

.Pick numbers that can simplify (pick the biggest square that goes into the number) .if you undo the root e.g 9 Square root to 3 then do it

Answer 97

.can find a square number or divide the two roots

Answer 98

.common rules on Algebra apply to Surds

Answer 99

.ignore the answer beside it and continue normally

Answer 100

.do it in the same way you expand a quadratic normally and remember to use the rules and simplify Integers= whole number

Answer 101

This means you need to get the square root out of the denominator 1. Multiply the root by itself in a fraction both as the numerator and denominator 2. On the top you should have a number and the root, then the same root on the bottom twice 3. Rule 1 means the two same roots equal the number in it so it changes the denominator to a number 4. You then divide the denominator by the singular number on the numerator 5. The answer will be the root and the divided number

Answer 102

.first you must multiply the root then add the number in its roots

Answer 103

The difference of two squares

Answer 104

1. Multiply the whole fraction by the denominator both top and bottom 2. Then lay out the new fraction 3. Complete any subtracting, adding, multiplying diving in the fraction 4. Then lay it out after

Answer 105

1. Rationalise the denominator 2. Combine into a normal fraction 3. Complete any subtracting, adding, multiplying diving in the fraction and expand the brackets 4. Rewrite the roots if necessary with the rules 5. Complete any subtracting, adding, multiplying diving in the fraction

Answer 106

Parallel lines never meet.

Answer 107

Perpendicular lines are at right angles. There is a 90° angle between them.

Answer 108

A corner or a point where two lines meet.

Answer 109

Angle Bisector: Cuts the angle in half. 1. Place the sharp end of a pair of compasses on the vertex. 2. Draw an arc, marking a point on each line. 3. Without changing the compass put the compass on each point and mark a centre point where two arcs cross over. 4. Use a ruler to draw a line through the vertex and centre point.

Answer 110

Perpendicular Bisector: Cuts a line in half and at right angles. 1. Put the sharp point of a pair of compasses on A. 2. Open the compass over half way on the line. 3. Draw an arc above and below the line. 4. Without changing the compass, repeat from point B. 5. Draw a straight line through the two intersecting arcs.

Answer 111

The perpendicular distance from a point to a line is the shortest distance to that line. 1. Put the sharp point of a pair of compasses on the point. 2. Draw an arc that crosses the line twice. 3. Place the sharp point of the compass on one of these points, open over half way and draw an arc above and below the line. 4. Repeat from the other point on the line. 5. Draw a straight line through the two intersecting arcs.

Answer 112

Perpendicular from a Point on a Line Given line PQ and point R on the line: 1. Put the sharp point of a pair of compasses on point R. 2. Draw two arcs either side of the point of equal width (giving points S and T) 3. Place the compass on point S, open over halfway and draw an arc above the line. 4. Repeat from the other arc on the line (point T). 5. Draw a straight line from the intersecting arcs to the original point on the line.

Answer 113

1. Draw the base of the triangle using a ruler. 2. Open a pair of compasses to the width of one side of the triangle. 3. Place the point on one end of the line and draw an arc. 4. Repeat for the other side of the triangle at the other end of the line. 5. Using a ruler, draw lines connecting the ends of the base of the triangle to the point where the arcs intersect.

Answer 114

1. Draw the base of the triangle using a ruler. 2. Measure the angle required using a protractor and mark this angle. 3. Remove the protractor and draw a line of the exact length required in line with the angle mark drawn. 4. Connect the end of this line to the other end of the base of the triangle

Answer 115

1. Draw the base of the triangle using a ruler. 2. Measure one of the angles required using a protractor and mark this angle. 3. Draw a straight line through this point from the same point on the base of the triangle. 4. Repeat this for the other angle on the other end of the base of the triangle.

Answer 116

1. Draw the base of the triangle using a ruler. 2. Open the pair of compasses to the exact length of the side of the triangle. 3. Place the sharp point on one end of the line and draw an arc. 4. Repeat this from the other end of the line. 5. Using a ruler, draw lines connecting the ends of the base of the triangle to the point where the arcs intersect.

Answer 117

A locus is a path of points that follow a rule. For the locus of points closer to B than A, create a perpendicular bisector between A and B and shade the side closer to B. For the locus of points equidistant from A, use a compass to draw a circle, centre A. For the locus of points equidistant to line X and line Y, create an angle bisector. For the locus of points a set distance from a line, create two semi-circles at either end joined by two parallel lines.

Answer 118

A point is equidistant from a set of objects if the distances between that point and each of the objects is the same.

Answer 119

Standard questions 1. Write it out in the normal ratio way (set out headings) 2. Multiply up the numbers up so they all on the same ratio 3. Add them up 4. The total divided by the total ratio number 5. The answer to step 4 multipled by the ratio for that thing (.when a question says e.g ‘five times as many blue discs as green discs’ the ratio is blue:5 green:1)

Answer 120

.You need the same amount of parts so you must multiply to get it

Answer 121

.if you multiply the outers together you get what it was previously and if you multiply the inerds you get that also .sometimes you’ll need to collect like terms

Answer 122

.if you have two ratios that are equal to each other you can form an equation, you can do this by multiplying the outers to outers and inners to the inners .if the questions say ‘show that’ whatever is on the equal side you want to isolate and sometimes further on you have to factorise your make it easier to divide and single out the term you want .if it’s minuses and you want it to be positive you can multiply by 1

Answer 123

Ratios can be placed in fractions: a/b = 1/4

Mock Flashcards

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