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Number Flashcards

1
Q

What is the product rule for counting?

A
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2
Q

How would you approximate / estimate this calculation?

A
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3
Q

How do you find the highest common factor and lowest common multiple of two numbers?

A
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4
Q

How do you find the prime factors of a number ?

A

Create a tree

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5
Q

How do simplify Surds ?
How do you simplify multiple of Surds?

A
  • find the largest square number that they will be divisible by
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6
Q

How do you expand two sets of single brackets , where the second bracket has a negative co efficient

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7
Q

How do you expand brackets using indice laws?

A
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8
Q

Can this be further simplified

A
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9
Q

How would you approximate a solution to an equation using iteration?

A
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10
Q

How do you show that an equation has a solution between two numbers ?

A
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11
Q

How do you use the iteration formula to find an estimate to the solution ?

A

Not as complicated as it looks,
You just slot in the values as the iteration formula is just a re arrangement of the solution

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12
Q

What are geometric sequences , and how do you find out the nth term?

A
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13
Q

What is the nth term for this sequence

A
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14
Q

How do you calculate the mean from ungrouped frequency tables?

A
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15
Q

How do you estimate the mean from grouped frequency tables ?

A
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16
Q

How do you find the range from ungrouped frequency tables?

A
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17
Q

How do you draw frequency polygons ?

A
  • use mid point
    *don’t draw the line to the origin
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18
Q

How do you convert an equation involving two variables ?

A

When using ratios in complex mode, convert to fractions and cross multiply

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19
Q

How do you determine a percentage from a fraction?

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20
Q

Describe the corresponding , co interior and alternate angles

A
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21
Q

How do you find the sum of angles in polygon , given sides ?

A
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22
Q

How do you find the size of exterior angles of a regular polygon?

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23
Q

How do you find the interior angles of a regular polygon?

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24
Q

What are the angles of elevation and angles of depression?

A
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25
Q

How do find the equation of a straight line , given it’s two points

A
  1. Find gradient
  2. Use this to find the y intercept
  3. Write equation without x and y values
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26
Q

How do you find the acceleration of a curved line?

A

You draw a tangent and find the gradient of the tangent .
A tangent only touches the line at one point

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27
Q

How do you find the ‘average ‘ rate of decrease?

A

Connect the two points with a straight line

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28
Q

How would you estimate the area under a curved line?

A

Split it up into smaller ‘strips’ , basically shapes
Are find the area of these linear shapes

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29
Q

How would you find the x or y intercept from an equation?

X+ 2y= 3

A
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30
Q

How would you find the co ordinates of a line segment?

A

The same applies when calculating the midpoint

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31
Q

How would you find the the gradient for the equation
2y+3x=4

A
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32
Q

How would you find the length of PQ

A

To find Point P you use simultaneous equations , as the two lines face a similar point

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33
Q

Describe the shape of cubic , exponential , reciprocal and quadratic graphs

A
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34
Q

What is the y intercept of exponential graphs?

A
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35
Q

What is the equation of a circle , when the centre of the circle is at the origin ?

A
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36
Q

How would you find the constants ?

A

You would use simultaneous equations, but instead if adding and subtracting you would use multiplication/division.

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37
Q

How would you find the approximate solutions of a quadratic equation from the graph of the corresponding quadratic function?

A
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38
Q

How do you calculate volume of a prism?

A
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39
Q

How do you calculate the volume of a pyramid?

A
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40
Q

How do you calculate the surface area of a cylinder?

A
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41
Q

How do you find the the upper and lower bound ?

A

Add or subtract half the accuracy

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42
Q

What is the difference between rounding and truncating?
Calculate the error interval of each with 3.5 to 1 d.p

A

Truncating is just cutting off, no matter what the end value is. Rounding considers the

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43
Q

How do you draw the front elevation , side elevation or plan of a 3D Shape

A
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44
Q

What are plans , front and side elevations?

A

The plan is the view from the top of a 3D solid
Elevations are horizontal views of a 3D object

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45
Q

How do you draw a 3D shape from the plan , side and front elevation?

A
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46
Q

What do these inequalities on a number line show ?

A
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47
Q

How do you simplify two ended inequalities?

A
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48
Q

What is the formula, for probability?

A
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49
Q

How would you solve this probability question?

A
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50
Q

What is the sum of all possibility outcomes ?

A

1

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51
Q

What are the probability notations , for intersection and union

A
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52
Q

What is the ratio method for proportion?

A
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53
Q

How do you solve compound rate questions?

A
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54
Q

How do you prove that two shapes are congruent?
What would be the structure of your proof?
Why ares like common justifications used

A

AAA, ASA, RHS(right angle , hypotenuse , side ), SSA

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55
Q

Describe fully the single transformation that maps shape A onto shape B

A
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56
Q

Enlarge the triangle with a scale factor of -1/3 using (3,1) as the centre of enlargement

A
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57
Q

What is angle OCA and why?

A

90°
Because the tangent meets the radius at 90°

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58
Q

Prove that angle OCA is 90°

A
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59
Q

What is angle COA and why?

A

2x , because angles at the centre are twice the angles at the circumference

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60
Q

Prove that angle COA is 2x

A
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61
Q

What is angle ABC and why ?

A

90° , because angles in a semi circle are always 90°

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62
Q

Why is angle ABC 90°

A
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63
Q

If angle CDA is 80° what is angle ABC?

A

100° , because opposite angles in a cyclical quadrilateral add up to 180°

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64
Q

If angle BAC is 85, then what is angle BDC?

A

85°. Because angles from the same segment are equal

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65
Q

Why is angle BDC also x ?

66
Q

If angle DBQ is 65° what is angle BCA?

A

65°, because of the alternate segment theorem

67
Q

Why is angle BCA = angle DBQ?

68
Q

How do you calculate the volume of a frustum?

69
Q

What is the quadratic formula?

70
Q

Factorising difference of two squares

71
Q

If CA =8cm , what is AB and why?

A

8cm , because two tangents from the same point are equal

72
Q

How do you convert time to decimal? ,

73
Q

How would you draw a cumulative frequency graph?

74
Q

How do you find the median class, from the cumulative frequency graph?

75
Q

How do you find the perimeter and area of a sector?

76
Q

How do you calculate the area and perimeter of a segment?

77
Q

Draw the tan graph

78
Q

How do you calculate the area of a kite ?

79
Q

How do you calculate the area of a trapezium?

80
Q

What is the difference between
mutually exclusive events and independent events?

A

Mutually exclusive events cannot take place at the same time.
Eg : when flipping a coin you cannot get heads AND tails at the same time
You can always find the intersection using the AND rule

Independent events don’t rely on the previous events , but you can do both

81
Q

How do you solve linear/arithmetic sequences ?

82
Q

How do you solve quadratic sequences?

83
Q

What is the product counting rule ?

84
Q

How do you draw box plots?

85
Q

Compare the following box plots

86
Q

How do you calculate percentage change ?

87
Q

What are the reverse percentages?

A

Basically just ratios

88
Q

How do you turn recurring decimals into fractions?
*dot notations

89
Q

How do you describe the effect of a transformation from f(x) to f(x+a)?

90
Q

Describe the Transformation from f(x) to f(x) +a

91
Q

Describe the transformation from
f(x) to f-(x)
f(x) to f(-x)

93
Q

What is the difference between bar charts and histograms ?

A

Bar charts are for distress data and histograms are for continuous data

94
Q

How would you use a histogram to complete a table?

95
Q

How would you use a histogram to complete a table?

A

Find the column of the ‘known data’ , then use this to find the f.d. Use this to figure out the y axis, by dividing the total amount of squares underneath it.

96
Q

How would, you solve this histogram , Q where the table is not given ?

A

You just draw the table yourself ,

97
Q

what are the law of indices ?

98
Q

How would you solve these adding Surds questions tho?

99
Q

How do you solve negative powers?

100
Q

Prove this indices rule?

101
Q

simplify

102
Q

How do you draw cumulative frequency graphs from a frequency table?
And then find the median

103
Q

How do you find the median , upper , lower and interquartile range when given a range of values ?

A

Use the total. If it is one less than a multiple of 4 , when add 1.

104
Q

How would you find the median of a frequency table ?

105
Q

How would you sketch the graph of this quadratic function?

106
Q

how would you identify if a quadratic equation has roots?

A

The roots are how many times it touches the x axis.
Perfect squares on,y have one root

107
Q

How would you determine the function of an equation from it’s graph?

108
Q

How do you solve quadratic inequalities?

109
Q

How do you find the line of symmetry of a quadratic graph?

A

You find the Turing point ,
And then from the x axis value write the verticals line as
X= value

110
Q

How do you solve regional inequalities?

A
  • sorry ignore diagram, the or equal to have solid lines , but the (<> ) only have dashed lines.
111
Q

How would you find the equation of the tangent of the circle , given the tangent of the circle

A

Find radius gradient , and then remember that the tangent acts at 90° to the radius
(The gradient will be the negative reciprocal)

112
Q

How do you find the equation of a circle ?

113
Q

How do you prove that vectors are parallel.

How do you prove that vectors are on a straight line?

A

They will be multiples of each other.

They will be parallel, and will share a common point

114
Q

angles in a paralellogram ?

A

opposite angles are equal

115
Q

angles in a kite?

A

the inner opposite angles are equal
*only one set of angles are similar

116
Q

How would you get the area of a similar shape given the volume ?

117
Q

What is the ‘curved surface area’?

A

The area of the curved part only , *not the flat top / base

118
Q

How would you solve this simultaneous equation?

119
Q

How do you multiply scalar vectors ?

120
Q

Solve the following hexagonal vectors

121
Q

What is an invariant point ?

A

A point that has the same co ordinates before and after a transformation

125
Q

Ratios Q

126
Q

Ratios Q

127
Q

Ratios Q

128
Q

How do you calculate the area of a hexagon?

131
Q

What does it mean when a line is parallel ?
Eg: equation is y=2x+2 going through the point (1,2)

A

When the line is parallel, it means the gradient (m) is the same , but the y intercept (c) would obviously change.
2=2(1)+c
2-2=c
C=0
Equation is
Y=2x

133
Q

How do you find the interquartile range from a cumulative frequency graph?

134
Q

How do you find the interquartile range from a cumulative frequency graph?

136
Q

Calculate the instantaneous rate

138
Q

What is the formula for the estimated median /UQ/LQ ?

139
Q

estimate the median

140
Q

Estimate the mean 😁

146
Q

What is a “curved surface area”?

A

The area of the curved part , leaving the flat base /bottom

149
Q

Vector question

152
Q

Regular hexagon area

154
Q

What is the difference between congruence and similarity ?

A

Congruence is when there has to be SSS! ASA, SSA (same shape and size)

Similarity is when it’s AAA (one is an enlargement of the other)

155
Q

Properties of a square

156
Q

Properties of a rectangle

157
Q

Parallelogram

158
Q

Rhombus

159
Q

Trapezium

160
Q

Kite

161
Q

Kite

Maths (6 decks)

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