Questions

Question 1

Answer 1

Question 2

Answer 2

Question 3

Answer 3

Question 4

Answer 4

Question 5

Answer 5

Question 6

Answer 6

Question 7

Answer 7

Question 8

Answer 8

Question 9

Answer 9

Question 10

Answer 10

Question 11

Answer 11

Question 12

Answer 12

Question 13

Answer 13

Question 14

Answer 14

Question 15

Answer 15

Question 16

Answer 16

Question 17

Answer 17

Question 18

Answer 18

Question 19

Answer 19

Question 20

Answer 20

Question 21

Answer 21

Question 22

Answer 22

Question 23

Answer 23

Question 24

Answer 24

Question 25

Answer 25

1. To go from y =x to x =y, plot a graph of x against y, then rotate 90°anti clockwise then reflect in Y axis (draw arrows on the original x and y axis to help. Then between first and end step with the co ordinates of any points from the x=y graph
2. Know that for a -x^2 the Turing point (a, b) in equation -(x -a)^2 +b

Question 26

Answer 26

Remember the constraints that logs apply, it can never be negative

Question 27

Answer 27

For a number to be an integer it cannot have any negative powers (as this would create a fraction)
One of the power laws is that the power can be distributed to the factors of the base.

Question 28

Answer 28

Question 29

Answer 29

Good triangle splitting fraction technique
ALSO PLEASE REMEMBER IT IS R^2 NOT R

Question 30

Answer 30

Check your solutions and be careful when substituting the hidden quadratic equations

Question 31

Answer 31

Question 32

Answer 32

Just know that you can switch the integral sign

Question 33

Answer 33

Know that log functions are strictly always increasing.
Know how to maximise / minimise equations

Question 34

Answer 34

“Closest to origin” means smallest distance

Question 35

Answer 35

Different method for completing the square with -1 as coefficient of x sqaured

Question 36

Answer 36

Using logs in inequalities and approximating “in between “ of logs

Question 37

Answer 37

Question 38

Answer 38

Watch the algebra

Question 39

Answer 39

The reflected points and reflection line are perpendicular to one another
Don’t stop and keep going after finding intersection points

Question 40

Answer 40

Logic?

Question 41

Answer 41

Question 42

Answer 42

Substituting logs and see how many digits a number to the power of 10 has (one less)

Question 43

Answer 43

Binomial expansion

Question 44

Answer 44

Question 45

Answer 45

Know that the square root of a number less than 1 (0.7) is greater than the number itself. Just like how squaring a number less than one gives a smaller number

Question 46

Answer 46

Using matrices in simultaneous

Question 47

Answer 47

Trapezium rule

Question 48

Answer 48

Minimum point

Question 49

Answer 49

Don’t forget the 10s (those numbers ending in digit 0)

Question 50

Answer 50

Really hard trigonometry question considering extreme values of sin and cos

Question 51

Answer 51

Question 52

Draw a quadratic and a quartic together:

Answer 52

Question 53

Answer 53

Question 54

Answer 54

KNOW that sin^2(°) and cos ^2 (°) can never both be =0 , as this is true for no value of sin^2 + cos^2 =1

Question 55

What are the characteristics of a positive quartic , “with 4 real solutions “?

Answer 55

Question 56

Answer 56

charactertistics of a quartic

Question 57

Answer 57

Question 58

Answer 58

Question 59

Answer 59

Question 60

Answer 60

Question 61

Answer 61

“Intersects “ means the discriminant is greater than or equal to zero (could be one or two solutions )

Question 62

Answer 62

Acknowledge the 2n hinting towards two separate series in one

Question 63

Answer 63

Diving through by cos ^2 to create a tan. BUT checking that cos (x) != 0 for this to happen

Question 64

Answer 64

Characteristics of the sin^2 graph include: no negative y values, maxima and minima always occur at 0 and 1. Also manipulating sin to find the roots of sin (root x) to find that the roots are not evenly spaced

Question 65

Answer 65

Just keep on subbing in values and trying to

Question 66

Answer 66

Fundamental Therom of calculus

Question 67

Answer 67

Plotting log/ exponential graphs with inequalities

Question 68

Answer 68

Approach all “must be trues” with an initial guinea pig.
Know that a square is also a rectangle
Know that the cube /square of decimals is so small

Question 69

Answer 69

“Largest value” for which previous term is greater than next term is minimum value -1

Question 70

Answer 70

Knowing sin values and working in radians really well. Drawing a clear graph and understanding the question

Question 71

Answer 71

Sine rule and diagram manipulation

Question 72

Answer 72

When you get to the sin^2 cos^2 phase sub in the 1=c^2 +s^2

Question 73

Answer 73

Integrating as a function properly using equations

Question 74

Answer 74

Cancelling out logs in powers

Question 75

Answer 75

Sequences question

Question 76

What are translational sin formula?

Answer 76

Question 77

Answer 77

Question 78

Answer 78

Question 79

Answer 79

Question 80

Answer 80

Integrating and substituting, integrating with constant

Question 81

Answer 81

Question 82

How does the trapezium rule work?

Answer 82

Please remember to draw in trapeziums from the last point NOT TRIANGLES

Question 83

Answer 83

Consider what goes on between the integer functions

Question 84

Answer 84

Question 85

Answer 85

Always check solutions esp if logs or square roots are involved

Question 86

What is the general shape of x2, x3, x4, x5, x6 on one graph

Answer 86

Question 87

Answer 87

Question 88

Answer 88

Square all terms

Question 89

Answer 89

Look carefully at question before diving in

Question 90

Answer 90

Question 91

Answer 91

Question 92

Answer 92

Question 93

Answer 93

Sometimes just look at options and substitute values

Question 94

Answer 94

Question 95

What are the angle formula for a circle in radians?

Answer 95

Question 96

Answer 96

Sin (180 - °) = °

Question 97

Answer 97

Question 98

Answer 98

Square rooting a square and quartic

Question 99

Answer 99

Check the leading coefficients rather than just looking at the power, because they can cancel each other out

Question 100

Answer 100

Get used to quickly differentiating to find the turning point of a graph to plot an overall shape. Look at the answers in the multiple choice to help you decide where you are heading

Question 101

Answer 101

Know this other equation used to represent a circle. In co ordinate geometry questions, look for things like if it is on the line y=x

Question 102

Answer 102

Question 103

Answer 103

Question 104

Answer 104

Question 105

Answer 105

Question 106

Answer 106

Using the cases of tending to infinity and tending to zero

Question 107

Answer 107

Sometimes minimum values can become maximum

Question 108

Answer 108

Multi nominal expansion and grouping

Question 109

Answer 109

More multi nominal expansion

Question 110

Answer 110

Looking at patterns of sums

Question 111

Answer 111

Question 112

Answer 112

Dummy variable and integrating each component of equation separately to get desired result