AS

Question 1

What are the indices rules?

Answer 1

Question 2

When should you complete the square?

Answer 2

When a quadratic equation will not factorise easily

Question 3

How do you complete the square? (using x2 +yx + c)

Answer 3

Write in the form (x + y/2)² -(y/2)² + c

Question 4

Complete the square of x² + 6x + 7?

Answer 4

(x+3)² -3² + 7

= (x+3)² -2

Question 5

Complete the square of 2x² + 8x + 7?

Answer 5

2[x² + 4x + 7/2]

= 2[(x+2)² -2² + 7/2)

= 2[(x+2)² - 1/2]

= 2(x+2)² - 1

Question 6

How woulkd you complete the square of -x² + 4x + 5

Answer 6

= -1[x² -4x -5]

Then complete as normal to get

-1(x-2)² + 9

Question 7

What is the quadratic formula?

Answer 7

Question 8

What is the discriminant of the quadratic formula?

Answer 8

b² - 4ac

Question 9

What happens when b² - 4ac > 0 ?

Answer 9

There are two real distinct roots

Question 10

What happens when b2 - 4ac = 0 ?

Answer 10

There is one real root (repeated)

Question 11

What happens when b2 - 4ac

Answer 11

No real roots

Question 12

What are the inequality symbols?

Answer 12

Same for not equal to but circle not shaded in

Question 13

How can you tell the line of symetry from completing the square?

Answer 13

(x + y)² + c

Curve is left by y and up by c

Question 14

What is a transformation of y = f(x-a)?

Answer 14

Transformation of the graph by (x+a,y)

Question 15

What is the transformation of y = f(a) + b?

Answer 15

Graph is transformed by (x,y+b)

Question 16

What is the transformation of y = af(x)?

Answer 16

Graph is strechted by scale factor a (parallel to y-axis)

(x,ay)

Question 17

What is the transformation of y = f(ax)?

Answer 17

Transformation of graph by 1/a parallel to x axis

((1/a) x, y)

Question 18

What is the transformation of y = -f(x)

Answer 18

Reflection of graph in x-axis

(x, -y)

Question 19

What is teh transformation of y = f(-x)?

Answer 19

Reflection of graph in y-axis

(-x, y)

Question 20

What order should be done with 2f(x+1)?

Answer 20

Stretch then translate

Question 21

What is the sine rule?

Answer 21

a/sinA = b/sinB = c/sinC

sinA/a = sinB/b = sinC/c

Question 22

What is the cosine rule?

Answer 22

a² = b² + c² -2bc x cosA

Question 23

What is the area of a non-right angle triangle ?

Answer 23

Area = 1/2 x base x height

Area = 1/2 x a x b x sinC

Question 24

What is the lowercase and uppercase letters in triangles?

Answer 24

Lowercase - side

Uppercase - Angle

Question 25

What are some values for the graph y=sinx ?

Answer 25

x = 0, y = 0 x = 90, y = 1 x = 180, y = 0 x = 270, y = -1 x = 360, y = 0

Question 26

What are some values of y=cosx?

Answer 26

x = 0, y = 1 x = 90, y = 0 x = 180, y = -1 x = 270, y = 0 x = 360, y = 1

Question 27

What is tanx equal to?

Answer 27

tanx = sinx/cosx

Question 28

What are some values of y=tanx?

Answer 28

x = 0, y = 0 x = 90, y = ∞ x = 180, y = 0 x = 270, y = ∞ x = 360, y = 0

Question 29

How do you find the values of sine after getting the principle value?

Answer 29

PV & 180 - PV Repeat every 360

Question 30

How do you find the values of cosine after getting the principle value?

Answer 30

PV, 360 - PV Every 360

Question 31

How do you find the values of tan after getting the principle value?

Answer 31

PV, PV +/- multiples of 180

Question 32

What is the equation that links sin²x and cos²x?

Answer 32

sin²x + cos²x = 1

Question 33

What is the √ (xy) ?

Answer 33

√ x \* √ y

Question 34

What are the forms of equations of a straight line?

Answer 34

y -y₁ = m(x-x₁) ax + by + c = 0

Question 35

What are the gradients of two lines for them to be perpendicular?

Answer 35

m₁ \* m₂ = -1 m₁ and m₂ are the gradients of each line

Question 36

What are the gradients for two straight lines to be parallel?

Answer 36

m₁ = m₂

Question 37

What is the equation of a circle?

Answer 37

(x-a)² + (y-b)² = r² r - radius a = x coordinate b = y coordinate

Question 38

What is the angle in a semicircle theorem?

Answer 38

Angle subtended across a circle's diameter is always a right angle

Question 39

What is the theorem involving angles at the centre and circumference of the circle?

Answer 39

The angle subtended at the centre is twice that at the circumference

Question 40

What is the theorem relating angles in the same arc?

Answer 40

Angles subtended by the same arc are equal

Question 41

What is the theorem relating cyclic quadrilateral?

Answer 41

Opposite angles in cyclic quadrilaterals add up to 180º

Question 42

What is the angle between a tangent and the radius of a circle?

Answer 42

90º

Question 43

What theorem relates chords and the centre of a circle?

Answer 43

Perpendicular from the centre of a circle bisects the chord