Pure Maths

Question 1

Describe the tangent graph

Answer 1

• Repeats every 180*
• Root at 0, every 180
• Vertical asymptote at 90, every 180
• S graph

Question 2

Describe the sin graph

Answer 2

• Root at 0, roots every 180
• “Wavelength” of 360*
• “Amplitude” of 1
• Looks like an EM wave

Question 3

Describe the cosine graph

Answer 3

• Symmetrical on either side of the y axis
• Roots at 90, roots every 180 + 90*
• Is a sin graph translated 90*

Question 4

What is tan (x) in terms of sin (x) and cos (x)

Answer 4

sin (x) / cos (x)

Question 5

sin^2 (x) + cos^2 (x) = ?

Answer 5

sin^2 (x) + cos^2 (x) = 1

Question 6

Process of integration

Answer 6

Integration = powers increased, coefficients decreased
Increase power by one, divide coefficient by new power
3x^2 => x^3

Question 7

Process of differentiation

Answer 7

Differentiation = powers decreased, coefficients increased
Multiply coefficient by power, decrease power by one
3x^2 => 6x

Question 8

f(x) passes through (4,8)

f(2x) = ?

Answer 8

f(2x) is a scale of factor 0.5 in the x direction
This would show a skinnier graph.
(4,8) would be (2,8)

Question 9

f(x) passes through (15, 20)

2f(x) = ?

Answer 9

2f(x) is a scale factor 2 in the y direction
where f(x) passes (15, 20), 2f(x) passes (15, 40)

Question 10

(1, 4) lies of the curve f(x)

f(x - 1) -> ?

Answer 10

f(x - 1) is a translation of +1 in the x
(1, 4) lies of the curve f(x)
f(x - 1) -> (2,4)

Question 11

(5, 8) lies on the curve of f(x)

f(x) - 4 -> ?

Answer 11

f(x) - 4 is a translation of -4 in the y
(5, 8) lies on the curve of f(x)
f(x) - 4 -> (5, 4)

Question 12

What is the sin rule

Answer 12

sin A / a = sin B / b

Question 13

What is the cosine rule

Answer 13

c^2 = a^2 + b^2 - 2ab*cos (C)

Question 14

What is the factor theorem

Answer 14

f(a) = 0 —> (x - a) is a factor