S2

Question 1

What is a population?

Answer 1

A collection of items/individuals

Question 2

What is a census?

Answer 2

When information is obtained from all members of a population.

Question 3

Give three advantages of a census.

Answer 3

• Every member is used.
• Unbiased
• Gives accurate answer

Question 4

Give three disadvantages of a census.

Answer 4

• Long time to do
• Expensive
• Difficult to ensure whole population surveyed

Question 5

What is a sample?

Answer 5

The chosen members of a population

Question 6

What is a sampling frame?

Answer 6

A list of all of the sampling units.

Question 7

Give three advantages of sampling

Answer 7

• Cheaper than census
• Destruction of all sampling units not needed (lifespan)
• Data easier to collect

Question 8

Give a disadvantage of sampling.

Answer 8

Bias can occur

Question 9

What is a random sample?

Answer 9

A sample in which every item has an equal chance of being selected

Question 10

What is a sampling distribution?

Answer 10

All of the potential outcomes and their probability

Question 11

What is a statistic?

Answer 11

A quantity calculated from the observations of a sample.

Question 12

What is a critical region?

Answer 12

The range of values which lead to H0 being rejected.

Question 13

What is the parametric form of an ellipse?

Answer 13

𝑥 = a cos θ , 𝑦 = b sin θ

Question 14

What is the parametric form of a hyperbola?

Answer 14

𝑥 = a cosh θ , 𝑦 = b sinh θ

Question 15

What is a hyperbola/ellipse?

Answer 15

A hyperbola/ellipse can be defined as the locus of a

point P which moves so that PS = e PN

Question 16

How is the locus of a point on an ellipse/hyperbola found?

Answer 16

• Find equation of tangent
• Find where tangent crosses axes.
• Find midpoint
• Solve for sinx/cosx
• sin^2+cos^2=1

Question 17

What is ∫ sec x tan x dx

Answer 17

secx

Question 18

What are the 4 methods for solving non-standard integrals?

Answer 18

• Multiply by 1
• Substitution
• Complete square
• Reverse chain rule

Question 19

For ∫x^n/(a^2+x^2)^1/2 dx, what substitution is best?

Answer 19

• u=a^2+x^2 when n is odd

- Trig/hyp when n is even

Question 20

How is a reduction formula for sin^nx found?

Answer 20

^n-1 x sin

Question 21

How is a reduction formula for cos^nx or tan^nx found?

Answer 21

^n-2 x …

Question 22

In = ∫ sinnx/

sin x dx solve?

Answer 22

sin[(n-2)x +2x]

Question 23

Volume of parallelepiped?

Answer 23

|a . (b × c)|

Question 24

Volume of a tetrahedron?

Answer 24

1/6|a . (b × c)|

Question 25

Distance from the point P (α, β, γ) (or point on plane) to the plane
ax + by + cz – d = 0?

Answer 25

𝑠 = |aα + bβ + cγ − d|

| √a2 + b2 + c2 |

Question 26

How is cartesian equation for plane found?

Answer 26

ax + by + cz – d = 0 is given by r. n = d (ie perpendicular vector)

Question 27

Reflection in plane?

Answer 27

OA’ = OA + 2AP

Question 28

Distance between skew lines.

Answer 28

d = (c − a) . b × d

|b × d|

Question 29

Normalise vector

Answer 29

divide by magnitude

Question 30

Diagonalise matrix

Answer 30

• Find eigenvalues
• Find eigenvectors
• Normalise eigenvectors
• Find orthogonal matrix
• Find diagonal matrix