Algebra and functions B1 Ch1-4

Question 1

< or > represented on a graph

Answer 1

Dotted line

Question 2

Bigger/smaller than or equal to on a graph

Answer 2

Solid line

Question 3

When does a quadratic have two solutions?

Answer 3

When the discriminant b²-4ac>0

Question 4

When does a quadratic have 1 solution?

Answer 4

When the discriminant b²-4ac=0

Question 5

When does a quadratic have no solutions?

Answer 5

When the discriminant b²-4ac<0

Question 6

If a quadratic has one solution, what does it look like on a graph?

Answer 6

It is a tangent to the x axis

Question 7

What is the domain?

Answer 7

The input values in a function

Question 8

What is the range?

Answer 8

The output values in a function

Question 9

What are the input values in a function called?

Answer 9

Domain

Question 10

What are the output values of a function called?

Answer 10

Range

Question 11

How do you find the roots of a function?

Answer 11

Put the function equal to zero, the roots are the values of x when the function equals zero

Question 12

What is a polynomial?

Answer 12

A finite expression with positive whole number indices

Question 13

In a reciprocal graph when k/x is positive in which quadrants of the graph is the line?

Answer 13

Top right and bottom left

Question 14

In a reciprocal graph when k/x is negative in which quadrants of the graph is the line?

Answer 14

Top left and bottom right

Question 15

In a reciprocal graph when k/x² is positive in which quadrants of the graph is the line?

Answer 15

Top left and top right

Question 16

In a reciprocal graph when k/x² is negative in which quadrants of the graph is the line?

Answer 16

Bottom left and bottom right

Question 17

What is the initial gradient of a positive cubic graph?

Answer 17

Positive

Question 18

What is the initial gradient of a negative cubic graph?

Answer 18

Negative

Question 19

What is the initial gradient of a positive quartic graph?

Answer 19

Negative

Question 20

What is the initial gradient of a negative quartic graph?

Answer 20

Positive

Question 21

y=f(x)+a transformation to f(x) in vector form

Answer 21

(0) (a)

Question 22

y=f(x+a) transformation to f(x) in vector form

Answer 22

(-a) (0)

Question 23

When transforming a graph which dimension do changes inside the bracket affect?

Answer 23

Horizontal, x movement

Question 24

When transforming a graph which dimension do changes outside the bracket affect?

Answer 24

Vertical, y movement

Question 25

In a fg(x) function which but is done first?

Answer 25

G

Question 26

How does y=f(x)+1 affect y=f(x)?

Answer 26

Move up one, Translate (0) (1)

Question 27

How does y=2f(x)affect y=f(x)?

Answer 27

Stretch x2 as tall

Question 28

How does y=-f(x)affect y=f(x)?

Answer 28

Reflect in x axis

Question 29

How does y=f(x+1) affect y=f(x)?

Answer 29

Move one left Translate (-1) (0)

Question 30

How does y=f(2x) affect y=f(x)?

Answer 30

Stretch x1/2 as wide

Question 31

How does y=f(-x) affect y=f(x)?

Answer 31

Reflect in y axis

Question 32

What are the two methods in partial fractions?

Answer 32

•equation coefficients/simultaneous equations •substitution

Question 33

How would you split the denominator (x+1)^2 x (x+6) into partial fractions

Answer 33

(x+1)^2 (x+1) (x+6)

Question 34

index laws

Answer 34

• a^m x aⁿ = a^m+n
• (a^m)ⁿ = a^mn
• (ab)ⁿ = aⁿbⁿ
• a^-m = 1/a^m
• a⁰ = 1

Question 35

how would you rationalise 1/(a-b^½)

Answer 35

multiply the numerator and doniminator by (a+b^½)