Year 1 Pure

Question 1

If b^2 -4ac = 0, what are the roots?

Answer 1

1 repeated, real root

Question 2

If b^2 -4ac > 0, what are the roots?

Answer 2

2 distinct, real roots

Question 3

If b^2 -4ac < 0, what are the roots?

Answer 3

2 imaginary roots (no real roots)

Question 4

What is the domain?

Answer 4

Range of x values

Question 5

What is the range?

Answer 5

Range of y values

Question 6

How do you find the roots of an equation?

Answer 6

Factorise it, then find the value of x for each bracket, that is your root.

Question 7

If a root appears once, what does it do?

Answer 7

Crosses the x axis

Question 8

If a root appears twice, what does it do?

Answer 8

Touches the x axis

Question 9

If a root appears thrice, what does it do?

Answer 9

If is a point of inflection

Question 10

What is a perpendicular bisector?

Answer 10

A line which cuts a line segment into 2 equal parts at 90 degrees

Question 11

What is a chord?

Answer 11

A line segment connecting the two points on a curve.

Question 12

What is a circumcircle?

Answer 12

A circle touching all vertices of a triangle or polygon

Question 13

What are the key circle properties? (4)

Answer 13

-The angle in a semi-circle is always a right angle
-The tangent to a circle is perpendicular to the radius at the point of intersection
-The perpendicular bisector of a chord will always go through the centre of a circle
-The perpendicular bisectors of two chords will always intersect eachother at the centre of the circle

Question 13

What is the cosine rule for lengths?

Answer 13

a² = b² + c² -(2bc cosA)

Question 14

What is the cosine rule for angles?

Answer 14

cosA = (b² + c² - a²)/(2bc)

Question 15

What is the sine rule for angles?

Answer 15

sinA/a = sinB/b = sinC/c

Question 16

What is the equation for area of a triangle? (sine rule)

Answer 16

area =0.5 x a x b x sinC

Question 17

Draw the CAST diagram.

Answer 17

S A
T C

Question 18

What are the key trig identities?

Answer 18

tanx = sinx/cosx
sin²x + cos²x = 1

Question 19

What is the sign for differentiating from first principles?

Answer 19

f’(x) = lim h->0 (f(x+h) - f(x))/h

Question 20

When you use the second derivative, and your value is greater than 0, is it a maximum or minimum?

Answer 20

Minimum

Question 21

When you use the second derivative, and your value is less than 0, is it a maximum or minimum?

Answer 21

Maximum

Question 22

When you use the second derivative, and your value is 0, is it a maximum or minimum?

Answer 22

Could be anything, even a point of inflection.

Question 23

What is the multiplication law for logs?

Answer 23

logx + logy = logxy

Question 24

What is the division law for logs?

Answer 24

logx - logy = log(x/y)

Question 25

What is the power law for logs?

Answer 25

logx^b = blogx

Question 26

f(x) = e^x, what is dx/dy?

Answer 26

e^x

Question 27

If f(x) = e^kx, what is dx/dy?

Answer 27

ke^kx

Question 28

What is lne^x equal to?

Answer 28

X

Question 29

What is e^lnx equal to?

Answer 29

x

Question 30

What is ln(x) equal to?

Answer 30

log(base e) x

Question 31

What does log(base a) n = x mean?

Answer 31

a^x = n