Pure 1 (non-calc)

Question 1

Describe the gradient of parallel lines

Answer 1

Equal

Question 2

Describe the gradient of 2 perpendicular lines

Answer 2

They multiply to give -1

Question 3

When 2 lines intersect, …

Answer 3

… both equations are satisfied.

Question 4

How do you find the intersection of two lines ?

Answer 4

Simultaneous equations

Question 5

What are the 3 steps to finding a perpendicular bisector?

Answer 5

1. Find midpoint.
2. Find gradient of line joining points.
3. Find equation of the bisector.

Question 6

Quote the discriminant.

Answer 6

b^2 - 4ac

Question 7

What is the quadratic formula?

Answer 7

                 2a

Question 8

If D>0 :

Describe roots

Answer 8

2 roots

Question 9

If D=0 :

Describe roots

Answer 9

1 root / repeated root (bounce)

Question 10

If D<0 :

Describe roots

Answer 10

No real roots / no solutions.

(Because you can’t square root a negative)

The graph line never touches the x-axis.

Question 11

What do you use to help you solve quadratic inequalities, and at what point do you use it?

Answer 11

You calculate the discriminant, then draw a graph (there will be a middle section where the line is below the x-axis where the equation is not satisfied, meaning you have to write 3 separate inequalities).

You solve until you have X^2 = on one side. Then draw your graph.

Question 12

What are the 5 things to include in a graph sketch?

Answer 12

1. Axes
2. All intercepts
3. Equations of lines
4. Points of intersection
5. Maxima and minima

Question 13

What is the equation of a circle?

Answer 13

(X-a)^2 + (y-b)^2 = r^2

Where centre is (a,b) and radius r.

Question 14

CE and ED are chords. Which angle is subtending by the arc between C and D?

Answer 14

Angle E

Question 15

Circumference & centre circle theorem

Answer 15

The angle at the centre is double the angle at the circumference.

Question 16

2 angles at the circumference + chord circle theorem:

Answer 16

Angles standing on the same chord are equal.

Question 17

What must a cyclic quadrilateral do?

Answer 17

Every corner must touch the circumference of the circle.

Question 18

Cyclic quadrilateral circle theorem

Answer 18

Opposite angles in a cyclic quadrilateral add up to 180 degrees

Question 19

Semicircle theorem

Answer 19

The angle at the circumference in a semicircle is a right angle.

Question 20

Tangent circle theorem x2

Answer 20

1. The angle between tangent and radius is 90 degrees.

2. Tangents which meet at the same point are equal in length.

Question 21

Bisector circle theorem

Answer 21

The perpendicular from the centre to a chord bisects the chord

Question 22

Alternate segment theorem:

Answer 22

The angle between a tangent and a chord is equal to the angle in the alternate segment.

Question 23

What do the gradients of odd power graphs start and end as?

Answer 23

Positive and positive , or negative and negative

Question 24

What do the gradients of even power graphs start and end as?

Answer 24

Negative and positive , or positive and negative

Question 25

How do you rationalise a surd denominator ?

Answer 25

You multiply by the inverse of the denominator.