General things

Question 1

recurring and terminating decimals

Answer 1

recurring decimals have one digit or a group of digits repeated forever

terminating decimals can be written exactly

Question 2

How do you prove something can be written as a recurring or terminating decimal?

Answer 2

terminating: denominator of the simplified fraction has prime factors of 2 and 5

make the fraction over 10/1000 and convert to a decimal

recurring: simplified fraction has prime factors of its denominator other than 2 or 5

Question 3

a) Show that 7/50 can be written as a terminating decimal
b) Show that 11/24 cannot be written as a terminating decimal
c) Show that 2/9 is equal to 0.222…
d) Hence, or otherwise, write 0.7222… as a fraction

Answer 3

a) 7/50 = 14/100 = 0.14
b) 11/24 = 11/2[3] x 3

denominator contains a factor other than 2 or 5 so decimal is recurring

c) (division) 2/9 = 0.222…

d) 0.7222 = 0.222… + 0.5
= 2/9 + 1/2
= 4/18 + 9/18 = 13/18

Question 4

Do you round significant figures?

Answer 4

yes

Question 5

Use the information below to find an appropriate degree of accuracy for the measurements.
Justify your answer

UB: 7.2618… cm
LB: 6.59963… cm

Answer 5

UB: 7.2… rounds to 7 (1 s.f.)

LB: 6.5… rounds to 7 (1 s.f.)

7 cm

Question 6

counting strategies to find total number of possible combinations

Answer 6

• systematic list (when there is a low number of possible choices)
• multiply the number of choices for each option

Question 7

a) how many 3 digits combinations can be made with these numbers: 456?

b) A lock on a briefcase has 3 dials.
The 1st dial can be any letter and the last 2 can be any digit from 0 to 9.
How many different ways are there of setting the code?

Answer 7

a) 456 465
546 564
645 654
six

b) letters: 26
digits: 10

26 x 10 x 10 = 2600

Question 8

Show that there are two different ways of solving the equation:

2y/3 + y-4/2 = 5

Answer 8

1) add the fractions by finding a common denominator

2y/3 + y-4/2 = 4y/6 + 3y-12/6
= 7y-12/6
then solve
7y-12/6 = 5
7y-12 = 30
7y=42
y=6

2) multiply each fraction out one at a time, while also multiplying the other fraction

2y/3 + y-4/2 = 5    (x3)
2y + 3y-12/2 = 15    (x2)
4y + 3y -12 = 30
then solve
7y-12 = 30
7y=42
y=6

Question 9

How do you find the gradient of a straight line using one point and algebra?

Use this example:

a straight line of gradient 2 passes through point (3,7)

Answer 9

• substitute the gradient
• substitute x and y values
• solve

y = mx + c
y = 2x + c

7 = 2x3 + c
7 = 6 + c
c = 1

y = 2x + 1

Question 10

What is the equation of a straight line in algebra?

Answer 10

y = mx + c

Question 11

a) what do parallel lines have in common?
b) what do perpendicular lines have in common?
c) a line L passes through the points (-3,6) and (5,4).

another line, P is perpendicular to L and passes through the point (0,-7).

Work out the equation of line P

Answer 11

a) same gradient

b) if a line has the gradient m, any perpendicular line has the gradient:
- 1/m

(reciprocal and going the other way)

c) gradient of L: -2/8 = -1/4
gradient of P: 1/0.25 = 4

y = 4x - 7

Question 12

turning point

Answer 12

point where directin of the curve changes

Question 13

shape of cubic graphs

x[3]

Answer 13

down, up, then down (or the other way around)

like an s shape

Question 14

lines that get closer together but never touch

Answer 14

asymptote

Question 15

shape of reciprocal graph

y = k/x

Answer 15

graphs get closer to a certain line but never touch

Question 16

coefficient

Answer 16

an unknown number of something

e.g. in a line the coefficient of x is just the gradient

Question 17

When do you have to change the sign on an inequality?

Answer 17

when multiplying or dividing by a negative number

Question 18

What value are cos x, sin x and tan x at 0 degrees on a graph?

Answer 18

cos x is 1
sin x is at 0
(graph goes from -1 to 1)

tan x is at 0

Question 19

What are the periods of cos x, sin x and tan x?

Answer 19

cos x and sin x: 360

tan x: 180

Question 20

4 angle properties

Answer 20

F angles: corresponding angles are equal

Z angles: alternate angles are equal

vertically opposite angles are equal

co-interior angles add up to 180

Question 21

sum of interior and exterior angles

Answer 21

interior: 180(n-2)
exterior: 360

Question 22

area of a sector

Answer 22

x/360 x πr[2]

Question 23

What do bearings always have?

Answer 23

3 figures

Question 24

sine rule

Answer 24

a/sin A = b/sin B = c/sin C

or the other way around

Question 25

cosine rule

Answer 25

a[2] = b[2] + c[2] - 2bc cos A

Question 26

circle theorems

Answer 26

angle in semi circle is 90

a radius bisects a chord

angle at the centre of an aroow shape is twice the angle at the circumference

opposite angles of a cyclic quadrilateral add up to 180

angles in the same segment/from the same point are equal

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

Question 27

frequency density

Answer 27

frequency/class width