Download Sequence Each term of a number sequence is made by adding 1 to

Sequence
Each term of a number sequence is made by adding 1 to the numerator and 2 to the
denominator of the previous term.
Here is the beginning of the number sequence:
1
3
,
2
5
3
7
,
4
9
,
5
11
,
, ...
(a)
Write an expression for the nth term of the sequence.
1 mark
n
(b) The nth term of a different sequence is n 2 + 1
The first term of the sequence is
1
2
Write down the next three terms.
2 marks
Total 3 marks
Rounding
(a)
Circle the best estimate of the answer to
72.34  8.91
6
7
8
9
10
11
1 mark
(b)
Circle the best estimate of the answer to
32.7 × 0.48
1.2
1.6
12
16
120
160
1 mark
(c)
Estimate the answer to
8.62  22.1
5.23
Give your answer to 1 significant figure.
…………………
1 mark
(d)
Estimate the answer to
28.6  24.4
5.67  4.02
…………………
1 mark
Total 4 marks
Operations
Look at these number cards.
0.2
2
10
0.1
0.05
1
(a)
Choose two of the cards to give the lowest possible answer.
Fill in the cards below and work out the answer.
×
=
...............
2 marks
(b)
Choose two of the cards to give the answer 100

=
100
1 mark
Total 3 marks
Look at this octagon:
y
C
D
-10
10
B
A
5
-5
0
5
-5
E
F
-10
10
x
H
G
(a)
The line through A and H has the equation x = 10.
What is the equation of the line through F and G?
..............................
1 marks
(b)
Fill in the gaps below:
x + y = 15 is the equation of the line through ............... and ...............
1 mark
(c)
The octagon has four lines of symmetry.
One of the lines of symmetry has the equation y = x
On the diagram, draw and label the line y = x
1 mark
(d)
The octagon has three other lines of symmetry.
Write the equation of one of these three other lines of symmetry.
..............................
1 mark
Numbers
This is what a pupil wrote:
For all numbers t and w,
1
1
2
t + w = t+w
Show that the pupil was wrong.
2 marks
Algebra
(a)
Find the values of a and b when p = 10
a
3 p3
2
a = ………………
1 mark
b
2 p 2 ( p – 3)
7p
b = ………………
1 mark
(b)
Simplify this expression as fully as possible:
3 cd 2
5 cd
1 mark
Locus
In the scale drawing, the shaded area represents a lawn.
There is a wire fence all around the lawn.
The shortest distance from the fence to the edge of the lawn is always 6m.
-
-
On the diagram, draw accurately the position of the fence.
3m
3m
Scale: 1cm to 3m
Lawn
2 marks
Rectangle rest
The diagram shows a rectangle that just touches an equilateral triangle.
Not drawn
accurately
x
20º
straight line
(a)
Find the size of the angle marked x
Show your working.
......................°
2 marks
(b)
Now the rectangle just touches the
equilateral triangle so that
ABC is a straight line.
A
Not drawn
accurately
B
D
E
Show that triangle BDE is isosceles.
C
2 marks
Locus
The diagram shows the locus of all points that are the same distance from
A as from B.
The locus is one straight line.
y
A
4
2
–4
–2
0
–2
0
2
4
x
B
–4
(a)
The locus of all points that are the same distance from (2, 2) and (– 4, 2) is also
one straight line.
Draw this straight line.
y
4
2
–4
–2
0
0
2
4
x
–2
–4
1 mark
(b)
The locus of all points that are the same distance from the x-axis as they are
from the y-axis is two straight lines.
Draw both straight lines.
y
4
2
–4
–2
0
0
2
4
x
–2
–4
1 mark
(c)
Look at points C and D below.
Use a straight edge and compasses to draw the locus of all points that are the
same distance from C as from D.
Leave in your construction lines.
C
D
2 marks
The scatter diagram shows the total amounts of sunshine and rainfall for 12 seaside
towns during one summer.
Each town has been given a letter.
The dashed lines drawn go though the mean amounts of sunshine and rainfall.
Sunshine
(hours)
H
700
C
E
600
K
A
D
500
L
J
G
I
400
B
300
F
200
100
0
0
10
20
30
40
Rainfall
(cm)
(a)
Which town’s rainfall was closest to the mean?
Town ...............................
1 mark
(b)
Draw a line of best fit on the scatter diagram.
2 marks
Use your line to find an estimate of the hours of sunshine for a seaside town that
had 30cm of rain.
............................... hours
1 mark
Supermarket
A customer at a supermarket complains to the manager about the waiting times at
the checkouts.
The manager records the waiting times of 100 customers at 1 checkout.
Results
40
40
30
30
Number
of
20
Customers
14
10
10
6
0
0
4
1
2
3
Waiting Time (minutes)
5
(a)
Use the graph to estimate the probability that a customer chosen at random will
wait for 2 minutes or longer.
.............................
1 mark
(b)
Use the graph to estimate the probability that a customer chosen at random will
wait for 2.5 minutes or longer.
.............................
1 mark
(c)
Calculate an estimate of the mean waiting time per customer.
Show your working.
You may complete the table below to help you with the calculation.
Waiting Time
(minutes)
Mid–point
of bar (x)
Number of
customers ()
0–
0.5
6
1–
1.5
14
2–
2.5
40
3–
3.5
30
4–5
4.5
10
x
3
100
……………… minutes
2 marks
(d)
The manager wants to improve the survey.
She records the waiting times of more customers.
Give a different way the manager could improve the survey.
1 mark
Computer Game
(a)
Alan has a guessing game on his computer.
He estimates that the probability of winning each game is 0.35
Alan decides to play 20 of these games.
How many of these games should he expect to win?
…………………
1 mark
(b)
Sue played the same computer game.
She won 12 of the games she played, and so she estimated the probability of
winning each game to be 0.4
How many games did Sue play?
Show your working.
2 marks
(c)
The manufacturers of another guessing game claim that the probability of winning
each game is 0.65
Karen plays this game 200 times and wins 124 times.
She says: ‘The manufacturers must be wrong’.
Do you agree with her? Tick () Yes or No.
Yes
No
Explain your answer.
-
1 mark