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Level 5
Sharing a quantity in a ratio
26 questions
Lesson
Not started
Mark as done
F
G
H
FGH
F
G
H
and
J
F
G
JFG
J
F
G
are similar isosceles triangles.
F
G
H
J
F
G
=
F
H
FG = FH
F
G
=
F
H
J
F
=
J
G
JF = JG
J
F
=
J
G
G
H
J
GHJ
G
H
J
is a straight line.
G
H
:
H
J
=
9
:
7
GH : HJ = 9 : 7
G
H
:
H
J
=
9
:
7
Find the ratio
F
G
:
F
J
FG : FJ
F
G
:
F
J
(3 marks)
●●●●●
Level 5
3 marks
Start
→
Mark as done
A
B
D
L
O
x
y
In the diagram
A
A
A
is the point
(
0
,
10
)
(0, 10)
(
0
,
10
)
B
B
B
is the point
(
15
,
0
)
(15, 0)
(
15
,
0
)
D
D
D
is the point on
A
B
AB
A
B
such that
A
D
:
D
B
=
2
:
3
AD : DB = 2 : 3
A
D
:
D
B
=
2
:
3
The line
L
L
L
passes through
D
D
D
.
The gradient of
L
L
L
is
2.5
2.5
2.5
L
L
L
passes through the point with coordinates
(
−
3
,
f
)
(-3, f)
(
−
3
,
f
)
Show that
f
<
−
16
f < -16
f
<
−
16
(5 marks)
●●●●●
Level 5
5 marks
Start
→
Mark as done
A box holds
y
y
y
counters:
x
x
x
are red,
3
3
3
are white and the others are yellow.
x
:
y
=
1
:
4
x : y = 1 : 4
x
:
y
=
1
:
4
Seb takes at random two counters from the box.
Find an expression, in terms of
x
x
x
, for the probability that both counters are the same colour.
Give your answer as a fraction in the form
a
x
2
+
b
x
+
c
d
x
2
+
e
x
\dfrac{ax^2 + bx + c}{dx^2 + ex}
d
x
2
+
e
x
a
x
2
+
b
x
+
c
where
a
a
a
,
b
b
b
,
c
c
c
,
d
d
d
and
e
e
e
are integers.
(5 marks)
●●●●●
Level 5
5 marks
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→
Ratio problems where the amounts change
18 questions
Lesson
Not started
Mark as done
In a box, the ratio of red beads to blue beads is 3 : 4. When 6 more red beads are added to the box, the ratio of red beads to blue beads becomes 9 : 8. Work out the original number of blue beads.
●●●●●
Level 5
4 marks
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→
Mark as done
Jar A and Jar B contain marbles in the ratio 5 : 3. When 8 marbles are moved from Jar A to Jar B, the two jars then contain marbles in the ratio 1 : 1. Work out how many marbles were in Jar A to begin with.
●●●●●
Level 5
4 marks
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→
Mark as done
In a drawer, the ratio of pens to pencils is
2
:
5
2 : 5
2
:
5
.
When
9
9
9
more pens are put in the drawer, the numbers of pens and pencils become
equal
.
Work out the total number of items in the drawer
after
the pens are added.
●●●●●
Level 5
3 marks
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→
Mark as done
Two boxes,
A
A
A
and
B
B
B
, contain counters in the ratio
7
:
3
7 : 3
7
:
3
.
When
12
12
12
counters are moved from box
A
A
A
to box
B
B
B
, the two boxes contain
equal
numbers.
Work out the total number of counters.
●●●●●
Level 5
3 marks
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→
Combining and relating ratios
21 questions
Lesson
Not started
Mark as done
In a company, the ratio of managers to staff is 1 : 8, and the ratio of staff to trainees is 4 : 3. There are 96 staff. Work out the total number of managers, staff and trainees in the company.
●●●●●
Level 5
4 marks
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→
Mark as done
The ratio
(
2
x
+
1
)
:
(
x
+
4
)
(2x + 1) : (x + 4)
(
2
x
+
1
)
:
(
x
+
4
)
is equal to the ratio
3
:
2
3 : 2
3
:
2
. Work out the value of
x
x
x
.
●●●●●
Level 5
3 marks
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→
Mark as done
The ratio
(
3
x
−
2
)
:
(
x
+
6
)
(3x - 2) : (x + 6)
(
3
x
−
2
)
:
(
x
+
6
)
is equal to the ratio
5
:
3
5 : 3
5
:
3
Work out the value of
x
x
x
.
●●●●●
Level 5
3 marks
Start
→
Mark as done
p
:
q
=
2
:
5
p : q = 2 : 5
p
:
q
=
2
:
5
and
q
:
r
=
10
:
7
q : r = 10 : 7
q
:
r
=
10
:
7
r
r
r
is
12
12
12
more than
p
p
p
.
Work out the value of
q
q
q
.
●●●●●
Level 5
4 marks
Start
→
Mark as done
The diagram shows three triangles,
O
A
B
OAB
O
A
B
,
O
C
D
OCD
O
C
D
and
O
E
F
OEF
O
E
F
.
O
A
C
E
B
D
F
O
A
C
E
OACE
O
A
C
E
and
O
B
D
F
OBDF
O
B
D
F
are straight lines.
A
B
AB
A
B
,
C
D
CD
C
D
and
E
F
EF
E
F
are parallel.
O
A
:
A
C
:
C
E
=
2
:
3
:
4
OA : AC : CE = 2 : 3 : 4
O
A
:
A
C
:
C
E
=
2
:
3
:
4
Show that
area of triangle
O
A
B
OAB
O
A
B
: area of
A
B
D
C
ABDC
A
B
D
C
: area of
C
D
F
E
CDFE
C
D
F
E
=
4
:
21
:
56
= 4 : 21 : 56
=
4
:
21
:
56
(3 marks)
●●●●●
Level 5
3 marks
Start
→
Mark as done
3
a
:
2
c
=
4
:
5
3a : 2c = 4 : 5
3
a
:
2
c
=
4
:
5
b
:
4
c
=
3
:
2
b : 4c = 3 : 2
b
:
4
c
=
3
:
2
Show that
a
+
b
:
b
+
c
=
14
:
15
a + b : b + c = 14 : 15
a
+
b
:
b
+
c
=
14
:
15
(3 marks)
●●●●●
Level 5
3 marks
Start
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