Transcript GCSE Booster - Whiteboard Maths

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SHAPE
HANDLING
SPACE & M
DATA
NUMBER
ALGEBRA
E
E
E
E
D
C
D
D
D
C
B
C
B
C
B
B
What fraction of the rectangle is
shaded red? (In simplest form)
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Answer
What fraction of the rectangle is
shaded red? (In simplest form)
1
3
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Explain?
What fraction of the rectangle is
shaded red? (In simplest form)
5 out of 15
are red.
1
5
1
=
15 3
3
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Divide top and bottom
by 5 (Highest common
factor) to simplify.
1
3
What is
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3
9

8
10
Answer
What is
3
9

8
10
5
12
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Explain?
What is
3
9

8
10
“Invert and multiply”. Multiplying
numerators and denominators,
then simplifying gives:
3
8
x
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10
9
=
30
72
5
12
Write the number below as a
product of its prime factors.
735
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Answer
Write the number below as a
product of its prime factors.
735
3 x 5 x 72
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The mass of Jupiter is approximately
2 390 000 000 000 000 000 000 000 000 kg.
Write this number in standard form.
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Answer
The mass of Jupiter is approximately
2 390 000 000 000 000 000 000 000 000 kg.
Write this number in standard form.
2.39 x 1027
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Explain?
The mass of Jupiter is approximately
2 390 000 000 000 000 000 000 000 000 kg.
Write this number in standard form.
Moving the decimal point
27 places to the right.
2.39 x 1027
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(a) How many balls are in the next pattern?
(b) What is the name of this number sequence?
?
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Answer
(a) How many balls are in the next pattern?
(b) What is the name of this number sequence?
6x6
5x5
4x4
?
Square Numbers
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9
Find a whole number
solution to :
n2 + 2n + 3 = 66
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Answer
Find a whole number
solution to :
n2 + 2n + 3 = 66
n=7
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Explain?
Find a whole number
solution to :
n2 + 2n + 3 = 66
72 + 2 x 7 + 3 = 66
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n=7
Expand:
(x - 2)(x - 6)
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Answer
Expand:
(x - 2)(x - 6)
x2 - 8x + 12
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Explain?
Expand:
(x - 2)(x - 6)
By inspection
x x x = x2
-6x - 2x = -8x
-2 x -6 = 12
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Or by single brackets
x(x - 6) - 2(x - 6)
= x2 - 6x - 2x + 12
x2 - 8x + 12
Evaluate V when p = - 3.
V = 7p2 +4p - 8
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Answer
Evaluate V when p = - 3.
V = 7p2 +4p - 8
43
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Explain?
Evaluate V when p = - 3.
V = 7p2 +4p - 8
V = 7(- 3)2 + 4(-3) - 8
V = 7 x 9 - 12 - 8
V = 63 - 20
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43
Calculate:
(a) the area of the wall
(b) the perimeter of the wall including the base
8½m
6m
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Answer
Calculate:
(a) the area of the wall
(b) the perimeter of the wall including the base
8½m
6m
Area = 6 x 8½ = 51 m2
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Perimeter = 6 + 8½ + 6 + 8½
= 29 m
Find the area of the
triangle.
9 cm
10 cm
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Answer
Find the area of the
triangle.
9 cm
10 cm
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Explain?
45 cm2
Find the area of the
triangle.
10 x 9
A=
2
= 45 cm2
9 cm
10 cm
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45 cm2
A lorry travels along a motorway from
junction 35 to junction 37. The journey time is
30 minutes. Find its average speed in mph.
35
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12 miles
36
15 miles
37
Answer
A lorry travels along a motorway from
junction 35 to junction 37. The journey time is
30 minutes. Find its average speed in mph.
35
12 miles
36
15 miles
37
54 mph
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Explain?
A lorry travels along a motorway from
junction 35 to junction 37. The journey time is
30 minutes. Find its average speed in mph.
35
12 miles
36
15 miles
37
Distance
Time
27
Speed =
= 54
½
Speed =
54 mph
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One of the formulae shown is for the
surface area of a cylinder. Use dimensions
to show which one it is.
(a ) 2 r (r 2  h 2 )
r
(b ) 2 r (r  h )
h
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(c ) 2 r 2 (r  h )
Answer
One of the formulae shown is for the
surface area of a cylinder. Use dimensions
to show which one it is.
(a ) 2 r (r 2  h 2 )
r
(b ) 2 r (r  h )
h
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(c ) 2 r 2 (r  h )
Explain?

One of the formulae shown is for the
surface area of a cylinder. Use dimensions
to show which one it is.
(a ) 2 r (r 2  h 2 )
r
(b ) 2 r (r  h )
h
(c ) 2 r 2 (r  h )

length x length = Area
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One counter is drawn from the bag
at random. What is the probability
that it is red?
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Answer
One counter is drawn from the bag
at random. What is the probability
that it is red?
8
2
=
12
3
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Explain?
One counter is drawn from the bag
at random. What is the probability
that it is red?
8 of the counters
are red out of a
total of 12 counters.
8
2
=
12
3
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Number of Visitors
The scatter graph with line of best fit shows information on
the number of daily visitors to a museum last summer.
500
450
400
350
300
250
200
150
100
0
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1
Use the line of best fit
to estimate the
number of visitors to
the museum on a day
when there is 4½
hours of sunshine.
2 3 4 5 6 7 8 9 10
Hours of Sunshine
Answer
Number of Visitors
The scatter graph with line of best fit shows information on
the number of daily visitors to a museum last summer.
500
450
400
350
300
250
200
150
100
0
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1
Use the line of best fit
to estimate the
number of visitors to
the museum on a day
when there is 4½
hours of sunshine.
2 3 4 5 6 7 8 9 10
 280 - 290
Hours of Sunshine
Explain?
Number of Visitors
The scatter graph with line of best fit shows information on
the number of daily visitors to a museum last summer.
500
450
400
350
300
250
200
150
100
0
Back to board
1
Use the line of best fit
to estimate the
number of visitors to
the museum on a day
when there is 4½
hours of sunshine.
2 3 4 5 6 7 8 9 10
 280 - 290
Hours of Sunshine
Use the histogram and frequency polygon to estimate the
mean time taken for the 45 runners to complete the race.
Time Taken for Race
Frequency
20
15
10
5
0
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10
20
30 40
Time in minutes
50
60
Answer
Use the histogram and frequency polygon to estimate the
mean time taken for the 45 runners to complete the race.
Time Taken for Race
Frequency
20
15
10
5
0
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10
20
30 40
Time in minutes
Explain?
50
60
32.8 mins
Use the histogram and frequency polygon to estimate the
mean time taken for the 45 runners to complete the race.
Time Taken for Race
Frequency
20
15
10
5
0
10
20
30 40
Time in minutes
50
60
32.8 mins
7 x 15 + 10 x 25 + 18 x 35 + 6 x 45 + 4 x 55
= 32.8
45
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Numbers in blue are the midpoints of the intervals.
The pointers on both spinners shown below
are spun. Calculate the probability of getting
a 6 on both spinners.
5
4
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6
3
1
2
1
8 2
3
7
6 54
Answer
The pointers on both spinners shown below
are spun. Calculate the probability of getting
a 6 on both spinners.
5
4
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6
3
1
2
1
48
Explain?
1
8 2
3
7
6 54
The pointers on both spinners shown below
are spun. Calculate the probability of getting
a 6 on both spinners.
5
4
6
3
1
2
1
48
1
8 2
3
7
6 54
1
1
x
6
8
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