Passport to grade C
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Transcript Passport to grade C
Passport to grade C
Add, subtract, multiply and divide
integers
•
•
•
•
382+674
491-378
23x74
55212
Add, subtract, multiply and divide
integers
•
•
•
•
382+674=1056
491-378=113
23x74=1702
55212=46
Round to significant figures and
estimate answers
Round to 1 significant figure
• 356
• 213
• 4587
• 35
• 684
• 12.7
Round to significant figures and
estimate answers
Round to 1 significant figure
• 356 400 check your answers
• 213 200
• 4587 5000
• 35
40
• 684
700
• 12.7 10
Round to significant figures and
estimate answers
Round to 1 significant figure
•
356 400 check your answers
•
213 200
•
4587 5000
•
35
40
•
684
700
•
12.7 10
Now use your rounded values to estimate answers. Step 1 round to 1 sig fig, step 2 calculate with your
rounded values.
Eg
2) 12.3 – 3.5
2.9x3.01=
3x3=9
1) 4.6x1.4=
3) (9.8+4.5)2.88
Round to significant figures and
estimate answers
Round to 1 significant figure
•
356 400 check your answers
•
213 200
•
4587 5000
•
35
40
•
684
700
•
12.7 10
Now use your rounded values to estimate answers. Step 1 round to 1 sig fig, step 2 calculate with your
rounded values.
Eg
1) 4.6x1.4= 5
2) 12.3 – 3.5=6 3) (9.8+4.5)2.88= 5
2.9x3.01=
3x3=9
Find HCF and LCM of 2 numbers
Highest Common Factor
Lowest Common Multiple
Find HCF and LCM of 2 numbers
Highest Common Factor
Lowest Common Multiple
Test question
(a) Write each of the numbers 36 and 80 as a product of prime factors.
36 = ...........................................
80 = ...........................................
[3]
(b)(i)Find the least common multiple (LCM) of 36 and 80.
...........................................
[2]
(ii)Find the highest common factor (HCF) of 36 and 80.
...........................................
[1]
Find HCF and LCM of 2 numbers
Highest Common Factor
Lowest Common Multiple
Test question
(a) Write each of the numbers 36 and 80 as a product of prime factors.
36 = 2x2x3x3..............................
80 = 2x2x2x2x5...........................
[3]
(b)(i)Find the least common multiple (LCM) of 36 and 80.
720.............................
[2]
(ii)Find the highest common factor (HCF) of 36 and 80.
4...............................
[1]
Add, subtract, multiply and divide fractions
Calculate the value
of:
1 1
4 8
a:
1
12
b:
2
12
c:
2
8
d:
3
8
Add, subtract, multiply and divide fractions
7
What is the value
of:
2 1
3 5
a:
1
2
c:
7
15
b:
1
2
d:
1
15
Add, subtract, multiply and divide fractions
8
Find the value of:
3
8
4
a: 2
b: 4
c: 6
d: 8
Add, subtract, multiply and divide fractions
10
What is the value
of:
1
24
2
a: 48
b: 24
c: 12
d: 6
Calculate percentage increase and
decrease
Increase the following rail fares by 10%.
a) £9.20
10% = …………………
New cost = ………………
b) £3.70
10% = …………………
New cost = ………………
c) £5.00
10% = …………………
New cost = ………………
d) £9.81
10% = …………………
New cost = ………………
Calculate percentage increase and
decrease
Increase the following rail fares by 10%.
a) £9.20
10% = 92p…………………
New cost = £10.12……
b) £3.70
10% = 37p…………………
New cost = £4.07……
c) £5.00
10% = 50p…………………
New cost = £5.50…………
d) £9.81
10% = 98p…………………
New cost = £10.79……
Calculate percentage increase and
decrease
decrease the following rail fares by 15%.
a) £9.20
10% = …………………
5%=
15%=
New cost = ………………
b) £3.70
10% = …………………
5%=
15%=
New cost = ………………
c) £5.00
10% = …………………
5%=
15%=
New cost = ………………
d) £9.81
10% = …………………
5%=
15%=
New cost = ………………
Calculate percentage increase and
decrease
decrease the following rail fares by 15%.
a) £9.20
10% = 92p
5%= 46p
15%= £1.38
New cost = £7.82
b) £3.70
10% = 37p
5%= 18.5p
15%= 55.5p
New cost =£3.15
c) £5.00
10% = 50p
5%= 25p
15%= 75p
New cost = £4.25
d) £9.81
10% = 98.1p
5%=49.05p
15%= £1.47
New cost = £8.34
Calculate the square root and cube
root of a number
Match these values to their square roots
49, 1, 81, 36, 25, 16, 4
1, 4, 7, 2, 6, 9, 5
Match these numbers to their cube roots
125, 216, 1, 27, 64, 8
1, 5, 4, 2, 6, 3
Add, subtract, multiply and divide
decimals
2.1+3.8=
8.12-5.9=
1.2x4=
4.81.2=
Add, subtract, multiply and divide
decimals
2.1+3.8=
8.12-5.9=
1.2x4=
4.81.2=
Now use your calculator to check
Add, subtract, multiply and divide
decimals
2.1+3.8=
8.12-5.9=
1.2x4=
4.81.2=
Now use your calculator to check
Exam question. How many bottles of water at £1.27
can Amy buy with a £5 note? How much change
will she have?
Write the prime factor decomposition
of a number
•
•
•
•
•
•
•
Also called the product of primes
300
600
120
60
55
550 check your results by multiplying the
together, you should get what you started with
Work with indices
•
•
•
•
•
evaulate
52 x 92
24 x 32 x 5
52 90
(22 )3
•
Simplify
•
•
•
•
52 x 52
24 x 22 2
92 90
(22 )3
Convert between fractions decimals
and percentages
Fraction
Decimal
=
0·9
=
=
0·53
Percentage
=
%
=
3%
=
53%
Share an amount in a ratio
4. Alan, Brendan and Chloe shared £768 in the ratio 5 : 4 : 3.
How much did each receive?
Alan
£ ....................................
Brendan £ ....................................
Chloe £ ....................................[3]
5. (a) A box contains 120 cubes.
Some of the cubes are black, the rest are white.
The black cubes and white cubes are in the ratio 2 : 3.
Calculate the number of black cubes and the number of white cubes in the box.
black cubes ................................
white cubes ................................[3]
(b) Another box also contains black cubes and white cubes in the ratio 2 : 3.
There are 160 black cubes.
How many white cubes are there?...................................[2]
Find the perimeter and area of a
square, rectangle and triangle
Area and perimeter
• Perry the ant walks around the edge of a
shape, when you calculate perimeter make
sure you have used all the edges
• There are no formulas you have to know for
perimeter except the circles one.
Area is the space a shape covers and
we find it by multiplying
4cm
3.8cm
7cm
8cm
4.5cm
6cm
7cm
9cm
5cm
4cm
18mm
10cm
12cm
Area is the space a shape covers and
we find it by multiplying
4cm
3.8cm
7cm
8cm
4.5cm
6cm
7cm
9cm
5cm
4cm
18mm
10cm
12cm
Factorise an expression
Example
Factorise 36-3x
= 3(12-x)
Now write and answer 5 of your own green
questions showing you can factorise an
expression
Set up and solve a linear equation
Construct, and then solve, an equation for each situation given below:
1. Think of a number. Subtract 9. The result is 25. What is the number?
2. Think of a number. Multiply it by 5, then add 12. The result is 52. What is the
number?
3. A number is trebled and added to 11. The result is 50. What is the number?
4.
The three angles in a triangle are c, c+20 and c+40. Find c.
5. A number added to twice the number gives an answer of 24. What is the number?
6. Three consecutive numbers added together make 48. What are they?
Round to decimal places
Round these numbers to one decimal place
(a) 4.26
(b) 7.31
(c) 5.4377
(d) 2.1804
(e) 12.5052 (f) 1.65
(g) 0.95
(h) 4.352
(i) 7.857
(j) 10.8501
Round to decimal places
Round these numbers to one decimal place
(a)4.26
4.3 (b)7.31
7.3 (c)5.4377 5.4
(d)2.1804 2.2 (e)12.5052 12.5 (f)1.65 1.7
(g)0.95 1.0
(h)4.352 4.4
(i)7.857 7.9
(j)10.8501 10.9
Explain (g) to a friend
Solve an inequality
3x<18
x>7 represent your solution on a number line
2x+1≥11
Plotofaa quadratic
graph
Find the area
compound shape
Calculate the area and circumference
of a circle
• Write down the formulae you need
• Calculate the area and perimeter of each shape
3.5cm
14cm
9cm
You now have half a passport…
• Work down the 4th column and write green
questions to convince your teacher you can do
the topics in this column.
Expand brackets
• Remember there is no equals sign so you do
not have to find an answer, just change the
way it looks, in this case make it not have
brackets.
• 3(a+2)
• 7(b-4)
• 3x(x+2)
• 5x(y-4)
Expand brackets
• Remember there is no equals sign so you do
not have to find an answer, just change the
way it looks, in this case make it not have
brackets.
• 3(a+2) 3a+6
• 7(b-4) 7b-28
• 3x(x+2) 3x2+6x
• 5x(2y-4) 10xy-20x
Use trial and improvement
• Work to 1 decimal place
a) x³+17=54
b) 2x³+5x=200
c) 5x²+60=120
d) x³+6=20
Use trial and improvement
• Work to 1 decimal place
a) X³+17=54
x=3.3
b) 2x³+5x=200 x=4.5
c) 5x²+60=120 x=3.5
d) X³+6=20
x= 2.4
Write and use nth trem
• Use these nth terms to generate the next 5
terms of the sequences, the first one has been
done for you
a) 3n+1 4, _, _, _, _, …..
b) 2n-3 -1, _, _, _, _, …..
c) n+10 11, _, _, _, _......
d) n²
1, _, _, _, _, …..
Write and use nth trem
• Use these nth terms to generate the next 5
terms of the sequences, the first one has been
done for you
a) 3n+1 4, 7, 10, 13, 16, …..
b) 2n-3 -1, 1, 3, 5, 7, …..
c) n+10 11, 12, 13, 15, 15......
d) n²
1, 4, 9, 16, 25, …..
Now find the nth terms of these
sequences
a)
b)
c)
d)
e)
4, 6, 8, 10, …..
3, 6, 9, 12, ….
1, 5, 9, 13, …..
10, 7, 4, …..
20, 24, 28, …..
Now find the nth terms of these
sequences
a)
b)
c)
d)
e)
4, 6, 8, 10, ….. 2n+2
3, 6, 9, 12, …. 3n
1, 5, 9, 13, ….. 4n-3
10, 7, 4, ….. 13-3n
20, 24, 28, ….. 4n+16
Plot linear graphs
• And use words like gradient and intercept
Plot these points
Plot these points
Girls
(3, 4)
Boys
(5, 6)
Plot these points
Girls
(3, 4)
(3, 0)
Boys
(5, 6)
(4, 6)
Plot these points
Girls
(3, 4)
(3, 0)
(3, -1)
Boys
(5, 6)
(4, 6)
(0, 6)
Plot these points
Girls
(3, 4)
(3, 0)
(3, -1)
(3, -0.5)
Boys
(5, 6)
(4, 6)
(0, 6)
(-1.5, 6)
Plot these points
Girls
(3, 4)
(3, 0)
(3, -1)
(3, -0.5)
(3, 6)
Boys
(5, 6)
(4, 6)
(0, 6)
(-1.5, 6)
(-6, 6)
Plot these points
Girls
(3, 4)
(3, 0)
(3, -1)
(3, -0.5)
(3, 6)
Boys
(5, 6)
(4, 6)
(0, 6)
(-1.5, 6)
(-6, 6)
Which point could sit on either line?
Plot these points
Girls
(3, 4)
(3, 0)
(3, -1)
(3, -0.5)
(3, 6)
( , )
Boys
(5, 6)
(4, 6)
(0, 6)
(-1.5, 6)
(-6, 6)
( , )
Plot these points
Girls
(3, 4)
(3, 0)
(3, -1)
(3, -0.5)
(3, 6)
Name your line
Boys
(5, 6)
(4, 6)
(0, 6)
(-1.5, 6)
(-6, 6)
Plot these points
Girls
(3, 4)
(3, 0)
(3, -1)
(3, -0.5)
(3, 6)
Boys
(5, 6)
(4, 6)
(0, 6)
(-1.5, 6)
(-6, 6)
Girls name a line to the left of your line
Plot these points
Girls
(3, 4)
(3, 0)
(3, -1)
(3, -0.5)
(3, 6)
Boys
(5, 6)
(4, 6)
(0, 6)
(-1.5, 6)
(-6, 6)
Boys name a line above your line
Plot linear graphs
Complete the table and plot y=4x+1
x
y
-1
0
1
1
2
9
Percentages without a calculator
1%
100%
10%
98%
£50
20%
60%
3%
35%
25%
Percentages without a calculator
£0.50
£50
1%
£5
100%
£49
10%
98%
£50
20%
3%
£10
£1.50
60%
35%
25%
£30
£17.50
£12.50
URGENT NEWS FLASH
URGENT NEWS FLASH
Maths exam markers
today have announced
that probability
questions must be
answered as a fraction
URGENT NEWS FLASH
Or a decimal....
URGENT NEWS FLASH
Or a percentage....
URGENT NEWS FLASH
Or as a word if they
give you words to
choose from....
URGENT NEWS FLASH
But never
URGENT NEWS FLASH
Ever....
URGENT NEWS FLASH
EVER......
URGENT NEWS FLASH
As a ratio
Write a probability..
• With a fraction
• Or a decimal
• Or a percentage
Volume of a prism
• What is the surface area of a cuboid with
dimensions 10 cm, 8 cm and 5 cm.
5 cm
8 cm
10 cm
Find the volume and surface area of
this prism
4
14cm
cm
5cm
Find the volume of this prism
1.5m
2m