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Simplify Fully
• m4 x m2
• 5m2t3 x 2m4t
• h9÷ h3
• 35e7x2
5e5x
• (m2)3
• x0
• 16 ½
• (4x6)1/2
m6
10m6t4
h6
7e2x1
m6
1
4 (power of ½ means square root)
2x3
• 3x + 2 = 17
3x = 15
x = 5
• 4x - 2 = 10
4x = 12
x = 3
Solve
• 3x + 5 = x + 10
2x + 5 = 10
2x = 5
x = 2.5
• 3x – 3 = 8x + 17
-3 = 5x + 17
- 20 = 5x
-4 = x
Factorise Fully
• 8x2 + 4x
• 6x2 + 12x
• 3xy2 + 9xy
• 2x + x2
4x(2x + 1)
6x(x + 2)
3xy(y + 3)
x(2 + x)
Factorise
• x2 + 7x + 10
• x2 - 6x + 8
• x2 + 3x -4
(x + 2)(x + 5)
(x - 4)(x -2)
(x + 4)(x -1)
Factorise
• x2 – 36
• y2 - 64
• x2 - 81
x2 – 62 = (x – 6) (x + 6)
y2 - 82 = (x – 8) (x + 8)
x2 - 92 = (x – 9) (x + 9)
Expand and simplify
• 3(4x + y)
• 3y(y – 3)
• (y + 8)(y – 3)
• (2x – 3)2
12x + 3y
3y2 – 9y
y2 -3y +8y -24 = y2 + 5y -24
(2x -3)(2x-3) = 4x2 -6x -6x + 9
= 4x2 -12x+ 9
Inequalities
X is an integer
State the possible values
1. -1 ≤ x < 3
2. 4 < x ≤ 7
3. -2 < x < 4
-1, 0 , 1, 2
5, 6, 7
-1, 0, 1, 2, 3
Solve the inequality
3x < 9
x < 3
4y > 12
y > 3
2x + 2 < + 12
2x < 10
x< 5
3y + 6 < 15
3y < 9
y < 3
1. 3x + 2 < 11
2. 4y – 2 > 10
3. 6x + 2 < 4x + 12
4. 3(y + 2) < 15
-3 < x ≤ 4
A box of grass seed covers 20m2
How many boxes are needed to cover the lawn
Area = 9 x 12 = 108 m2
Area = 9 x 6 = 54 ÷ 2 = 27 m2
Total area = 108 + 27= 135m2
Seven boxes required
2m
6m
5m
2m
Mrs Philips is going to cover the floor with floor
boards
One pack covers 2.5 m2
How many packs does she need?
Area = 5 x 2 = 10 m2 Area = 4 x 2 = 8 m2
Total area = 10 + 8= 18 m2
Eight boxes required
Calculate the Volume of the Prism
Calculate CSA
Area = 4 x7 = 28 cm2
Area = 5 x 2 = 10 c m2
CSA = 10 + 28 = 38cm2
Volume = 38 x 10 = 380cm3
Calculate the Volume of the Prism
4 cm
5 cm
3 cm
7 cm
Diagram
accurately drawn
NOT
Calculate CSA
4 x 3 = 12 ÷ 2 = 6 cm2
Volume = 6 x 7 = 42 cm3
1. What time did Jasmine leave home?
2. For how long did Jasmine stop to talk to her friend
on the way to the park
3. Jasmine stayed at the park for ½ hour, then
walked home at a steady rate of 7.5 km/hr
Jasmine's journey to the park
9.10am
10 mins
The perimeter of the shape is 38 cm
Calculate the area
2x – 1
2x
3x -2
+ 3x + 1
10x -2
10x -2 = 38
10x = 40
x = 4 calculate lengths
8
7
13
Area = 8 x7 =56m2
Area = 8 x 6 = 48 ÷ 2
= 24cm2
Area = 56 + 24 = 80c m2
Find the value of x
3x - 15
2x
2x
+ 2x + 24
9x +9
Angles in a quadrilateral = 360o
So 9x + 9 = 360
9x = 351
x = 39
Calculate the value of x – give reasons
53 – Corresponding angle
180 – 53 = 127
Angles on straight line
28
Vertically opposite
180 – 127 – 28 = 25
Angles in a triangle
add to 180
Calculate angle x
Exterior
angle of
Hexagon
= 360 ÷ 6
= 60 Exterior
angle of
Octagon
= 360 ÷ 8
= 45
x = 60 + 45 = 105
nth term
• 3 6 9 12.........
• 1 7 13 19........
• 5 12 19 26........
3n
6n - 5
7n - 2
State two things wrong with this question
1)
2)
Design a better question
No timescale
Response boxes overlap
How much money do you spend using your
mobile phone in a week?
None £1-£5 £6-£10 £11-£15 > £15
Here is part of Gary's bill
Work out how much Gary has to pay for the units of electricity used
Units used
7155
-7095
60
Cost
60 x 15 = 900
which = £9
Standard form
• Write as an ordinary number
• 8.5 x 10 4
• 6.7 × 10–3
• Write in standard form
• 867000
• 0.00045
85000
0.0067
8.67 x 105
4.5 x 10 - 4
Compare the distributions
Median girls = 29 boys = 25.5 / Girls have highest median
IQR girls = 8 boys = 9 / Boys have highest IQR
+ 12
12
27
45
+ 27
+ 45
+ 57
57
60
CHECK
estimate
• 31 x 9.87
0.509
• 84 x 10
23
• 26 x 33
0.235
• 30 x 10 = 300 = 600
0.5 0.5
• 80 x 10 = 800 = 40
20 20
• 30 x 30 = 900 = 4500
0.2 0.2
16 gingerbread 8 gingerbread 24 gingerbread
180 flour 90 flour 270 flour
40 ginger 20 ginger 60 ginger
110 butter 55 butter 165 butter
30 sugar 15 sugar 45 sugar
1 + 3 + 5 = 9
180 = 20
9
Need
Cement 1 x 20 = 20 kg
Sand = 3 x 20 = 60 kg
Gravel = 5 x 20 = 100 kg
He does not have enough
cement, as he needs 20 kg
and he has 15 kg
2 9
3 1 6 5 3 9
4 3 9 3 4 6 2 8
5 2 4 5
2 9
3 1 3 5 6 9
4 2 3 3 4 6 8 9
5 2 4 5
KEY
2 9 = 29
• £1.82 x 15 =
• 3.28 x 13 =
• 4.56 x 1.8=
Remove decimals
Multiple – box method
Put decimals back in
Express 120 as a product of its prime factors.
Find the highest common factor (HCF) of 90 and 120
602
302
2 15
3 5
120 =2 x 2 x 2 x 3 x 5
120 =2 x 2 x 2 x 3 x 5
90 = 2 x 3 x 3 x 5
HCF = 2 x 3 x 5 =30
• Janice asks 100 students if they like biology or chemistry or
physics best.
• 38 of the students are girls.
• 21 of these girls like biology best.
• 18 boys like physics best.
• 7 out of the 23 students who like chemistry best are girls.
• Work out the number of students who like biology best.
Biology Physics Chemistry Total
Girls 21 10 7 38
Boys 28 18 16 62
Total 49 28 23 100
The area of the triangle is equal to the area of
the square
What is the perimeter of the square
Area triangle = 9 x 8 = 72÷ 2 = 36 cm2
Area square = 36 cm2
Length of each side of square = 6 cm
6 + 6 + 6+ 6 = 24 cm
V = 3b + 2b2
Find the value of V when b = –4
s = 3d + 8
Write d in terms of s
V = 3 x (-4) + 2 x (-4)2
V = - 12 + 2 x 16
V = - 12 + 32
V = 20
d → x 3 → +8 →
sd ← ÷3 ← -8 ← s
S – 8 = d
3
Express the area in terms of
7cm
7cm
10cm
Area = r2
= x 7 x 7 cm 2
= 49 cm 2
Volume = 4 9 x 10
= 490 cm3

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Higher revision

  • 1. Simplify Fully • m4 x m2 • 5m2t3 x 2m4t • h9÷ h3 • 35e7x2 5e5x • (m2)3 • x0 • 16 ½ • (4x6)1/2 m6 10m6t4 h6 7e2x1 m6 1 4 (power of ½ means square root) 2x3
  • 2. • 3x + 2 = 17 3x = 15 x = 5 • 4x - 2 = 10 4x = 12 x = 3 Solve • 3x + 5 = x + 10 2x + 5 = 10 2x = 5 x = 2.5 • 3x – 3 = 8x + 17 -3 = 5x + 17 - 20 = 5x -4 = x
  • 3. Factorise Fully • 8x2 + 4x • 6x2 + 12x • 3xy2 + 9xy • 2x + x2 4x(2x + 1) 6x(x + 2) 3xy(y + 3) x(2 + x)
  • 4. Factorise • x2 + 7x + 10 • x2 - 6x + 8 • x2 + 3x -4 (x + 2)(x + 5) (x - 4)(x -2) (x + 4)(x -1)
  • 5. Factorise • x2 – 36 • y2 - 64 • x2 - 81 x2 – 62 = (x – 6) (x + 6) y2 - 82 = (x – 8) (x + 8) x2 - 92 = (x – 9) (x + 9)
  • 6. Expand and simplify • 3(4x + y) • 3y(y – 3) • (y + 8)(y – 3) • (2x – 3)2 12x + 3y 3y2 – 9y y2 -3y +8y -24 = y2 + 5y -24 (2x -3)(2x-3) = 4x2 -6x -6x + 9 = 4x2 -12x+ 9
  • 7. Inequalities X is an integer State the possible values 1. -1 ≤ x < 3 2. 4 < x ≤ 7 3. -2 < x < 4 -1, 0 , 1, 2 5, 6, 7 -1, 0, 1, 2, 3
  • 8. Solve the inequality 3x < 9 x < 3 4y > 12 y > 3 2x + 2 < + 12 2x < 10 x< 5 3y + 6 < 15 3y < 9 y < 3 1. 3x + 2 < 11 2. 4y – 2 > 10 3. 6x + 2 < 4x + 12 4. 3(y + 2) < 15
  • 9. -3 < x ≤ 4
  • 10. A box of grass seed covers 20m2 How many boxes are needed to cover the lawn Area = 9 x 12 = 108 m2 Area = 9 x 6 = 54 ÷ 2 = 27 m2 Total area = 108 + 27= 135m2 Seven boxes required
  • 11. 2m 6m 5m 2m Mrs Philips is going to cover the floor with floor boards One pack covers 2.5 m2 How many packs does she need? Area = 5 x 2 = 10 m2 Area = 4 x 2 = 8 m2 Total area = 10 + 8= 18 m2 Eight boxes required
  • 12. Calculate the Volume of the Prism Calculate CSA Area = 4 x7 = 28 cm2 Area = 5 x 2 = 10 c m2 CSA = 10 + 28 = 38cm2 Volume = 38 x 10 = 380cm3
  • 13. Calculate the Volume of the Prism 4 cm 5 cm 3 cm 7 cm Diagram accurately drawn NOT Calculate CSA 4 x 3 = 12 ÷ 2 = 6 cm2 Volume = 6 x 7 = 42 cm3
  • 14. 1. What time did Jasmine leave home? 2. For how long did Jasmine stop to talk to her friend on the way to the park 3. Jasmine stayed at the park for ½ hour, then walked home at a steady rate of 7.5 km/hr Jasmine's journey to the park 9.10am 10 mins
  • 15. The perimeter of the shape is 38 cm Calculate the area 2x – 1 2x 3x -2 + 3x + 1 10x -2 10x -2 = 38 10x = 40 x = 4 calculate lengths 8 7 13 Area = 8 x7 =56m2 Area = 8 x 6 = 48 ÷ 2 = 24cm2 Area = 56 + 24 = 80c m2
  • 16. Find the value of x 3x - 15 2x 2x + 2x + 24 9x +9 Angles in a quadrilateral = 360o So 9x + 9 = 360 9x = 351 x = 39
  • 17. Calculate the value of x – give reasons 53 – Corresponding angle 180 – 53 = 127 Angles on straight line 28 Vertically opposite 180 – 127 – 28 = 25 Angles in a triangle add to 180
  • 18. Calculate angle x Exterior angle of Hexagon = 360 ÷ 6 = 60 Exterior angle of Octagon = 360 ÷ 8 = 45 x = 60 + 45 = 105
  • 19. nth term • 3 6 9 12......... • 1 7 13 19........ • 5 12 19 26........ 3n 6n - 5 7n - 2
  • 20. State two things wrong with this question 1) 2) Design a better question No timescale Response boxes overlap How much money do you spend using your mobile phone in a week? None £1-£5 £6-£10 £11-£15 > £15
  • 21. Here is part of Gary's bill Work out how much Gary has to pay for the units of electricity used Units used 7155 -7095 60 Cost 60 x 15 = 900 which = £9
  • 22. Standard form • Write as an ordinary number • 8.5 x 10 4 • 6.7 × 10–3 • Write in standard form • 867000 • 0.00045 85000 0.0067 8.67 x 105 4.5 x 10 - 4
  • 23. Compare the distributions Median girls = 29 boys = 25.5 / Girls have highest median IQR girls = 8 boys = 9 / Boys have highest IQR
  • 24. + 12 12 27 45 + 27 + 45 + 57 57 60 CHECK
  • 25.
  • 26. estimate • 31 x 9.87 0.509 • 84 x 10 23 • 26 x 33 0.235 • 30 x 10 = 300 = 600 0.5 0.5 • 80 x 10 = 800 = 40 20 20 • 30 x 30 = 900 = 4500 0.2 0.2
  • 27. 16 gingerbread 8 gingerbread 24 gingerbread 180 flour 90 flour 270 flour 40 ginger 20 ginger 60 ginger 110 butter 55 butter 165 butter 30 sugar 15 sugar 45 sugar
  • 28. 1 + 3 + 5 = 9 180 = 20 9 Need Cement 1 x 20 = 20 kg Sand = 3 x 20 = 60 kg Gravel = 5 x 20 = 100 kg He does not have enough cement, as he needs 20 kg and he has 15 kg
  • 29. 2 9 3 1 6 5 3 9 4 3 9 3 4 6 2 8 5 2 4 5 2 9 3 1 3 5 6 9 4 2 3 3 4 6 8 9 5 2 4 5 KEY 2 9 = 29
  • 30. • £1.82 x 15 = • 3.28 x 13 = • 4.56 x 1.8= Remove decimals Multiple – box method Put decimals back in
  • 31.
  • 32. Express 120 as a product of its prime factors. Find the highest common factor (HCF) of 90 and 120 602 302 2 15 3 5 120 =2 x 2 x 2 x 3 x 5 120 =2 x 2 x 2 x 3 x 5 90 = 2 x 3 x 3 x 5 HCF = 2 x 3 x 5 =30
  • 33. • Janice asks 100 students if they like biology or chemistry or physics best. • 38 of the students are girls. • 21 of these girls like biology best. • 18 boys like physics best. • 7 out of the 23 students who like chemistry best are girls. • Work out the number of students who like biology best. Biology Physics Chemistry Total Girls 21 10 7 38 Boys 28 18 16 62 Total 49 28 23 100
  • 34. The area of the triangle is equal to the area of the square What is the perimeter of the square Area triangle = 9 x 8 = 72÷ 2 = 36 cm2 Area square = 36 cm2 Length of each side of square = 6 cm 6 + 6 + 6+ 6 = 24 cm
  • 35. V = 3b + 2b2 Find the value of V when b = –4 s = 3d + 8 Write d in terms of s V = 3 x (-4) + 2 x (-4)2 V = - 12 + 2 x 16 V = - 12 + 32 V = 20 d → x 3 → +8 → sd ← ÷3 ← -8 ← s S – 8 = d 3
  • 36. Express the area in terms of 7cm 7cm 10cm Area = r2 = x 7 x 7 cm 2 = 49 cm 2 Volume = 4 9 x 10 = 490 cm3