GCSE MATHEMATICS Higher Tier GUIDED REVISION SHEET 1

GCSE MATHEMATICS Higher Tier
GUIDED REVISION SHEET 1
1. Express the following decimals as fractions.
a) 0.36
i i i i i
b) 0.115
c) 0.8 i .
2. Express the following decimals as fractions.
a) 0.12 i b) 0.385
i i c) 0.125
i i .
3. a) Prove that 0.46
i i = 46
99 .
*b) Hence express 0.346
i i as a fraction.
4. a) Prove that 0.28
i i = 28
99 .
i i
*b) Hence express 0.428
as a fraction.
5. Calculate the area of the segment shown in the diagram.
8 cm
O
12 cm
8 cm
6. Calculate the area of the segment shown in the diagram.
9 cm
O
14 cm
9 cm
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7. ABCD is a rhombus with side length 10 cm.
B
Angle BAD = 60 o .
10 cm
ABD is a sector of a circle with centre A.
CBD is a sector of a circle with centre C.
A
60°
C
a) Calculate the area of the triangle ABD.
b) Calculate the shaded area.
D
8. Solve the following equations, giving your answers to 2 decimal places.
a) x 2 + 6x 3 = 0 b) x 2 + 2x 5 = 0
c) x 2 8x + 1 = 0 d) x 2 4x + 2 = 0
e) 2x 2 + 4x 2 = 0 f) 3x 2 2x 2 = 0.
9. A shopkeeper normally sells his goods at 60% above cost price.
In a sale he reduces his price by 30%.
What percentage profit does the shopkeeper make on goods sold in the sale?
10. A shopkeeper normally sells his goods at 75% above cost price.
In a sale he reduces his price by 25%.
What percentage profit does the shopkeeper make on goods sold in the sale?
( + )
11.2 12.5 7.31
11. Find the greatest possible value of
.
14.2
All the numbers are given correct to three significant figures.
Write down your full calculator display.
( + )
6.2 2.5 7.9
12. Find the greatest possible value of
.
3.2
All the numbers are given correct to two significant figures.
Write down your full calculator display.
( )
18.1 12.9 7.35
13. Find the least possible value of
.
11.2
All the numbers are given correct to three significant figures.
Write down your full calculator display.
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Answers.
1. a)
36
99
b)
115
999
c)
8
9 .
2. a)
11
90
b)
382
990
or
191
495
c)
124
990
or
62
495 .
3. b)
343
990 .
4. b)
424
990
or
212
495 .
5. Angle = 97.18075578 o .
Area of sector = 54.2797305 cm 2 .
Area of triangle = 31.74901573 cm 2 .
Subtract:
area of segment = 22.5 cm 2 (1 decimal place).
6. Angle = 102.1151175 o .
Area of sector = 72.18092314 cm 2 .
Area of triangle = 39.59797975 cm 2 .
Subtract:
area of segment = 32.6 cm 2 (1 decimal place).
7. a) 43.30127019 cm 2 .
b) 18.12 cm 2 (2 decimal places).
8. a) x = 6.46 or 0.46 b) x = 0.45 or 1.45
c) x = 0.13 or 7.87 d) x = 0.59 or 3.41
e) x = 2.41 or 0.41 f) x = 0.55 or 1.22.
9. 12%.
10. 31.25.
11. 15.79372792.
12. 20.8333…
13. 8.8164222…
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GCSE MATHEMATICS Higher Tier
HOMEWORK
1. Express the following decimals as fractions.
i i
.
a) 0.2 i b) 0.126
2. a) Prove that 0.16
i i = 16
99 .
*b) Hence express 0.316
i i
as a fraction.
3. Calculate the area of the segment shown in the diagram.
10 cm
O
16 cm
10 cm
4. Solve the following equations, giving your answers to 2 decimal places.
a) x 2 + 8x 3 = 0 b) 2x 2 3x 1 = 0.
5. A shopkeeper normally sells his goods at 65% above cost price.
In a sale he reduces his price by 30%.
What percentage profit does the shopkeeper make on goods sold in the sale?
6. Find the greatest possible value of
( )
12.1 19.9 8.18
12.6
.
All the numbers are given correct to three significant figures.
Write down your full calculator display.
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Answers.
1. a)
2
9
b)
125
990
or
25
198 .
2. b)
313
990 .
3. Angle = 106.2602047 o .
Area of sector = 92.7295218 cm 2 .
Area of triangle = 48 cm 2 .
Subtract:
area of segment = 44.7 cm 2 (1 decimal place).
4. a) x = 8.36 or 0.36 b) x = 0.28 or 1.78.
5. 15.5%.
6. 11.3997012.
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