Transcript Mental Maths - Bishopston Comprehensive School Moodle

GCSE - Higher
P2 Calculator
Assessment 1
Question 1
(i) Find the value of:
(give your answer to 1 dp)
Using a Calculator
7.8
12.5 – 6.8
(ii) Find the value of:
(give your answer to 3 sf)
√2.7³ – 15.3
Question 2
Standard Form
Use you calculator to work out the value of
the following, giving your answers in standard
form.
(i) 2.71 × 106 – 4.8 × 105
(ii) 3.4 × 106 ÷ 1.7 × 10-2
Question 3
Trial & Improvement
Solve by Trial & Improvement to 1dp:
x³ + 4x = 48
Question 4
% Change
A house’s value decreases from £165,000
to £130,000. Find the % decrease in its
value to the nearest %.
Question 5
% – Compound Interest
A person invests £5,000 for 3 years at a rate
of 3.75% per annum. Calculate the value of
their investment after the 3 years.
Question 6
% – Finding the Original
A leather settee is reduced in a sale by 30%.
It now costs £595. Calculate the price of the
settee before the reduction.
Question 7
Nth Term & Sequences
(i) Find the Nth term in the following sequence:
1, 4, 7, 10, 13
(ii) What would the 20th term be?
Question 8
Straight Line Graphs
Find the equation of the line that passes
through the points (-1, -1) and (3, 7).
Question 9
Mean from Grouped Data
The table shows the amount spent per
week in a supermarket by 30 families.
Calculate the mean amount spent per week.
Amount (£)
0 < x ≤ 40
40 < x ≤ 60
60 < x ≤ 80
80 < x ≤ 100
100 < x ≤ 120
Freq
3
7
12
6
2
Question 10
Pythagoras’ Theorem
Find the length of side AB, give your answer
to 1dp.
C
15 m
A
28 m
B
Question 11
Trigonometry
Find the length of side BD to 1 dp.
B
30º
D
50º
A
C
Question 12
3D Trigonometry
In the cuboid find angle GAC to 1 dp.
H
G
F
8 cm
E
A
D
C
12 cm
B
Question 13
Sine & Cosine Rules
Find side AC to 2 dp.
A
55º
65º
B
9 cm
C
Question 14
Expanding Brackets
Expand and simplify the following:
(i) 2(4x + 5) – 3(x – 2)
(ii) (x + 6)(x – 7)
Question 15
Algebraic Problem – Linear
The rectangle has a perimeter of 28 cm.
Form an equation and solve it to find x.
3x + 4
2x
Question 16
Simplify:
(i) (2 – √3 )²
Rationalise the denominator
(ii)
12
√3
Surds
Question 17
Quadratic – Forming Expressions
The rectangle has an area of 30 cm². Show
that it satisfies the equation: 2x² – 7x – 45 = 0
2x + 3
x-5
Question 18
Solve
2x² – 7x – 45 = 0
giving your answers to 2 dp.
Quadratic – Formula
Question 19
Circles
Calculate the area of the segment AOB to 1 dp.
A
65º
O
12 cm
B
Question 20
A sphere has a volume of 3000 cm³.
Calculate its radius to 2 dp.
Volume
End of
Assessment
Answers
Question 1
(i) Find the value of:
(give your answer to 1 dp)
Using a Calculator
7.8
12.5 – 6.8
1.368421053 = 1.4 (1 dp)
(ii) Find the value of:
(give your answer to 3 sf)
√2.7³ – 15.3
2.093561559 = 2.09 (3 sf)
Question 2
Standard Form
Use you calculator to work out the value of
the following, giving your answers in standard
form.
(i) 2.71 × 106 – 4.8 × 105
2,230,000 = 2.23 × 106
(ii) 3.4 × 106 ÷ 1.7 × 10-2
200,000,000 = 2 × 108
Question 3
Trial & Improvement
Solve by Trial & Improvement to 1dp:
x³ + 4x = 48
x=3
x=4
x = 3.2
x = 3.3
(3)³ + 4(3) = 39
(4)³ + 4(4) = 80
(3.2)³ + 4(3.2) = 45.568
(3.3)³ + 4(3.3) = 49.137
Closest 1 dp guess
x = 3.3
(1 dp)
too small
too big
too small
too big
Question 4
% Change
A house’s value decreases from £165,000
to £130,000. Find the % decrease in its
value to the nearest %.
% Change = Change × 100
Original
% Change = 35,000 × 100
165,000
= 21%
Question 5
% – Compound Interest
A person invests £5,000 for 3 years at a rate
of 3.75% per annum. Calculate the value of
their investment after the 3 years.
1st year
3.75 × £5000 = £187.50
100
2nd year 3.75 × £5187.50 = £194.53
100
3rd year
Value: £5187.50
Value: £5382.03
3.75 × £5382.03 = £201.83
100
Final Value: £5583.86
Question 6
% – Finding the Original
A leather settee is reduced in a sale by
30%. It now costs £595. Calculate the
price of the settee before the reduction.
100% = Original Price
70% = New Price
70% = £595
1% = £8.50
100% = £850
(595 ÷ 70)
(8.5 × 100)
Question 7
Nth Term & Sequences
(i) Find the Nth term in the following sequence:
1
2
3
4
5
Nth
1, 4, 7, 10, 13
3n – 2
(ii) What would the 20th term be?
3(20) - 2
60 - 2
58
?
Question 8
Straight Line Graphs
Find the equation of the line that passes
through the points (-1, -1) and (3, 7).
y = mx + c
c=
m=
y = 2x + 1
Question 9
Mean from Grouped Data
The table shows the amount spent per
week in a supermarket by 30 families.
Calculate the mean amount spent per week.
Amount (£)
0 < x ≤ 40
40 < x ≤ 60
60 < x ≤ 80
80 < x ≤ 100
100 < x ≤ 120
Freq
3
7
12
6
2
30
Mid
M×F
20
60
50
70
350
90
110
840
540
220
£2010
£2010
30
= £67
Question 10
Pythagoras’ Theorem
Find the length of side AB, give your answer
to 1dp.
a² + b² = h²
C
(15)² + b² = (28)²
225 + b² = 784
15 m
28 m
b² = 784 – 225
b² = 559
A
B
b = √559
= 23.6 m
(1 dp)
Question 11
Trigonometry
Find the length of side BD to 1
dp.
BC
B
28 × sin 50º = Opp
BC = 21.4
21.4
30º
D
BD
(1dp)
cos 30º = A
21.4
21.4 × cos 30º = A
50º
A
sin 50º = O
28
C
BC = 18.5
(1dp)
Question 12
3D Trigonometry
In the cuboid find angle GAC
to 1 dp.
H
G
Pythagoras
AC = 15.6
(1dp)
F
8 cm
E
8 cm
Trigonometry
tan x =
8
15.6
D
C
x = tan-1 8 ÷ 15.6
A
12 cm
B
x = 27.1º
(1dp)
Question 13
Sine & Cosine Rules
Sine Rule
Find side AC to 2 dp.
a
sin A
b
=
sin B
A
9
55º
sin 55
=
9 × sin 65
65º
B
9 cm
C
sin 55
AC = 9.96
b
sin 65
= b
(2dp)
Question 14
Expanding Brackets
Expand and simplify the following:
(i) 2(4x + 5) – 3(x – 2)
(ii) (x + 6)(x – 7)
5x +16
x² – x – 42
Question 15
Algebraic Problem – Linear
The rectangle has a perimeter of 28 cm.
Form an equation and solve it to find x.
3x + 4
10x + 8 = 28
2x
x=2
Question 16
Simplify:
(i) (2 – √3 )²
Surds
7 - 4√3
Rationalise the denominator
(ii)
12
√3
4 √3
Question 17
Quadratic – Forming Expressions
The rectangle has an area of 30 cm². Show
that it satisfies the equation: 2x² – 7x – 45 = 0
2x + 3
(2x + 3)(x - 5) = 30
x-5
Area = L × W
2x² - 10x + 3x - 15 = 30
2x² - 7x - 15 - 30 = 0
2x² - 7x - 45 = 0
Question 18
Solve
Quadratic – Formula
a=2
2x² – 7x – 45 = 0
b=–7
c = – 45
giving your answers to 2 dp.
7 ± √409
4
- b ± √b² - 4ac
2a
-- 7 ± √(-7)² - 4(2)(-45)
2(2)
+ 7 ± √49 -- 360
4
1st Soln
2nd
Soln
7 + √409 = 6.81
4
7
– √409
4
= -3.31
(2 dp)
(2 dp)
Question 19
Circles
Calculate the area of the segment AOB to 1 dp.
Area O = π × r²
A
65º
O
12 cm
B
Area AOB = 65 × π × r²
360
= 65 × π × (12)²
360
= 81.7 cm²
(1 dp)
Question 20
Volume
A sphere has a volume of 3000 cm³.
Calculate its radius to 2 dp.
Vol = 43 × π × r³
3000 = 43 ×
π × r³
3000 × 3 =
4×π
r³
r³ = 716.2
r = 716.2 = 8.95 cm (2dp)
3