Math term 2 Flashcards
Calculate 56-32+78
102
reciprocal of 4/5
5/4
reciprocal of 2
1/2
the lowest temperature recorded at scott base in antartica is -57°C. The highest temperature recorded at Scott base is 63.8°C more than this.
Whats the highest temperature recorded at Scott base
-57°C + 63.8°C = 6.8°C
The lowest temperature recorded in a town is -45°C. The highest temperature recorded there is 58.5°C more than this.
What is the highest temperature recorded in the town?
Highest temperature = -45°C + 58.5°C = 13.5°C
Rashid changes 30,000 rupees to dollars when the exchange rate is $1=68.14 rupees. How many dollars does he recieve
Dollarsreceived
Dollarsreceived=
Exchangerate
Rupees
Substitute the given values:
30
,
000
68.14
≈
440.23
Dollarsreceived=
68.14
30,000
≈440.23
IN a class of 30 students, 18 study mathematics, 15 study science and 10 study both subjects
(i) how many students study only mathematics?
(ii) how many study only science
(iii) how many study neither subjects.
(i) (M∖S)=18−10=8
(ii) (S∖M)=15−10=5
(iii) 18+15−10=23
Now:
𝑛
(
Neither
)
=
30
−
23
=
7
n(Neither)=30−23=7
Express 84 as a product of its prime factors.
84=2*
2
×3×7
Find the HCF and LCM of 24 and 36
Factorsof24:1,2,3,4,6,8,12,24
Factorsof36:1,2,3,4,6,9,12,18,36
Commonfactors:1,2,3,4,6,12
The highest common factor is 12.
HCF = 12
Multiplesof24:24,48,72,96,120,144
Multiples of 36: 72 108 144 180
LCM = 72
(i) Factorise the expression x²-5x+6=0
(ii) Hence solve the equation
(i) we need to find two numbers that multiply to 6 and add up to -5.
The numbers that work are -2 and -3
Thus factories to (x-2)(x-3)=0
(ii) x−2=0
x=2x = 2x=2
x−3=0x - 3 = 0x−3=0
x=3x = 3x=3
Factorise 3x²+11x-4
(3x−1)(x+4)
The population of town P increased from 20,000 to 25000 in one year. What is the percentage increase?
20000/25000 × 100
5000/20000 × 100
0.25×100 = 25%
The population of town Q increased from 15,000 to 18,000 in one year. What is the percentage increase?
18,000−15,000=3,000
Percentage Increase =
3,000/15,000 × 100
0.2 × 100 = 20%
A jacket originally costs $80. During a sale it is offered at a 25% discount what is the price of the jacket after the discount ?
25/100 × 80
= 0.25 × 80
= 20
80-20= $60
A watch costs $120 the price increase by 20% what is the new price of the watch ?
20/100 × 120
= 0.2×120= 24
120+24= $144
Emily invests 2500 at an annual interest rate of 6% for 3 years. How much money will she collect at the end of 3 years ?
A=(1+r/100×3)
2500 (1+6/100×3)
= 2500 (1+0.18)
= 2500 × 1.18
= $2950
If mike earns $15 per hour for his work how much does he earn if he does work for 2 hours and 45 minutes
45 minutes = 45/60 = 0.75 hours
2+ 0.75= 2.75
15× 2.75 = 41.25
Factorise the expression 12m+18n-8p-6q
(12m+18n)-(8p-6q)
6(2m+3n)-2(4p+3q)
The following ages of 10 students of Cambridge class
22,25,30,22,25,28,30,25,22,30
Find the mean and range and median too
What is the modal age of the classroom
Range is 30-22= 8
Median is 25+25/2= 25
Mean is 259/10= 25.9
The modal age of the classroom is 22,25,30
Expand and simplify 5(x+4)-2(x-4)
5x+20-2x+8
Combine like terms
5x-2x+20+8
Group them
(5x-2x)(+20+8)
3x+28
Expand and simplify (x+7)(4+x)
4x+x²+28+7x
x²+4x+7x+28
x²+(4x+7x)+28
x²+11x+28
Expand and simplify (x+3)(2+x)
2x+x²+6+3x
x²+(2x+3x)+6
x²+5x+6
Imran invests $1200 at annual si please interest rate of 5%. How much money does he collect after 3 years?
A= (1+r/100×t)
A= 1200(1+5/100×3)
A= 1200 ( 1+ 0.15)
A= 1200 × 1.15
A= $1380
If midoriya earns $15 per hour for his work, how much does he earn if he does a work for 2 hours and 34 minutes?
34/60
0.56+2= 2,56
= 2.56×15
= 38.4
Factorise the expression; 18y-3ay+12x-2ax
(18y-3ay)= 3y(6-a)
(12x-2ax)= 2x(6-a)
3y(6−a)+2x(6−a)
(3y+2x)(6-a)
Given the formula A=P(1+rt)
Make t the subject of the formula.
A=p(1+rt)
A=p+prt
A-p/pr=prt/pr
t=A-p/pr
Write 0.8 as a fraction.
8/10
Write 28% as a decimal.
0.28
Write 55% as decimal
0.55
Write 4876 to the nearest hundred
4900
The diagram shows a rectangle with a length of 5x+3 and a width of 2x-4 find an expression for the perimeter of the rectangle.
(1)Given that the perimeter of the rectangle is 38 cm find the value of x and use it to find the area of the rectangle
P=2(L+W)
P= 2 (5x+3+2x-4)
P= 2(5x+2x+3-4)
P= 2 (7x-1)
P= 14x-2
(1) 14x-2=38
14x=40 since you add the 2
So divide both sides with 14
So x= 40/14 which is 2.87
3^-2×3^x=81 find the value of x
3^-2+x=3^4
-2+x=4
x=4+2
=6
4^x+1×4^2=256
x=1
At the end of the day, a shopkeeper has 18 apples left. This is 7/20 of the number he had at the beginning of the day.
Find total number of apples
20/7 × 18= 51.43 apples
The volume of a cylinder is 1970cm³
The height of the cylinder is 12.8cm
Calculate the radius of the cylinder
V=πr²h
r²=V/πh
r²= 1970/ 3.14×12.8
r²= 1970/ 40.192
r²= 49.01
r= square root of 49.01
= 7cm
The volume of a cylinder is 2500 cm³, and the radius is 5 cm. Calculate the height
31.85cm
radius of a cylinder is 7 cm, and the height is 10 cm. Calculate the volume.
Use the formula
1538.6cm³
