Sec 3 Na Math
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Originally posted by Darkness_hacker99:
Expand (x+2)^2
Nah. Can't
Q6a.
4x^2 + 16
= 4(x^2 + 4)
=4(x^2 [b]+ 2^2)
= 4(x + 2)(x + 2)
=4(x + 2)^2
Remember
(a^2 - b^2) = (a + b)(a - b)[/b]
It's wrong.
(a+b)^2 = a^2 + 2ab + b^2
(a-b)^2 = a^2 - 2ab + b^2 -
Q7What is the approximate surface area of a cone whose slant height is 6 inches and whose radius is 3 inches? Use the formula:
A=TTr^2 + TTrs
Q8.Which statement is correct?
27% < 1/4 (Twenty seven percent is less than one fourth)
12% = 1/8 (Twelve percent is equal to one eighth)
3 3/5 = 335% (Three and three fifths is equal to three hundred thirty five percent)
2/3 > 66% (Two thirds is greater than sixty six percent)
Q9.What is the surface area of a rectangular solid whose length is 6 centimeters, depth is is 5 centimeters, and height is 4 centimeters?
Q10.How much water will fit in an aquarium that is shaped like a box and is 10 inches high, 6 inches wide, and 14 inches long? -
Originally posted by Deadly:huh u dun make sense leh.
how come 4(x^2 + 2^2) = 4(x + 2)(x + 2)
only 4(x^2 + 4x + 2^2 = 4(x + 2)(x + 2)
Sorry it's my mistake.Originally posted by ndmmxiaomayi:Expand (x+2)^2
It's wrong.
(a+b)^2 = a^2 + 2ab + b^2
(a-b)^2 = a^2 - 2ab + b^2
I guess I am really drunk on coke.
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Q11.Which problem has an answer of 25%?
10 is what percent of 50?
25 is what percent of 75?
25 is what percent of 125?
20 is what percent of 80?
Q12.One day, a person went to horse racing area, Instead of counting the number of human and horses, he instead counted 74 heads and 196 legs. Yet he knew the number of humans and horses there. How did he do it, and how many humans and horses are there?
Q13.y = log x
If y = 10, then what is x?
Q14.What place in this world can have their temperatures Fahrenheit and Celsius equal?
Q15.You have two block of clay in cube form and the edges are 10 cm. How many spheres with a radius of 5 cm can you make with that amount of clay
Q16.A 'snooker' table (measuring 8 metres by 4m) with 4 'pockets' (measuring 0.5m and placed at diagonal slants in all 4 corners) contains 10 balls (each with a diameter of 0.25m) placed at the following coords:
2m,1m...(white ball)
...and red balls...
1m,5m... 2m,5m... 3m,5m
1m,6m... 2m,6m... 3m,6m
1m,7m... 2m,7m... 3m,7m
The white ball is then shot at a particular angle from 0 to 360 degrees (0 being north, and going clockwise).
Just to make it clear, a ball is 'potted' if at least half of the ball is in area of the 'pocket'
Assuming the balls travel indefinitely (i.e. no loss of energy via friction, air resistance or collisions), answer the following:
a: What exact angle/s should you choose to ensure that all the balls are potted the quickest?
b: What is the minimum amount of contacts the balls can make with each other before they are all knocked in?
c: Same as b, except that each ball - just before it is knocked in - must not have hit the white ball on its previous contact (must be a red instead of course).
d: What proportion of angles will leave the white ball the last on the table to be potted
This question is for my Cousin -
7) Surface area of cone = (pi X r X s) + (pi X r^2)Originally posted by FaTal.ZenGetSu:Q7What is the approximate surface area of a cone whose slant height is 6 inches and whose radius is 3 inches? Use the formula:
A=TTr^2 + TTrs
Q8.Which statement is correct?
27% < 1/4 (Twenty seven percent is less than one fourth)
12% = 1/8 (Twelve percent is equal to one eighth)
3 3/5 = 335% (Three and three fifths is equal to three hundred thirty five percent)
2/3 > 66% (Two thirds is greater than sixty six percent)
Q9.What is the surface area of a rectangular solid whose length is 6 centimeters, depth is is 5 centimeters, and height is 4 centimeters?
Q10.How much water will fit in an aquarium that is shaped like a box and is 10 inches high, 6 inches wide, and 14 inches long?
= (3.14 X 6 X 3) + (3.14 X 3^2)
= 56.52 + 28.26
= 84.78 sq inches
8 ) 1/4 X 100 = 25%
Therefore, 27% < 25% is not true.
1/8 X 100 = 12.5%
Therefore 12% = 1/8 is not true.
2/3 X 100 = 66.67%
Therefore 2/3 > 66% is true.
9) Surface area of rectangular solid = 2lw + 2lh + 2wh
= 2 X 6 X 5 + 2 X 6 X 4 + 2 X 5 X 4
= 60 + 48 + 40
= 148 sq cm
10) Volume = length X breadth X height
= 10 X 6 X 14
= 840 cubic inches -
11) 10 is x% of 50Originally posted by FaTal.ZenGetSu:Q11.Which problem has an answer of 25%?
10 is what percent of 50?
25 is what percent of 75?
25 is what percent of 125?
20 is what percent of 80?
Q12.One day, a person went to horse racing area, Instead of counting the number of human and horses, he instead counted 74 heads and 196 legs. Yet he knew the number of humans and horses there. How did he do it, and how many humans and horses are there?
Q13.y = log x
If y = 10, then what is x?
Q14.What place in this world can have their temperatures Fahrenheit and Celsius equal?
Q15.You have two block of clay in cube form and the edges are 10 cm. How many spheres with a radius of 5 cm can you make with that amount of clay
Q16.A 'snooker' table (measuring 8 metres by 4m) with 4 'pockets' (measuring 0.5m and placed at diagonal slants in all 4 corners) contains 10 balls (each with a diameter of 0.25m) placed at the following coords:
2m,1m...(white ball)
...and red balls...
1m,5m... 2m,5m... 3m,5m
1m,6m... 2m,6m... 3m,6m
1m,7m... 2m,7m... 3m,7m
The white ball is then shot at a particular angle from 0 to 360 degrees (0 being north, and going clockwise).
Just to make it clear, a ball is 'potted' if at least half of the ball is in area of the 'pocket'
Assuming the balls travel indefinitely (i.e. no loss of energy via friction, air resistance or collisions), answer the following:
a: What exact angle/s should you choose to ensure that all the balls are potted the quickest?
b: What is the minimum amount of contacts the balls can make with each other before they are all knocked in?
c: Same as b, except that each ball - just before it is knocked in - must not have hit the white ball on its previous contact (must be a red instead of course).
d: What proportion of angles will leave the white ball the last on the table to be potted
This question is for my Cousin
10 = x/100 X 50
x = 20
25 is x% of 75
25 = x/100 X 75
x = 33.33
25 is x% of 125
25 = x/100 X 125
x = 20
20 is x% of 80
20 = x/100 X 80
x = 25
The bold one is the answer
12) Let x be the number of humans, y be the number of horses
Humans - 2 legs
Horses - 4 legs
All animals - 1 head
2x + 4y = 196 - (1)
x + y = 74 - (2)
(1)/2: x + 2y = 98 - (3)
(2) - (3): -y = -24
y = 24
Sub y = 24 into (2),
x + 24 = 74
x = 74 - 24
= 50
Therefore, there are 50 humans and 24 horses
13) y = log x
10 = log x
x = log 10
= 1 (not too sure, someone check for me)
14) Maths or common sense question?
15)... I need to recall how to do first
16) Don't know -
y = log xOriginally posted by ndmmxiaomayi:13) y = log x
10 = log x
x = log 10
= 1 (not too sure, someone check for me)
10 = log x
10^10 = x
x = 100
qn 15)
total volume of clay available
= 10*10*10*2
= 2000 cm³
volume of each sphere
= 4/3*pi*5³
= approx. 523 cm³
number of sphere u can form using the clay
= 2000/523
= 3 -
who know question 16? i know it is hard
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Your cousin is at which level?
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National U Singapore
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Maths faculty I guessOriginally posted by FaTal.ZenGetSu:National U Singapore
You expect us to be able to answer that?
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anyway... i would guess for question 16, you can actually draw lines of motion to the holes to determine which is the best way to hit it
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Never mind about the Q16.
My new homework just come. A few question i dun know.
Q1.An atom of helium has a mass 6.8 * 10^-27 kilograms.
a) Express this mass in grams.Giving your answer in standard form.
b) A room contains 9*10^22 atoms of helium. Find the mass of helium in the room. Give your answer in grams as a normal decimal number.
Q2. Given that A=h(4m+h),express m in terms h and A. -
Q1a Mass in Kg = 6.8 * 10^-27Originally posted by FaTal.ZenGetSu:Never mind about the Q16.
My new homework just come. A few question i dun know.
Q1.An atom of helium has a mass 6.8 * 10^-27 kilograms.
a) Express this mass in grams.Giving your answer in standard form.
b) A room contains 9*10^22 atoms of helium. Find the mass of helium in the room. Give your answer in grams as a normal decimal number.
Q2. Given that A=h(4m+h),express m in terms h and A.
Mass in g = 6.8 * 10^-27/ 1000
= 6.8 * 10^-27-3
= 6.8 * 10^-30g
Double check please.
Q1b
1 mole of any particle have 6*10^23 particle (Avogadro Constant)
1 mol. of Helium have 6 * 10^23 atoms of Helium.
Find number of mol. of Helium:
9 * 10^22 / 6 * 10^23
= 0.15 mol.
Use this rule.
Mass = 0.15 * 4
= 0.6g
Q2.
double check please.
Chemistry: List of mole calculation
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Simplify 4/2x+2 - 1/x
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(x-1)/x(x+1)Originally posted by FaTal.ZenGetSu:Simplify 4/2x+2 - 1/x -
Should be the simplest form already unless they wanna factorise the 4 out.Originally posted by ndmmxiaomayi:If it's really 4x^2 + 16 leh?
4(x^2 + 4) ?
Cos this expression is always positive. -
4x²+16Originally posted by FaTal.ZenGetSu:Q6: Factorise the following algebraic expressions completely
(a) 4x²+16
= 4(x²+4) -
For my Sec 1 sister Express homework.
Q1.Express
(a) 0.0052785 correct to three significant figures,
(b) $478.93 correct to the nearest $10,
(c)0.02734cm^3 in mm^3
Q2. (a) Find the lowest common multiple of 54 and 60.
(b) Two athlets A and B start their long distance race together afrom the starting point of the 400-metre running track at 0655. Given that athlete A take 54s to complete one round and sthlete B take 60s to complete one round,at what time will they next meet at the starting point?
Q3 Two towns,A and B,are 27.5km apart. A cyclist leaves A at noon and rides toward B at a steady speed of 15km/h for 50 min. He then contimues the rest of his journey at a steady speed of 12km/h. Calculate the time of arrival of B.
Q4. In a hexagon,three of the angles are 123,132 and 150 and the other three angles are equal. Calculate one of the equal angles.
Q5.Slove the equation X/2 - 3/4 = 2/3 x -1.
(B) Given that p=2,q=-1 and r=0.5,calculate the value of PQ-2/R
Q6. A solid cylinder has a height of 20cm and a base of radius 14cm.Taking pie to be 22/7,calculate
A) its volume
B) its total surface area. -
Q1.Express
(a) 0.0052785 correct to three significant figures,
(b) $478.93 correct to the nearest $10,
(c)0.02734cm³ in mm³
(a) 0.00528
(b) $480
(c) 27.34mm³
Q2. (a) Find the lowest common multiple of 54 and 60.
(b) Two athlets A and B start their long distance race together afrom the starting point of the 400-metre running track at 0655. Given that athlete A take 54s to complete one round and athlete B take 60s to complete one round,at what time will they next meet at the starting point?
(a) 540
(b) 0704hrs
Q3 Two towns,A and B,are 27.5km apart. A cyclist leaves A at noon and rides toward B at a steady speed of 15km/h for 50 min. He then contimues the rest of his journey at a steady speed of 12km/h. Calculate the time of arrival of B.
2.05pm -
Q4. In a hexagon,three of the angles are 123,132 and 150 and the other three angles are equal. Calculate one of the equal angles.
Total sum of angles = 720º (6-2)×180º=720º
Angle = 105º
Q5a) Solve the equation x/2 - 3/4 = 2/3x -1.
b) Given that p=2,q=-1 and r=0.5,calculate the value of pq-2/r
(a) ½x - ¾ = 2/3x - 1
6x² - 9x = 8 - 12x Multiply by 12x
6x² + 3x - 8 = 0
x = -1.43 or 0.931
(b) -6
Q6. A solid cylinder has a height of 20cm and a base of radius 14cm.Taking pie to be 22/7,calculate
A) its volume
B) its total surface area.
Volume = 22/7×(14cm)²×20cm = 12320cm³
Surface Area 22/7×2×(14cm)² + 22/7×28cm×20cm = 2992 cm³ -
4/2x+2 - 1/x = 2/x+1 - 1/xOriginally posted by FaTal.ZenGetSu:Simplify 4/2x+2 - 1/x
= 2(x) - 1(x+1)/x(x+1)
= (2x - x -1)/x(x+1)
= (x - 1)/x(x+1) -
1a) 0.0052785 after rounding to 3 significant figures is 0.00528Originally posted by FaTal.ZenGetSu:For my Sec 1 sister Express homework.
Q1.Express
(a) 0.0052785 correct to three significant figures,
(b) $478.93 correct to the nearest $10,
(c)0.02734cm^3 in mm^3
Q2. (a) Find the lowest common multiple of 54 and 60.
(b) Two athlets A and B start their long distance race together afrom the starting point of the 400-metre running track at 0655. Given that athlete A take 54s to complete one round and sthlete B take 60s to complete one round,at what time will they next meet at the starting point?
Q3 Two towns,A and B,are 27.5km apart. A cyclist leaves A at noon and rides toward B at a steady speed of 15km/h for 50 min. He then contimues the rest of his journey at a steady speed of 12km/h. Calculate the time of arrival of B.
Q4. In a hexagon,three of the angles are 123,132 and 150 and the other three angles are equal. Calculate one of the equal angles.
Q5.Slove the equation X/2 - 3/4 = 2/3 x -1.
(B) Given that p=2,q=-1 and r=0.5,calculate the value of PQ-2/R
Q6. A solid cylinder has a height of 20cm and a base of radius 14cm.Taking pie to be 22/7,calculate
A) its volume
B) its total surface area.
1b) $478.93 to the nearest $10 is $479
1c) 1cm^3 = 1000mm^3
0.02734cm^3 = 1000 X 0.02734
= 27.34mm^3
2a) LCM of 54 and 60 = 540
2b) LCM of 54 and 60 = 540
0655 + 540 = 0704
3) Distance covered in 1st 50 minutes = 50/60 X 15
= 12.5km
Distance left to cover = 27.5 - 12.5
= 15km
Time taken for 2nd part of journey = Distance/Speed
= 15/12
= 1.25h
Total time taken = [60 + (0.25 X 60)] + 50
= 75 + 50
= 125 minutes
= 2h 5 min
Arrival time = 1200h + 2h 5min
= 1405h
4) (720 - 123 - 132 - 150)/3 = 105
5a) X/2 - 3/4 = 2/3 x -1
(2x - 3)/4 = 2/(3x - 1)
(3x - 1)(2x - 3) = 8
6x^2 - 7x + 3 = 8
6x^2 - 7x - 5 = 0
(2x + 1)(3x - 5) = 0
x = -1/2 or x = 5/3
5b) PQ - 2/R = 2(-1) - 2/0.5
= -2 - 1
= -3
6a) Volume of cylinder = pi X r X r X h
= 22/7 X 14 X 14 X 20
= 12320 cubic cm
6b) Surface area of cylinder = (2 X r X r X pi) + (2 X pi X r X h)
= (2 X 14 X 14 X 22/7) + (2 X 22/7 x 14 X 20)
= 1232 + 1760
= 2992 sq cm
Edit: corrected errors
Thanks to tammy. -
paiseh.Originally posted by ndmmxiaomayi:3) Distance covered in 1st 50 minutes = 50/60 X 15
= 12.5km
Distance left to cover = 27.5 - 12.5
= 15km
Time = Distance/Speed
= 15/12
= 1.2h -
My careless mistake!Originally posted by ^tamago^:paiseh.