Q&A - PSLE Math
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abc_parent:
Hi
Q16) [There is a diagram for this question. Please help if you have it]
The figure below consists of three circles. The smallest circle has centre O and radius of 4cm. The biggest circle has centre O and radius of 10cm. The diameter of the biggest circle also cuts through the centre of the medium-sized circle. The medium-sized circle touches the other two circles as shown. The three regions formed are coloured red, white and blue as shown.
(a) Find the radius of the medium-sized circle.
(b) Find the area of the white region. Use a calculator to obtain the value of pi. (Give your answer correct to 2 decimal places.)
(c) Express the area of the red region as a fraction of the area of the blue region.Ans:(a) 7cm (b) 103.67cm square (c) 16/51
For Q16, the more challenging part is finding the radius of the medium sized circle. Once a student is able to do it, the rest of the question is straightforward.
Hope this helps.
Best wishes![](\"http://farm5.static.flickr.com/4107/4998225539_8b8d80a791_b.jpg\")
http://farm5.static.flickr.com/4107/4998225539_8b8d80a791_b.jpg\">
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tianzhu:
Many thanks for teaching me about how to use above steps.
HiLer:
Q14. The diagram above, not drawn to scale, shows the dimensions of wheels of Kens bicycle. he pushed his bicycle down a slope 3m long. How many complete revolutions did the wheel make?
(sorry cant diagram)
To answer this question, you need to find the circumference of the wheel.
You may insert images by following the following steps.
1) Do a print screen of the portion you want to upload.
2) Edit using Paint. Cut out the portion of the question you want to upload.
3) Save file in pictures
4) Go to Flickr (Free sign up as member) or other storage sites. Upload file. Select biggest/medium size. Right click to copy URL of image.
5) Coming back to Kiasuparents forum, click insert image button.
Best wishes
Ler -
Ler:
Hi
Many thanks for teaching me about how to use above steps.
Yoy're welcome.
Best wishes -
abc_parent:
Refer to http://1.bp.blogspot.com/_NGNaLTzN5_U/SrxEbsPoXFI/AAAAAAAAD2M/kxImZTWdIqE/s1600-h/Maths0609SA2P2NYFractionQ06A.JPGQ6) Muthu and Beng Huat had some money. If Muthu gave Beng Huat $360. both would have an equal amount of money. If Beng Huat gave Muthu $180, Beng Huat would have 1/3 as much money as Muthu.
(a) How much money did Muthu have?
(b) How much money did Beng Huat have?abc_parent:
Refer to http://1.bp.blogspot.com/_NGNaLTzN5_U/SrxEbSHZwDI/AAAAAAAAD2E/ga95OPhLkOI/s1600-h/Maths0609SA2P2NYFractionQ09A.JPGQ9) Mr Kuah, a canteen vendor, had a container completely filled with oil. On the first day, he used 1 litre more than 1/2 of the original amount of oil in the container for his cooking. On the second day, he used 2 litres more than 1/3 of the remaining oil in the container. On the third day, he used 6 litres more than 1/7 of the oil left in the container. In the end, there were still 6 litres of oil in the container.
How many litres of oil were there in the container at first?abc_parent:
Refer to http://4.bp.blogspot.com/_NGNaLTzN5_U/SrxCC0Mik4I/AAAAAAAAD0U/JUyLNBpK1lM/s1600-h/Maths0609SA2P2NYRatioQ12A.JPG and http://www.1800-teacher.com/images/fbfiles/images/P6_160910_Ratio.jpgQ12) Given that p : (q+r)=1:3, r : (q+s)=1: 2 and p : s=2 : 5.
(a) p:q:r:s
(b) Find (r+q) : (p+s)abc_parent:
Refer to http://2.bp.blogspot.com/_NGNaLTzN5_U/SrxBdiupjrI/AAAAAAAADz0/SzuIy0v5zX0/s1600-h/Maths0609SA2P2NYSpeedQ17A.JPG.Q17)Ahmad started travelling from Town P towards Town Q at 7am. After travelling for some time, he passed Steve who was travelling at an average speed of 80km/h in the opposite direction. After travelling for another 2 hours, Ahmad reached Town Q while Steve was still 40km away from Town P.
(a) If Ahmad reached Town Q at 1pm, what was his average speed?
(b) If Steve started his journey from Town Q, at what time did he leave Town Q?abc_parent:
Refer to http://4.bp.blogspot.com/_NGNaLTzN5_U/SrxEa7u6fKI/AAAAAAAAD18/ogX5J0DWc5Q/s1600-h/Maths0609SA2P2NYFractionQ18A.JPG and http://www.1800-teacher.com/images/fbfiles/images/P6_160910.jpg.Q18)Mdm Ang bought some highlighters, pens and mechanical pencils. 1/4 of them were highlighters. The number of pens she bought was 6 more than 1/2 the total number of all the items and the remaining were mechanical pencils. Each of the highlighters, pens and mechanical pencils cost $2.10, $4.05, $1.60 respectively. She spent a total of $227. 10 on all the items. How many pens did she buy altogether?
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abc_parent:
Q6) Mrs Siva has some sweets. If she gives 5 sweets to each of her pupils, she will have 4 sweets left. If she gives 12 sweets to each of her pupils, she will need 73 more sweets. How many pupils are there?
73+4=77
12-5=7
Number of pupils = 77÷7=11abc_parent:
3+5+7+9+11+13+15+17+19+21=5x24=120Q9) Find the value of
(3 + 5 + 7 + ... + 21) / (40 + 60 + 80 + .... + 360)
40+60+80+.....+360=20( 2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18 )
=20(8x20+10)
=3400
Value of = (3 + 5 + 7 + ... + 21) / (40 + 60 + 80 + .... + 360)= 120/3400=3/85abc_parent:
BeforeQ13) The ratio of $2 notes to $5 notes in Joan's piggy bank was 13: 8. She exchanged 20 pieces of $2 notes for some $5 notes, after which, the ration of $2 notes to $5 notes became 4:5. What was the total value of $2 notes and $5 notes in the piggy bank at first?
$2 : $5
13 :8
Change
20 each of $2 notes ($40) exchanged for 8 each of $5 notes ($40).
( 13u-20 )/( 8u+8 )=4/5
33u=132
u=4
Before
Value of $2 notes = 13u = 13x4x$2= $104
Value of $5 notes = 8u = 8x4x$5=$160
Total value = $(104+160) = $264
Total value of $2 notes and $5 notes in the piggy bank at first=$264abc_parent:
Area of quarter circle inside square of 10x10=1/4x3.14x10x10=78.5 cm²Q15) [This question contains a picture. Please help if you have it.]
The figure below consists of 2 identical semicircles, a larger semicircle and a circle. The diameter of the big semicircle is 40cm. Find the shaded area. (Take pi = 3.14)
Area of A =(10x10)-78.5 = 21.5 cm²
Area of C =(10x10)-21.5-21.5=57 cm²
Area of B = (1/4x3.14x20x20)-(2x78.5+100)= 314-257=57 cm²
Shaded area = (57+57+57+57) cm² = 228 cm²
Uncle Tianzhu,
There is a better method by moving around and pls assist for the drawings when you have time.Thanks.abc_parent:
Draw a top view of the figure for visualisation and understanding.Q16) The figure below shows a solid made up of 10 identical cubes. When the solid is painted black the total area being painted is 360 cm square.
(a) What is the volume of the solid?
(b) How many more cubes must be added to change this solid into a big cube with a volume of 729 cm cube?
Painted surface
Bottom-> 6
1st layer -> 16
2nd layer -> 8
3rd layer -> 10
Total = 40 painted sides = 360 cm²
1 side -> 360 cm²÷40= 9 cm²
Square root of 9 = 3cm
(a) Total volume = 3x3x3x10 = 270 cm³
Cube root of 729= 9 cm
9÷3= 3
Number of cubes need = 3x3x3 = 27
27-10=17
(b) 17 more cubes must be added. -
abc_parent:
Q7) The figures below, X and Y, are 2 identical isoceles triangles. Both figures contain a square of a different size. Given that the area of the square in Figure X is 360 cm square, find the area of the sqaure in Figure Y.
Area of figure X = 2x360 cm²=720 cm²
Area of figure Y = 9x small triangles (Pls draw dotted lines to help you to visualise the 9 small Δs)
Area of square in figure Y= 4 small triangles
= 720÷9x4=320 cm²abc_parent:
Angle DHR =180⁰-129⁰ = 51⁰Q9) This question has a picture. Please help if you can.]The figure below is not drawn to scale. PQRS is a square and CBRD is a rectangle. BRE is a straight line. Given that angle DRF= 136 degree and angle SHD = 129, find the ratio of angle HRB to angle ERF.
Angle DHR = Angle HRB = 51⁰ (alternate angles)
Note (1): Not sure whether alternate angles are taught at P6 level or not?
Angle DRH =90⁰-51⁰=39⁰
Angle QRD =90⁰-39⁰=51⁰
Angle QRE =90⁰-51⁰=39⁰
Angle ERF=136⁰-51⁰-39⁰=46⁰
Ratio of Angle HRB to Angle ERF = 51:46
Note (2): This question had been posted by \"firebird\" before and had been solved. -
abc_parent:
Hi everyone again - please help
Is your child - DS or DD taking 2010 PSLE Exams?abc_parent:
I don't know how to control the size of the diagram in KSP forum as the diagram that I have loaded will become very big.So, it's better not to upload diagram to avoid the risk of being banned by KSP chief/mods.Q4)There is a diagram so please help if you have it
You may wish to read Uncle Tianzhu's http://www.kiasuparents.com/kiasu/forum/viewtopic.php?t=280&postdays=0&postorder=asc&start=1800 dated 17 Sep 2010 06:48 on how to insert images.abc_parent:
40-4=36Each link of a chain has an outside length of 40cm, and the metal is 4cm thick.The diagram below shows a chain which is made up of 4 links. Find the maximum length, in cm, of a chain which is made up of 10 links.
36-4=32
36x2=72
32x8=256
72+256=328
Maximum length of a chain which is made up of 10 links = 328 cmabc_parent:
Volume of 4 cubes =(4.5x24x8) cm³ = 864 cm³Q12) Figure 1 below shows a rectangular tank containing 6 cubes and filled with water to its brim. In figure 2, four cubes were removed from the same tank and the water level dropped by 4.5cm. After that, a certain amount of water was drained off the tank until the water level reaches the same height as the remaining cubes. Find the volume of water in the tank in Figure 2.
Length of a cube = cube root of (864÷4)=6 cm
Hieght of water in figure 2 = 6 cm
Volume of 2 cubes = 2x216 = 432 cm³
Volume of water in figure 2 = (6x8x24)-432=1152-432 = 720 cm³
Volume of water in the tank in figure 2 = 720 cm³abc_parent:
(a) Perimeter of shaded parts = (pix12)+13+13+10=73.699...cm= 73.70 cm (2 decimal places)Q13) The figure below is made up of 4 shaded parts formed by a circle and an isosceles triangle XYZ. The circle has a diameter of 12 cm and in the triangle XYZ, XY = XZ = 13cm and YZ = 10cm.
(a) Calculate the perimeter of the shaded parts.
(b) Calculate the difference between shaded parts 'A' and 'B'.
A+C-(B+C)
=A+C-B-C
=A+B
Area of A+C = 1/2xpix6x6= 18pi cm²
Area of B+C = 1/2x5x12= 30 cm²
Difference = 18pi-30 = 26.548..... = 26.55 cm² (2 decimal places)
(b) The difference between shaded area 'A' and 'B' = 26.55 cm² (2 decimal places)
Note
(1) Take pi as per your calculator.
(2) Area C is the unshaded area of 1/2 of the triangle XYZ.
(3) There are typo errors in your question posted here, pls refer to the original question for exact wordings. -
abc_parent:
Constant distance concept where the ratio of time is inversely proportional to ratio of speed.Constant time concept where ratio of speed is directly proportional to ratio of distance.Q17)Mr Tan took 6 h to drive from Town A to Town B. Mr Lim who started at the same time as Mr Tan, took 4 hours to drive from Town B to Town A. When they met each other, they were 48km away from the midpoit of Town A and Town B.
(a) Calculate the distance between Town A and Town B.
(b) Calculate the speed of Mr Tan.
There is an excellent posted by Uncle Dharma explaining the above concept somewhere in KSP forum but I cannot find it. Uncle Dharma - Pls help.
Ratio of time
Tan : Lim
6 : 4
Ratio of speed
Tan : Lim
4 : 6
Ratio of speed was proportional to ratio of distance->
4u+48+48=6u
2u=96
u=48
10u=480 km
(a) Distance between Town A and Town B = 480 km
(b) Speed of Mr Tan = 480km ÷6h = 80 km/habc_parent:
1/5 of J = 3/10 of B+120Q18) 20% of John's savings is $120 more than 30% of Brian's savings. After John spent 5/6 of his savings and Brian spent 1/2 of his savings, John has $20 more than Brian. Find the savings of John at first.
J=15/10 of B +600 = 1.5B+600
Before
J: 1.5u+600
B: u
After
J: 0.25u+100
B: 0.5u
0.25u+100=0.5u+20
0.25u=80
u=320
1.5u=480
480+600=1080
Savings of John at first = $1080
There is a shorter method than the above method and pls wait for others to post. -
abc_parent:
Does anyone know where to find the complete step by step solutions for SCGS Prelims. Not sure how you feel about it but I cannot do most of the questions in paper 2.
Pls post those questions in paper 2 from http://www.orlesson.org/orp/09Ma/2009-P6-Math-SA2-SCGS.pdf that you cannot do and I am sure that many people in KSP forum are willing to help you. -
abc_parent:
There's also much discussion about prelims 2010. May I know where I can find them and find the solutions?
Over http://psle2010a.blogspot.com/, http://www.onsponge.com/forum/35-thinkingmathonsponge.html and KSP forum.
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