September homework - Geometry

Q1.  (1)

Q2. (2)

Q3. (3)

Q4. angle x = 149 degree

Q5. angle z = 45 degree (alternate angle)

Q6. angle a = 40 degree (angle on a straight line and isoscellis triangle)

Q7. Find Angle XYZ

Angle XYZ = 180 - 20 -20 -30 -30 = 80
(sum of angles on a straight line =180)

iMaths Practise 3

1. There are 1500 pupils in upper primary in ABC school. 1/4 of the boys and 2/3 of the girls are in lower primary. 60% of the upper primary pupils are boys while the rest are the upper primary girls.

(a) What is the ratio of the total no. of boys to the total no. of girls in the school? (Express your answer in the simplest form)

(b) 900 girls in the lower primary do not wear spectacles. Of all the lower primary pupils, what is the percentage of girls who wears spectacles?


2. Peter has $8 more than Ben. Then, Peter gave 1/4 of his money to Ben. As a result, the ratio of the amount of money Peter had to the amount of money Ben became 5:7. How much money did Peter give to Ben?


3. Harry spent 1/2 of his money on some muffins and 3/5 of his remaining money on 5 pieces of cakes. Each piece of cake cost thrice as much as muffins. How many muffins did he buy?


4. The ratio of Xavier’s savings to Henry’s savings was 6:7.

Xavier and Henry shared the cost of a game set in the ratio 4:5 respectively
Xavier used 2/3 of his saving to pay for his share of the game set. Henry was left with $150 after paying for his share.

a) What was Henry's saving’s before paying for his share of the game set?

b) What was the cost of the game set?




5. There are 160 red marbles and some blue marbles in a box. If 3/8 of the blue marbles is taken out of the box and 50 new red marbles are put into the box, the ratio of the number of red marbles to the number of

blue marbles becomes 7:9. How many blue marbles are there in the box?


*6. A boutique owner bought 1.5 times as many skirts as dresses. She spent $1496 altogether. A dress costs $4 more than a skirt. The total cost of the skirts was $136 more than the total cost of the dresses. Find the cost of 2 skirts and 1 dress.

iMaths Practise 2 Solution

Q1. Case 1
X = unit + 30
Y = unit - 30

Case 2
X = unit + 30 + 18
Y = unit - 30 - 18
unit+30+18 = 4(unit-30-18)
unit+48 = 4units-192
3 units = 240
1 unit = 80
At first, X = unit+30 = 80+30=110

At first,number of beads in Box X was 110.

Q2. In the end, all 3 containers became equal.
So, P=Q=E = 162 divided by 3 = 54
R(Original) = 54 divided by 3 = 18
Q(Before giving R and after receiving from P)= 54+18x2 = 90
Q(Original) = 90 divided by 3 = 30
P(Original) = 54+30x2 = 114

Number of buttons in container P at first = 114.

Q3. In the end,
X = 115
Y = 90
2/3 of Y = 90
Y = 135
X = 115-(90÷2)=70
2/3 of X = 70
X = 70x3/2= 105
Y = 135-(70÷2) = 100
4/5 of Y = 100
Y = 125
X = 105-(100÷4) = 80

AT first, there were 80 marbles in Box X and 125 marbles in Box Y.

Q4. (7+½)x2=15
(15÷2)+½ = 8
Number of chocolate bars that the third child got = 8.

Note
1st child got 32 chocolate bars
2nd child got 16 chocolate bars
3rd child got 8 chocolate bars
4th child got 7 chocolate bars

Total = 63 chocolate bars.

Q5. Women = 1/5
Men + Children = 4/5
Men = 2/5x4/5 = 8/25
Children = 1-1/5-8/25 = 12/25
12/25 of total = 266+266x2 = 798
8/25 of total = 532

Number of men in the hall = 532.

Q6. Cloths = 5/9
Gifts = 1/3
Mother + Left = 1-5/9-1/3 = 1/9
1/9 of the total = $1500+$560 = $2060
Total for Samuel= $2060x9 = $18540

Total for Samuel and Nigel = ($18540/4)x9 = $41715

Q7. 3N + J = 40.80
       2N + 2J = 45.20 (86 - 40.80)
        J - N = 4.4
 Rewriting N as J -4.4
       3J - 13.20 + J = 40.80, J = 54/3 = 13.50

Q8. 0.7 blue + 0.7 red --> 91 (adding both)
7 blue + 7 red --> 910 (times by 10)
1 blue + 1 red --> 130 (divide by 7)

P5 - i-Maths Practise 2

1. 2 boxes X and Y, contained some beads. If 30 beads were transferred from Box X to Box Y, both boxes would have the same number of beads. If 18 beads were transferred from Box Y to Box X, Box X would have 4 times as many beads as Box Y. How many beads were there in Box X at first?





2. 3 containers P,Q and R had 162 buttons altogether. Some buttons were transferred from container P to container Q and the number of buttons in container Q becomes thrice its original number. Then some buttons were transferred fron container Q to container R and the number of buttons in container R becomes thrice its original number. As a result, the number of buttons in the 3 containers became equal. How many buttons were there in container P at first?






3. There were some marbles in X and Y. 1/5 of the marbles in Box Y were transferred to Box X. Then 1/3 of the marbles in Box X were transferred to Box Y. Finally, 1/3 of the marbles in Box Y were transferred to Box X. As a result, there were 115 marbles in Box X and 90 marbles in Box Y. How many marbles were in each box at first?






4. 4 children share a box of chocolate bars. The first child took 1/2 of the total bars of chocolate and 1/2 of a chocolate bar. The second child took 1/2 of the remaining bars and 1/2 of a chocolate bar. The third child took 1/2 of the remaining bars and 1/2 of a chocolate bar. The fourth child took the remaining 7 bars. How many bars of chocolate did the third child get?






5. 1/5 of the audience in a hall are women. 2/5 of the remaining audience are men. The rest are children. If there are 266 boys in the hall and the number of girls is twice as many as the number of boys, find the number of men in the hall.





6. The original amount of money Samuel had to the original amount of money Nigel had was 4:5.
After Samuel spent 5/9 of his money on clothing, 1/3 of it on gifts and gave $1500 to his mother, he had $560 left. What was the total amount of money both men had originally?






7. Nasir and Janice shared $86 .When Nasir spent 3/5 of his money and Janice spent 1/3 of her money,they spent $40.80 altogether.What was the sum of money that Janice received?






8. 0.2 of the blue caps and 0.5 of the red caps is equal to 38.
0.5 of the blue caps and 0.2 of the red caps is equal to 53.
What is the total number of blue and red caps?

Solution to P5 - i-Maths Practise 1

P5 - i-Maths Practice 1

1. Kathy and Diana read a total of 30 books in January. In February, Kathy read 9 books fewer than Diana who had read thrice as many as she did in January. If both of them read a total of 45 books in February, how many books did Kathy read in the 2 months?


2. Paul has some 10-cent coins and 50-cent coins. The coins add up to $10.70. If there are five more 10-cent coins than 50-cent coins, how many 10-cent coins are there?


3. There are some $5 and $2 notes in a wallet. There are 9 more $2 notes than $5 notes in the wallet. The total value of the money in the wallet is $186. What is the difference in the total amount between the $2 notes and the $5 notes?


*4. Mrs Li had some 50-cent coins and 20-cent coins in a purse. She counted 12 more 50-cent coins than 20-cent coins and the total value of 50-cent coins is $21 more than the total value of 20-cent coins.
a) How many 50-cent coins were there in the purse?
b) What was the total value of the 50-cent coins in the purse?


5. Ben has four time as many stamps as Calvin. How many stamps must Ben give to Calvin so that they each will have 130 stamps.


6. Mr Chng bought a box of pens. 1/5 of the pens were red pens and the rest were black pens. He gave away 1/2 of the red pens and 3/8 of the black pens and had 168 pens left. How many black pens were there in the box at first?


7. Mrs Priya had some buttons. She bought another 143 buttons. She divided all the buttons equally into 8 boxes. She then used 228 buttons for some blouses and gave away 1 box of buttons. If she had 409 buttons left, how many buttons did she have at first?


8. Timothy had some marbles. He gave ½ of them to Jerry and 1/8 of the remainder to Austin. His father gave him 144 marbles and then he had as many marble as he had at first. How many marbles did he have at first?


9. Jane and her friends went to a restaurant for a buffet dinner. The charge for the buffet was $24 per person and 1person dines free for every 4 paying persons. How many people were there if they paid $408 altogether?


10. The total cost of 9 similar bags and 12 similar books is $108. The total cost of 4 such bags and 4 such books is $44. Find the difference between the cost of a bag and a book?