R1 - Ratio Practice

(Part 1) TEACHING(15-20mins)                                           

1. Ratio, equivalent ratio, dividing a qty in a given ratio

(Part2) PRACTICE (35-60mins)

1. 18 : 24 =        : 4

2. 5 : 3 : 8 = 35 :        : 56

3.  1  :  1 =  3  : ____

     4     6

4. 0.6 :  5 = 24  : _____

             8

5.  ¾ : 1 ½ =  _____ : ______

6.  200g : 1kg = _______ : _______

7.  15 seconds :  30 mins :  1 hour  =  _______  :  ______  :  ______

8.  A: B = 3 :2  , A : C = 3 : 8

            B  :  C =  ______ :  ______

9.  A  :   B =  7  :  2 ,   B  :  C = 5  :  1

           A  :  B  :  C  =  ______  : _______  : _______

10.  A  :  B  =  6  :  7,  B  :  C  = 4  :  5

           A  :  B  :  C  =  ______  : _______  : _______

(II) Word Problems (25- 45 mins)                     

11. Ray and Carla shared a packet of sweets in the ratio of 2 : 7. IF there were 45 sweets in the packet, how many sweets did Carly receive?

12. A piece of rod was cut into 2 pieces in the ratio of 3 : 5. If the length of the shorter piece was 18 cm, find the length of the original piece of rod.

13. 2/5 of Ann’s saving is as much as ¼ of Joel’s saving. Find the ratio of Ann’s saving to Joel’s saving.

14.  Chan and David shared some marbles. Chan had 2/7 of the number of marbles David had. What was the ratio of the total number of marbles the boys had to the number of stickers Chan had to the number of marbles David had? (18/9/p1/s)

(1) 9:2:7 

(2) 9:7:2 

(3) 7:2:5 

(4) 7:5:2 

15.  Mat and Minah had some cookies in the ratio 5 : 2. Mat ate 38 cookies and Minah made another 43 cookies. Then Mat and Minah had the same number of cookies. How many cookies did Minah have at first? (27/p1/s)

For question 16 and 17.
The ratio of Anson's savings to Billy’s savings became 3:11 after Anson gave 1/10 of his savings to Billy. Both later spent the same amount of money at a book fair. In the end, the ratio of Anson’s savings to Billy’s savings became 1:9 and Billy had $264 more than Anson. (11/p2/s)

16. What was the ratio of Anson's savings to Billy’s savings at first?

17. How much savings did Anson had at first?

Extra
Ratio Word Problems Method

I. Solve 1-steps Word Problems 
II. Word Problems: 2 sets of ratio 
III. Word Problems: Overlap/Common-Part Ratio 

1.  Kenny’s mass is 7/3 of Lionel’s mass. The total mass of the boy is 85 kg.
(a) Find the ratio of Kenny’s mass to Lionel mass.

(b) What fraction of Kenny’s mass is Lionel’s mass?

(c) what fraction of the total mass of the boys is Kenny mass?

(d) Find Kenny’s mass.

2.*  15 mangoes cost $10. Three brothers shared the cost of 60 mangoes in the ratio 1 : 2 : 2. What was the cost for the smallest share?

3.*  Bobby has a number of 10c, 20c and 50c coins in the ratio 5 : 2 : 1. The total value of all the coins is $166. What is the total value of the 20c coin?

4.*  There are three types of cookies in a box. The ratio of the number walnut cookies to chocolate cookies is 4  :  5. The ratio of the number of raisin cookies to the total number of walnut and chocolate is 5 : 6.

What fraction of the cookies in the box are chocolate cookies?

5.*  Zoe drew three circles to form a figure. The areas of the circles were in the ratio 1 : 4: 16. She then shaded some parts of the figure as shown. What fraction of the figure was 

shaded?

6*. In the figure below, PQRS is a rectangle and QRT is a right-angled triangle with sides measuring 30 cm, 40 cm and 50 cm. The perimeter of the shaded part is 174 cm.

What is the ratio of the area of the triangle to the area of the shaded part? Give your answer in the simplest form.

TheMathbooklets Content Page 

Practice Content Page 

Ratio Answer Keys

1.         3

2.         21

3.         2

4.         25

5.         1:2

6.         1:5

7.         1:120:240

8.         1:4

9.         35:10:2

10.      24:28:35

11.      10

12.      48cm

13.      8:5

14.

15.      54

SP1-L31 Speed Practice

(Part 1) TEACHING(10-15mins)                                

1. Time,Writing speed in km/h, m/min, cm/s

2. Rate and Speed

(Part2) PRACTICE (25-40mins)

Start Time:                    End Time:              
For question 1 – 2.
The table below shows the daily payment rates for a restaurant worker. (15/p2/18f)

1. Jim worked from Tuesday to Sunday. How much was he paid?

2. If Jim was paid $110 for working 5 days continuously, which day could he have started to work?

3.  Anna swims 450m in 5 mins. Find her swimming speed in m/min.

4.   The distance between Town A and Town B is 216 km. John rides his car at a speed of 54 km/h. How long will John take to travel from Town A to Town B?

5.  A car travelled at a speed of 60 km/h for 3 ½ h. Find the distance travelled?

6.    Michael cycled at an average speed of 24 km/h. How far did he travel after cycling for 120 minutes? (10/p1/s)

(1) 5km

(2) 12 km

(3) 48 km

(4) 72 km                                                             

7.   Sharon took 10 minutes to cycle from her house to the park which was 3 km away. What was Sharon’s average speed? (18/p1/s)

For question 8 – 9.

John left Town G at 10 00 and drove to Town H at an average speed of 60 km/h. Half an hour later, Ian left Town G and drove to Town H travelling along the same route as John. He met John at a petrol station at 13 00 before reaching Town H at 1400. The petrol station was 10 km from Town H. (13/p2/s

8. Find the distance between Town G and Town H.

9. Find the average speed of Ian for the whole journey. (assuming he did not stop at the petrol station. Give your answer correct to the nearest whole number.)

10.*  A postbox is 450 m from Wendy’s house. Wendy took 10 min to walk from her house to the postbox and back again. what was her average walking speed?
Extra
1.* Tracy took ¾ h to jog 6 km. What was her average jogging speed in km/h?

2.*  Water from a tap leaks at a rate of 15 ml per min. At this rate, how much water is leaked in 2 hours? Give your answer in litres

3.*  Mary and Cindy started cycling at the same time along a 4.5 km track. Both did not change their speeds from start to finish. Mary cycled at 375 m/min. when she reached the end of the track, Cindy was 600 m behind her. What was Cindy’s cycling speed in m/min?

4.*  Danny and Elise started jogging at the same time along the route shown below. Both did not change their speeds throughout. After 35 min, Danny was at the halfway point and Elise was 300 m behind. Danny reached the end point 5 min before Elise. What was the distance of the route?

TheMathbooklets Content Page 
Practice Content Page 

Speed Answer Keys

1.         $140

2.         Tuesday

3.         90 m/min

4.         4 h

5.         210 km

6.         90 m/min

7.         3

8.         190 km

9.         74 km

AL1-L32 Algebra Practice : Notation, Algebraic Expression

(Part 1) TEACHING(15-20mins)                                         

1. Using a letter to represent a known no, notation, representation and interpretation

2. Simplify linear expression (excluding bracket)

3. Solving simple linear equation (whole number coefficient)

(Part2) Core PRACTICE (35-55mins)                 

State the algebraic expression for each of the following.

1.  Add 5 to K

2.  Y more than 8

3.  Subtract x from 12

4. 11 less than z

Find the value of each expression when p =6

5    10 p – 13

6.    12 – 4 p

                3

7.    3p + 1

         4      2

8.    7p + 9

            3

Simplify

9.    3y +4y – 2y

10.  8c + 5 – 2c -3

11.  5t + 8 – t

(II) Word Problems 

12. Find the value of 8𝑤− 3w if 𝑤= 4 (18/s/17)
                                           2

13.  What is the value of 21w – w +1 when w = 2? 

                                        10

14. *  What is the value of 10 + 3y  when y = 4?

                                                 2

For Question 15 and 16.
John has y sweet. Peter has 4 times as many sweets as John. Peter bought another 9 sweets.

15. Find the number of sweets Peter has more than John after he bought another 9 sweets in terms of y.

16. If John has 27 sweets. How many more sweet does John have than Peter?

Extra

1.  Mary had $4y. After buying some cloth at $7 per metre, she had $y left. How many metre of cloth did she buy?

2.   At a concert, there were X men and twice the number of women. During the interval, 4 men and 7 women left the concert.

(a)   How many people left during the interval?

(b)   How many people were there at the concert after the interval?

(c)   If X = 400, how many people were there at the convert after the interval?

3.*  Randy sold (4k + 1) tickets on Monday. He sold K more tickets on Tuesday than on Monday. How many tickets did he sell altogether? Give your answer in terms of k in the simplest form.

4.*  Three boys collected plastic bottles for recycling. Jona collected 2Y bottles which was half as many as what Zack collected. Zack collected 7 bottles more than Lionel. Hoe many bottle did they collect altogether? Give your answer in terms of Y in the simplest form.

5.*  Joyce had 4w apples. She ate 1 apple and gave w apples to her friend. Joyce’s sisters then ate half of the remaining apples. Hoe many apples had she left? Give your answer in terms of w in the simplest form.

6. Find the value of each expression when q = 2

a    11q – 13

b.   42 – 4q

                5

c.    9q + 27

         4

d.    14 p + 5
             7

7. State the algebraic expression.

a.  Add 2p to 10

b.  12 more than K

c. Subtract 8 from 3J

d. Y less than 4

8.  Simplify

a.  3y + 7 + y – 2

b.  4d - 5 – 2d - 3

TheMathbooklets Content Page 
Practice Content Page 

Algebra Answer Key

1.         k+5

2.         Y+8

3.         12 –x

4.         z-11

5.         47

6.         6

7.         5

8.         17

9.         5y

10.      6c + 2

11.      4t + 8

12.      26

13.      3.2

14.      60

15.      4y + 9

16.      117