Grade 4 Canadian Math Kangaroo Contest Sample Paper

ID : ca-4-Kangaroo [1]

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Answer Answer t he quest quest ions ions (1)

In a clock, the ho ur hand is point ing between digits digits 5 and 6, and the minute hand is po inting at 3. What is t he current current t ime? ime?

(2)

How many many triangles are there in t he f igure below? below?

(3)

What is t he minim minimum um num number of line line segments required to ma make ke letter F ?

(4 )

If

= 8,

= 28,

= 20 and

= 18,

f ind the value value of

.

Choose correct answer(s) from given choice (5)

Find Find the next f igure.

a.

b.

c.

d.

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ID : ca-4-Kangaroo [2] (6 )

If the areas o f square X and rectangle rectangle Y are same, same, then f ind the length length o f square X. Y

X

16 cm

36 cm

(7 )

a. 24 cm

b. 23 cm

c. 26 cm

d. 25 cm

The following table shows the number of ACs manufactured by two companies in 3 days. day Com Company pany A Com Company pany B

1

36

44

2

24

28

3

20

16

Whic Whichh of the f ollowing ollowing statements statements is true?

(8)

a. In the first two days Company A

In the f irst and last day Company Company A b. In

manufactured more ACs than Company B.

manufactured more ACs than Company B.

c. In 3 days Company A manufactured more

d. In the last two days Company A and

ACs t han Co mpany B.

Company B manufactured same number of ACs.

Which expression shows perimeter (Z) of the rectangle. Y

32 cm

40 cm

(9 )

a. Z = 2 X (40 X 32)

b. Z = 2 X (40 + 32)

c. Z = 2 X (40 - 32)

d. Z = 2 + (40 + 32)

Paul went to the market with $580. He bought two of the following three items, but we don't know which two. How much money will he be left with?

$31 0

$ 280

$2 90

a. 13

b. 10

c. 11

d. 8




will you you get af ter connecting co nnecting the 3 dots on grid line? line? (10) What shape will

riangle a. T riangle

b. Straight line

c. Square

d. None of these

Fill in the blanks (11) If all the English English alphabet alphabet lett ers are writt writt en in reverse reverse order, the lett er at 6th place place to the right

of letter S will be (12)

?

If

= 30,

=

(13)

Following Following shape is ma made de of several small small cubes.

f raction of cubes are not visible visible in

the picture sho wn below. below.

(14)

30 m

A cat t akes 8 ro unds o f t he f ield as sho sh o wn in t he pict ure. T he number number expressio expressio n below shows t he distance covered by the cat: 8 x P = Q m = R km Values of P, Q and R are

,

and

respect ively.

30 m

(15)

+ + + + -4 = + + + + +


= 75 =



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Answers (1)

5:15 hours Step 1

When hour hand is between 5 and 6, and minute minute hand is at 3, clock will will loo k as f ollowing,

Step 2

Since Since hour hand is af ter 5, clock is sho wing wing 5 hours Step 3

Since minute hand is at 3, clock is showing 3 × 5 = 15 minutes Step 4

T heref ore t ime ime sho shown wn by clock is is 5:15 hours



ID : ca-4-Kangaroo [6] (2)

32 Step 1

T here will will be 8 such triangles in this picture

Step 2


Step 3


Step 4


Step 5


Step 6





Step 7


Step 8

To tal number number of trianglge trianglge,, = 8 + 4 + 4 + 4 + 4 + 4 + 4 = 32

(3)

3 Step 1

We have have been asked to f ind the minim minimum um numb number er of line line segments required to ma make ke the letter F. Step 2

If we loo loo k at the letter F, we will will not ice that the lett er F can be f ormed by 3 line line segments segments.. Step 3

T heref ore, t he mini minimu mum m num number of line line segments required to ma make ke lett lett er F are 3.




44 Step 1

Let us f irst try to f ind ind the value value of each each one of

,

,

and

.

Step 2

We are to ld: Since 4

= 8. mean 8, one one

8

will mean:

4

= 2.

Step 3

Now No w remember:

=2

Step 4

Next Next we are told: t old: = 28 We can can use the above f act act to f ind the value value of one We know

= 2. So,

.

= 4 × 2 = 8.

We can now say:

+ 8 = 28

or

= 28 - 8 = 20

Since 5

= 20, o ne

will mean:

20 5

= 4.

Step 5

Now remember: remember:

= 4.

Step 6

In this way we can find: = 4 and =1 Step 7

Now itit is easy to f ind the valu valuee of by using the values of each each shape we fo und: =2

+5

+4

+4

= 2 × 2+ 5 × 4 + 4 × 4 + 4 × 1 = 4 + 20 + 16 16 + 4 [Remember: Do Do all multiplications multiplications bef ore doing additions t o make make sure your answer is right.]

= 44




d.

Step 1

We can can see t hat in each success successive ive picture, picture, the triangl t rianglee is rotat ro tat ing clock-wise. clock-wise. Step 2

Simi Similarl larly, y, the cloud is also rot ating clock-wise. Step 3

In the last picture, picture, the triangle triangle is is at the lef t- bott om. Theref ore in the next picture, picture, it sho uld be at at t he top-lef top-lef t. Step 4

Simi Similarl larlyy in last picture, the cloud is at the t op- right. T heref ore in the next picture, it sho uld be at at t he bot bot to m-right. Step 5

Therefore, the next picture will be as follows:

(6 ) a. 24 cm Step 1

From picture picture we can see t hat length and width o f rectangles are 36 cm and 16 cm respectively. Area o f rect angle, = Length × Width Widt h = 36 × 16 ⇒

= 57 6 cm2

⇒

Step 2

Since Since are of square is same as area of rectangle, rectangle, Area o f square sq uare = 576 57 6 cm2 (Length (Length of square) square)2 = 57 6 cm2 (Length of square) = √576 cm (Length (Length of square) square) = 24 cm

⇒ ⇒ ⇒




Company B manuf manuf actured same number number of ACs. ACs. d . In the last two days Company A and Company Step 1

Let us o bserve the given table and check check f or every option optio n individual individually. ly. Step 2

Company A ma manuf nuf actured 36 + 24 = 60 ACs and company company B Opt ion a: a: In the f irst two days, Company manu anuff actured actured 44 + 28 = 7 2 ACs, ACs, T his tells tells us that in the f irst t wo days days Company Company A manuf ma nuf actured f ewer ACs ACs than t han Company Company B. B. Hence Hence the given given st atement is f alse. Step 3

In the f irst and last day, Company Company A ma manuf nuf actured 36 + 20 = 56 ACs and Option b: In company B manufactured 44 + 16 = 60 ACs, This tells us that in the first and last day Company Company A manuf manuf actured f ewer ACs ACs t han Company Company B. B. Hence Hence the given stat em ement ent is f alse. Step 4 Opt ion c: c: In 3 days, Company A manufactured 36 + 24 + 20 = 80 ACs and company B

manuf actured 44 + 28 + 16 = 88 ACs, This t ells manuf ells us that in 3 days days Company A manuf manuf actured f ewer ACs ACs than t han Company Company B. Hence Hence the t he given given st atement is f alse. Step 5

In the last two days, Company Company A ma manuf nuf actured 20 + 24 = 4 4 ACs and company B Option d: In manufactured 16 + 28 = 44 ACs, This tells us that in the last two days Company A and Company Company B manuf manuf actured same number number of ACs. ACs. The stat s tat em ement ent is t rue. Step 6

So we f ound out that st atement atement d is t rue. (8)

b . Z = 2 X (40 + 32)




b . 10 Step 1

Paul Paul went went t o t he market market with $580 and and he could could buy two o f the t hree items items sshown hown to us. We We have not not been told to ld whic whichh two items did he buy. We need need to f igure this o ut. Step 2

When he went went t o t he market market and bought t wo tthings, hings, he must must have had had enough money money to buy buy both of those t hing hings. s. Step 3

Let us look at the price of the shoes carefully. Price of the shoes is $310, which is higher than the price of the other two items. If we add the price of the shoes ($310) with the price of any one of the other two items, the total money Paul would need would have been more than the t he amount amount of money he was carrying carrying.. Step 4

This means, Paul could not have bought the shoes, and he bought the shirt and the trousers. Step 5

This means, the money Paul spent = Price of the shirt + Price of the trousers = $280 + $290 = $570. Step 6

T he amount amount of money Paul Paul will will be left with = Amount Amount of money he he carried carried to the market market Amo Amo unt o f money mone y he s pent = $580 - $57 0 = $10. riangle (10 ) a. T riangle Step 1

On connecting the dots, it will look as following:

Step 2

It can be seen that this is a t riangle. riangle.




M Step 1

Let us write all Engli English sh alphabets in reverse order: ZYXWVUTSRQPONMLKJIHGFEDCBA Step 2

ZYXWVUT S RQPONMLKJIHGFEDCBA 1 2 3 4 5 6 Step 3

On counting, counting, we we f ind that the letter at the 6th place place on right right of the letter S is occupied by M. (12)

25 Step 1

It is given that value of 6 circle circle shapes is 30. Theref ore value value of one circl circlee shape = 30 ÷ 6 = 5 Step 2

Since Since now we know value value of one circle shape, we we can f ind value value of 5 circle circle shapes as, as , = 5 × 5 = 25

(13)

80

150

Step 1

Let us first count the number of cubes along the length, breadth and the height. Step 2

Along t he lengt leng t h, t here are 6 cubes, cubes , alo ng t he breadt br eadt h t here are 5 cubes, cubes , and along alo ng t he height height there are 5 cubes. Step 3

T he to tal number number of cubes in the given given box will be 6 × 5 × 5 = 150. Step 4

T here are only three f aces of the cube visible. visible. T he number number of cubes visible visible will will be equal equal to 70. Therefore the number of cubes not visible will be equal to 150 - 70 = 80. Step 5

The f raction raction o f the cubes cubes no t visibl visiblee will will be be equal equal to


80 150

.



120

9 60

0.96

Step 1

The mouse takes 8 rounds of the field, which means it covers 8 times the perimeter of the ground. So So we’ll have to f ind the perime perimeter ter f irst. Step 2

The perimeter of a shape or region is equal to the sum of its sides. For the given rectangle it’ll be: 30m + 30m + 30m + 30m = 120m. Hence P = 120m. Step 3

We’re given that Q = 8 x P, or Q = 8 x 120m, or 960m. Step 4

Also given t hat R = Q in kilo meters, meter s, and Q = 960m. Since Since 1 km = 1000m, o r 1m = 0.001km, we can say that 960m = 0.96km, 0.96km, which is t he required value of R.

(15)

54



Grade 4 Canadian Math Kangaroo Contest Sample Paper

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