Practice paper for Australian NAPLAN Math exam for year 5...

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Answer Answer t he quest ions ions (1)

Jeff buys buys 91 sacks of f oo dgrains, dgrains, but has to sell it all at a loss . He sells sells it at

12

of the price price

13 he bought it at, and gets $135492. If instead, he he wants wants to make a prof prof it o f

3

o ver the price he

7 bought it at , then at what what price does does he have have to sell the whole whole lot at ? (2)

(12% (12% of 25) - (25% of 12) = ?

(3)

Find the values values of

(4 )

> 10

=7 and

< 5

.

Find the lo west natural number number which which when divided divided by 8, 4 0, 16 leaves the remainder remainder of 5 in each case.

(5)

How many many triangles are there in the f igure belo belo w?

Choose correct answer(s) from given choice (6 )

Donald buys 570 t owels, paying paying $26.50 $26.50 f or each to wel. wel. He decides decides to sell each each to wel f or $27 .50. How many towels does he have to sell at this price to completely cover his cost? a. $538

b. $550

c. $569

d. $561

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(7 )

If and

= 8,

= 26

= 4,

= 20

Find the value value of

+

+

+

a. 24

b. 21

c. 23

d. 26

(8) A square sq uare is bro b ro ken in t wo pieces .

If one piece is is as s hown above, which which is the o ther piece ?

(9 )

a.

b.

c.

d.

Find the rule rule f or pattern sho wn below, below, 195

210

2 25

24 0

a. Count ing by 15 15

b. Count ing by 50 50

c. Count ing by 5

25 d. Count ing by 25

(10) The day after tomorrow is my brother's birthday. On the same day next week is the festival of

Holi. If to day is Saturday, what what will the day af ter Ho li be? a. Sunday

b. Friday

c. Wednesday

d. Tuesday

(11) Find the missing number.

81361 , 82861 , _______ , 85861 , 87 361. a. 89361

b. 84361

c. 79361

d. 74 361 361

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Fill in the blanks (13) The s um of two numbers numbers is 12101. If one o f the addends addends is 54 23 greater greater than t he other

addend, then the larger addend is is (14) Age o f Edward is 22 years yea rs and age a ge o f Sharo n is 33 years yea rs.. The sum su m of t heir age a ge in ro r o man

numbers numbers is

.

(15) A bear is chas ch asing ing a mo use. us e.

6m

7m

8m

9m

10m

1 1m

12 m

T he bear st arts at 6 m and and jumps jumps 2 m every time. time. T he mouse s tart s at 9 m and jum jumps ps 1 m every every time. time. If they bot h start at the same same time, time, the bear would reach reach the mous e af ter

jumps. jumps.

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Answers (1)

$209690

(2)

0 Step 1

(12% of 25) = 25 × 12/100 12/100 ⇒

(12% of 25) = (12 × 25)/100 25)/100

Step 2

(25% of 12) = 12 × 25/100 25/100 ⇒

(25% of 12) = (12 × 25)/100 25)/100

Step 3

Now we can can f ind value value of required express express ion, (12% (12% of 25) - (25% of 12) = (12 × 25)/100 - (12 × 25)/100, =0

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(3)

=4 ,

=11

Step 1

The f irst st atement atement means that

is 7 more than

.

For example, their values could be: = 1,

= 8 ,or

= 2,

= 9 ,or

= 3,

= 10,

... and so on Step 2

But it is given given that

is greater than 10. T heref o re, the pos sible values values are,

= 4,

= 11 ,or

= 5,

= 12 ,or

= 6,

= 13,

... and so on Step 3

But But it is also given given that

is less than 5. Theref ore, among among the above poss ibili ibilities, ties, the

o nly po po ss ible ible value value is, =4 ,

(4 )

=11

85 Step 1

T he lowest number number which which is divisible by 8, 40, 16, is the Least Common Common Multiple (LCM (LCM)) o f 8, 40, 16 Step 2

T he LCM LCM o f 8, 40, 16 = 80. Step 3

Now we need to f ind the number number which which leaves the remainder remainder o f 5 when divided divided by these numbers. T his number should be 5 more t han the LCM. LCM. T heref o re, the required number number = LCM LCM (8, 40, 16) + 5 ⇒

= 80 + 5

⇒

= 85 85

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(5)

32 Step 1

T here will will be 8 such t riangles riangles in t his picture

Step 2

T here will will be 4 such triangles in this picture

Step 3

T here will will be 4 such triangles in this picture

Step 4

T here will will be 4 such triangles in this picture

Step 5

T here will will be 4 such triangles in this picture

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Step 6

T here will will be 4 such triangles in this picture

Step 7

T here will will be 4 such triangles in this picture

Step 8

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

(6 )

b. $550

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(7 )

c. 23 Step 1

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

,

,

and

.

Step 2

We are to ld: Since 2

= 8. mean 8, one one

will mean:

8

= 4.

2 Step 3

Now remember: remember:

=4

Step 4

Next we are told: = 26 26 We can use the above f act to f ind the value value of one We know

= 4. So,

.

= 5 × 4 = 20.

We can now say:

+ 20 = 26

or

= 26 - 20 = 6

Since 2

= 6, o ne

will mean:

6

= 3. 3.

2 Step 5

Now remember: remember:

= 3.

Step 6

In this way we we can f ind: = 2 and

=2

Step 7

Now it is easy to f ind the value value of

+

+

+

by

using the value values s o f each each shape we we f ound: + =2

+

+ +4

+ +2

=2×4+ 3+4 ×2+2×2 = 8 + 3 + 8 + 4 [Remember: Do Do all multiplications multiplications be f ore doing additions t o make make sure your answer is right.]

= 23 23

( 8)

c.

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(9 )

a. Count ing by 15 Step 1

If we obs erve the given series of numbers, numbers, every consecutive number number increases increases by 15: 210 - 195 = 15, 225 - 210 = 15, 24 0 - 225 = 15 .. ... Step 2

Hence Hence the rule f or t he given given patt ern is: count ing by 15. 15.

(10 ) d. Tuesday Step 1

It is given that today is Saturday, therefore day after tomorrow it will be Monday Step 2

Since Since my my brot her's birthday is o n Mo Mo nday, Ho Ho li will will also be o n Monday Step 3

Theref ore day af ter Holi will will be be T uesday

(11) b. 84361 Step 1

Let us subtract t he f irst number number f rom the second number: number: 82861 - 81361 = 1500 Step 2

Sim Similarl ilarly y subtract t he second number number f rom the t hird, hird, third number number f rom the f ourt h, f ourth number number from the f ift h and so on. Step 3

It is clear fro m the above steps that t here is is a dif f erence erence of 1500 between between each each cons ecutive number number in t his s eries. Hence Hence the missing number would be: 82861 + 1500 = 84361

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(12) b.

♠♠♠♠♠♠♠♠ Step 1

Loo k at the all of the f igures igures caref caref ully ully and not not ice ice that in f igure igure

♠♠♠♠♠♠♠♠ T he number number of ♠ in in selected box = 2 and the tot al num number ber of ♠ = 8 Step 2

Now the f raction raction o f the number number of ♠ in in the selected selected box t o the to tal number number of ♠ in in given given f igure igure =

2

=

8

1 4

Step 3

Therefo re the figure figure

♠♠♠♠♠♠♠♠ shows f raction raction

1

.

4

(13)

87 62 Step 1

It is given that , Smaller addend + Larger addend = 12101 Step 2

It is also given given that larger addend addend is 5423 greater t han smaller smaller addend, addend, theref ore Smaller addend + (Smaller addend + 5423) = 12101 Step 3

Using above relation we can see that if we subtract 5423 from sum, we should get double of smaller addend Step 4

2 × Smalle Smallerr addend = 12101 - 5423 2 × Smaller addend = 6678 Small Smaller er addend = 6678/2 = 3339 Step 5

Larger addend = Small Smaller er addend + 54 23 = 3339 + 5423 = 87 62

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(14)

LV Step 1

Let us f irst f ind the sum of their ages ages in numeral numeral fo rm: rm: 22 + 33 = 55 years. years. Step 2

Now we will will covert 55 into Roman numerals. numerals. Step 3

We should remember remember f ollowing basic rules to f or m Roman numerals: numerals: a. Repetition i. Repetition o f a Roman Roman numeral numeral means means addition. ii. Only I,I, X, C and M can be repeat repea t ed. iii. V, L and D can never be repeat ed. iv. No numeral can be repeated mo mo re than t hree times. times. b. Additio Additio n and Subtraction of numerals numerals i. A smalle smallerr numeral numeral writt writt en to the right o f a larger num numeral eral is is always added to t he larger numeral. ii. A smalle smallerr numeral numeral writt writt en to the lef t o f a larger num numeral eral is is always always s ubtracted f rom the larger numeral. numeral. iii. V, L and D are never subt racted. ract ed. iv. I can be subtr sub tracted acted f ro m V and X. v. X can can be subtracted f rom L and C. vi. When a smaller numeral numeral is placed between two larger larg er numerals , then th en it is always always s ubtracted f rom the larger numeral imm immediately f ollo wing wing it. vii. vii. Only a single symbol symbol can be subtracted f rom anot her single symbol. symbol. Subtraction Subtraction can not not be done with with groups of symbols. symbols. viii. viii. A symbol can can not be s ubtracted f ro m anot her one that is more more t han 10 times times greater than it. For exam e xample: ple: We can can not write write IL to convey 50 - 1 = 49 because L (50 ) is 50 times I (1). We can can no t write write LM to convey 1000 - 50 = 950 because M (1000) is 20 times L (50). Step 4

Based on the abo ve rules, we may may break the given number number into easy repeating and no nrepeating units o f Roman num numerals erals as 50 + 5. Step 5

T he roman numeral numeral f or 50 is L, L, 10 is X and 5 is is V, and since we we know that to add two Roman numerals, numerals, we write the smaller smaller numeral numeral to the right o f the larger numeral. numeral. So So 55 is LV. LV.

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(15)

3 Step 1

Af t er 1 s t jump, bear will will be at 8 and mous e will be at 10 Step 2

Af t er 2 nd jump, jump, bear will be at 10 and mous e will be at 11 Step 3

Af t er 3 rd jump, bear will be at 12 and mouse will be at 12 Step 4

T heref o re, bear will will catch mous mous e in 3 jump jumps. s.

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