Quarter 2: PT-CONJECTURES, INDUCTIVE AND DEDUCTIVE REASONING
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- Q1
Which conjecture, if any, could you make about the product of an odd integer and an even integer?
The product will be an even integer.
The product will be negative.
It is not possible to make a conjecture.
The product will be an odd integer.
30s - Q2
Eileen studied the sum of the angles in pentagons and made a conjecture.
Which conjecture, if any, did she most likely make?
The sum of the angles in a pentagonis always 360°.
It is not possibleto make a conjecture.
The sum of the angles in a pentagon is always 180°.
The sum of the angles in a pentagonis always 540°.
30s - Q3
Which conjecture, if any, could you make about the sum of two even integers and one odd integer?
It is not possibleto make a conjecture.
The sum will be an odd integer.
The sum will be an even integer.
The sum will be negative.
30s - Q4
Lila created the following table.
Based on this evidence, which conjecture might Lila make? Is the conjecture valid?
The sum of the digits of a multiple of 3 is a multiple of 6;
yes, this conjecture is valid.
The sum of the digits of a multiple of 5 is a multiple of 6;
yes, this conjecture is valid.
The sum of the digits of a multiple of 5, is a multiple of 6;
no, this conjecture is not valid.
The sum of the digits of a multiple of 3, is a multiple of 6;
no, this conjecture is not valid.
30s - Q5
Justin gathered the following evidence.
17(22) = 374 14(22) = 308 36(22) = 742 18(22) = 396
Which conjecture, if any, is Justin most likely to make from this evidence?
When you multiply a two-digit number by 22, the last and first digits of the
product are the digits of the original number.
None of the above conjectures can be made from this evidence.
When you multiply a two-digit number by 22, the first and last digits of the
product form a number that is twice the original number.
When you multiply a two-digit number by 22, the first and last digits of the
product are the digits of the original number.
30s - Q6
Which conjecture, if any, could you make about the product of two odd integers?
The product will be negative.
It is not possible to make a conjecture.
The product will be an even integer.
The product will be an odd integer.
30s - Q7
Jason createdthe following table toshow a pattern.
Jason could make any of the above conjectures, based on this evidence.
The sum of the digits of a multiple of 27 is divisible by 9.
The sum of the digits of a multiple of 27 is equal to 9.
The sum of the digits of a multiple of 27 is an odd integer.
30s - Q8
Emma works part-time at a bakery shop in Panadero. Today, the baker made 20 apple pies, 20 cherry pies, and 20 bumbleberry pies.
Which conjecture is Emma most likely to make from this evidence?
People are more likely to buy apple pie than any other pie.
People are more likely to buy bumbleberry pie than any other pie.
Each type of pie will sell equally as well as the others.
People are more likely to buy cherry pie than any other pie.
30s - Q9
Gary works at a bicycle store in Davao City. For the start of summer, the manager of the store has ordered 50 mountain bikes and 10 racing bikes.
Which conjecture is Gary most likely to make from this evidence?
Racing bikes will likely sell better than mountain bikes.
Either type of bike will sell equally well.
Mountain bikes will likely sell better than racing bikes.
It will rain all summer and no one will ride bicycles.
30s - Q10
Jessica noticed a pattern when dividing these numbers by 4: 53, 93, 133.
Determine the pattern and make a conjecture.
When the cube of an odd number that is 1 more than a multiple of 4 is divided
by 4, the decimal part of the result will be .75.
When the cube of an odd number that is 1 more than a multiple of 4 is divided
by 4, the decimal part of the result will be .25.
When the cube of an odd number that is 1 less than a multiple of 4 is divided
by 4, the decimal part of the result will be .75.
When the cube of an odd number that is 1 less than a multiple of 4 is divided
by 4, the decimal part of the result will be .25.
30s - Q11
Bill made the following conjecture:
When you add a multiple of 6 and a multiple of 9, the sum will be a multiple of 6.
Is the following equation a counterexample to this conjecture?
12 + 27 = 39 Explain.
Yes, it is a counterexample, because 39 is not a multiple of 6.
No, it is not a counterexample, because 39 is a multiple of 3.
Yes, it is a counterexample, because 39 is a multiple of 3.
No, it is not a counterexample, because 39 is not a multiple of 9.
60s - Q12
Jackie made the following conjecture.
The square of a number is always greater than the number.
Which choice, if either, is a counterexample to this conjecture?
1. 0.52 = 0.25 2. (–5)2 = 25
Neither Choice1 nor Choice 2
Choice 1 only
Choice 2 only
Choice 1 and Choice2
60s - Q13
Rosie made the following conjecture:
All polygons with five equal sides are regular pentagons.
Which figure, if either, is a counterexample to this conjecture?
Figure A only
Neither FigureA nor Figure B
Figure A and FigureB
Figure B only
60s - Q14
Sasha made the following conjecture:
All polygons with six equal sides are regular hexagons.
Which figure, if either, is a counterexample to this conjecture? Explain.
Figure B is a counterexample, because all six sides are equal and it is not a regular hexagon.
Figure A is a counterexample, because all six sides are equal and it is a regular hexagon.
Figure B is a counterexample, because all six sides are equal and it is a regular hexagon.
Figure A is a counterexample, because all six sides are equal and it is not a regular hexagon.
60s - Q15
Tashi made the following conjecture:
All polygons with equal sides are regular.
Which figure, if either, is a counterexample to this conjecture?
Figure A and FigureB
Figure A only
Figure B only
Neither Figure A nor Figure B
60s
