KTET Paper 1: Mathematics Test - 4 - KTET MCQ

For the given pattern, general equation = 6 + 4(n - 1), where n is the number of the stage.
Therefore, in 15^th stage, number of matchsticks = 6 + 4(15 - 1) = 6 + 56 = 62

The sum of fractions can easily be calculated by taking the LCM of the denominators.
Here, all the three fractions have the same denominator, i.e., 6.
∴ (1/6) + (2/6) + (7/6)
= (1+2+7)/6= (1+2+7)/6
= 10/6
= 5/3

Given:
Length of rectangle = (4x + y)
Breadth of rectangle = (3x + y)
Formula Used:
Area of Rectangle = Length × Breadth
(x + a)(x + b) = x² + (a + b)x + ab
Calculation:
Area of Rectangle = Length × Breadth
⇒ Area of Rectangle = (4x + y) × (3x + y)
⇒ Area of Rectangle = 12x² + 7xy + y²
∴ Area of rectangle is 12x² + 7xy + y²
The correct option is 4 i.e. 12x² + 7xy + y²

Innovations in teaching of mathematics can be diversified in terms of teaching methods, educational resources and different learning processes.

He has to teach them with the help of pictorial representation which means visual representation like photography or pictures etc. Representation of an activity that stands as an equivalent of something or results in an equivalent expression or fraction, depiction, portrayal representation by drawing.

Mathematics is a subject matter of complex abstractions and mainly deals with patterns, shapes, sizes, figures, and data analysis. It is based on practical usability in all aspects of life.

• The concepts for which the proof or verification is done by experimentation or activities are better understood by learners and are retained in their brains for a longer period of time. 

If a teacher puts himself in place of the learner, then he/she may understand the conception and misconception of students easily.

By using the long division method: 
10084/ 12) 121012
12/101
96/52
48/4
The number 121012 is completely not divided by 12.
Hence, the remainder is 4.

Brainstorming process is developed by Alex F. Osborn. It is the oldest and best-known technique for stimulating creative thinking. It is the most fruitful exercise to solve complex and critical problems.

• In Brainstorming, many creative minds work together and apply their diverse thinking patterns to achieve the same learning goals. Ideas are generated spontaneously by the learners.
• It is a democratic technique of teaching in which the student is the active role player. The teacher gives one problem or topic to the entire class and allots time.
• Within the given time, the student must create ideas. The role of the teacher in this method is just to consider all the ideas and arise on conclusions based on the healthy discussion.
• It provides more ideas and views to the child as in this process thought arising in the mind of the learner is noted down for further discussion and use.
• It helps to achieve the higher order of cognitive objectives as it just demands the active participation of the child in the learning process by making them think and note the ideas in their own style. 

Hence, it could be concluded that all of the above statements are true about brainstorming.

Bus 3 takes least time as it takes= 21:55 – 16:45 = 5 hrs 10 mins.

In △ ABC,
AB = 5 cm, AC = 7 cm, ∠A = 90º
In △ DEF,
FD = 5 cm, EF = 7 cm and ∠F = 90°
Concept used:
The Side-Angle-Side theorem of congruency asserts that two triangles are congruent if two sides and the angle created by these two sides are equivalent to two sides and the included angle of another triangle.
Calculation:


In △ ABC and △ DEF,
AB = FD = 5 cm
AC = EF = 7 cm
∠A = ∠F = 90°
ΔABC ≅ ΔFDE  [S-A-S rule]
The two triangles ΔABC ≅ ΔFDE by SAS congruence rule.

Diagnostic tests are nothing but small tests based on the taught topic. These tests are usually taken to get an idea of how much the student had understood about that topic. Moreover, it also helps in knowing the gap in any children's understanding. If the student doesn't perform well then surely that student had not understood the topic correctly.
Hence, the correct answer is, 'to know the gaps in children’s understanding.'

Use option elimination here.
(1) = 12/3 = 4
2) 3.337 is equivalent to 3.34 but not equal to 3.34.
Hence, (2) is the correct choice for the question.
3) Area of square of side 10 cm = 10² = 100 cm²
Area of rectangle = 12.5 * 8 = 100 cm²
So, areas are equal.
4) 3348 m = 3 km 348 m

Procedural fluency is the ability to apply procedures efficiently, accurately, flexibly. It is the ability to build or modify procedures from other procedures. It also recognizes that which strategy or procedure is more appropriate than others. It is the ability to solve particular kinds of problems using more than one approach.
Hence, the correct answer is, 'Ability to solve particular kind of problems using more than one approach.'

Concept used:
The total angle made at the centre of the pie chart is 360° 
Calculation:
Number of students playing volley Ball = 48
Total number of students = 50 + 48 + 60 + 22 = 180
The measure of central angle representing the students playing volley Ball = (48/180) × 360° = 96° 
∴ The angle made by the volleyball playing student is 96°.

Here, the teacher is developing a lesson and taking students 'from concrete to abstract concept'.

Mathematics is always about understanding concepts. Finding clues and then using them to solve the problem is the basic way. Using different formulas according to the need and making the connection across the concepts is the final step.
It is a teacher’s duty to explore the changing nature of pedagogy and new approaches to the development of what kind of guidance will allow mathematics to be a guide rather than a gatekeeper to many career paths. So, to become a good mathematician one needs to understand, apply, and make connections across the concepts.
Hence, the correct answer is "Understand, apply and make connections across the concepts".

From a psychological point of view, the dominant model of human learning is of the child as an information processor, attempting to derive meaning from experience by subjecting it to several modes of processing like classification or categorisation of new information and relating those to the existing experiences to derive meaning. There are three main features of the human information processing system which have very direct implications for introducing young children to the world of formal mathematics.

• Learning by induction: As human beings, we appear to be very able to engage in the process of induction (inferring general rules or patterns from a range of particular cases), but relatively less well-equipped for deductive reasoning (the opposite process of inferring particular cases from the general rule). Inductive reasoning is the basic process whereby children can easily make sense of their world by classifying and categorising experience into increasingly structured conceptual structures and models.
• Limited ‘working memory’ capacity: While teaching mathematics we usually are not aware that human being has a limited capacity of processing information. For example, Miller has demonstrated from a whole range of evidence that we hold only about seven separate pieces of information in our short-term or ‘working’ memory. We know the procedures we must go through to get the answer to the second sum, and we can carry out each of the separate computations involved. What we cannot do is hold all the information in our head at once. While we are working out one part, the result of the previous computation is very likely to be forgotten. This happens all the time for children with much smaller numbers and less complicated procedures.
• Development of metacognitive awareness and control: The third general feature of the human processing system which we must consider is that it is a system that not only learns but learns how to learn. When one is aware of his/ her ways of thinking or learning, what the American psychologist has termed ‘meta-cognition’, he/she acquires more ability to control over his/her actions and learning.

It should be noted that the questions asks for 'young children', while axioms and postulates are introduced after the secondary stage.
Hence, we conclude that the human information processing system does not have an understanding of axioms and postulates which have very direct implications for introducing young children to the world of formal mathematics.

Given:
x² +  1/x² = 10
Squaring both sides,

Given that,
1 × 1 = 1
11×11=121
111×111=12321
Now,
11111 × 11111 = 123454321

For this question, The relation is given below-

Hence, Option (3) is correct.

A sharp memory is necessary to remember the mathematical formulas for different steps of calculation. Therefore, memory has an important role to play in learning of mathematics.

In the given problem, there are so many possible multiples of 24
For example, 2 × 12 = 24, 3 × 8 = 24
So, the question that has more than one answer is called an open-ended question.

In statistics, a frequency distribution is a list, table or graph that displays the frequency of various outcomes in a sample

Calculation:
Total number of students obtained marks between 12 to 18 = 9
Total number of students obtained marks between 18 to 24 = 12
∴ Total number of students obtained marks between 12 to 24 = 9 + 12 = 21

The best remedial strategy to remove errors in his writing is to provide him a worksheet with partially solved problems to complete the missing gaps.

As we know that the diagonal of a rhombus meet at 90°. So, we will be applying the Pythagoras theorem to find out the side of a rhombus and will be multiplying it by 4 and as we know all the sides of a rhombus are equal and the perimeter is equal to the sum of all sides of a figure. Let us divide the diagonal into two equal halves, i.e., 4 cm and 3 cm.
Now applying Pythagoras theorem, by taking the side of a rhombus as x cm.
(x)² = (4)² + (3)²
⇒ x² = 16 + 9
⇒ x² = 25
⇒ x = √25 = 5
Therefore, Perimeter of rhombus = 4 × 5 cm = 20 cm.

In any classroom it is not very likely that any two students learn the same thing; in the same way; at the same place. We are finally beginning to realize that in order to assist each pupil and to capitalize on his or her natural inclination to understand, we must be able not only to diagnose his or her style of learning but to accept it.

•  Each of us has a style of learning as an individual and as our own personality. These styles could be cate$orized as visual (reading), aural (listening), and physical (actively doing things).

In analytic method, we start from the result that we have to prove and obtain the result that we are given.

As 3(1/3)can be written as 10/3.
Now, dividing 10/3 by 1/6.
⇒ (10/3) ÷ (1/6)
⇒ (10/3) × (6/1)
⇒ 20
Therefore, 20, 1/6 are there in 3(1/3).
Hence, the correct answer is 20.

Mathematics learning is an enjoyable process. Children consider it a difficult, boring, and fearful subject.