KTET Paper 1: Mathematics Test - 1 - KTET MCQ

On dividing 19,009 by 11, quotient = 1,728 and remainder = 1.
On dividing 9,090 by 11, quotient = 826 and remainder = 4.
On multiplying the remainders, we get
4 x 1 = 4

Given,
Principal (P) = ₹1000
Time (t)=1 year
Rate (r)=10% p.a.
We know, SI= (P×t×r)/100
∴ SI = (1000×1×10)/100 = ₹100
Hence, the correct answer is ₹100.

Given:
Time taken to cover 50 km is 8 hours
Speed on his foot is 4 km/h
Speed on bicycle is 10 km/h
Formula used:
Speed = Distance/Time
Calculation:
Let the distance covered on foot be x km
Distance covered by bicycle is (50 - x) km
According to question
⇒ x/4 + (50 - x)/10 = 8
⇒ (5x + 100 - 2x)/20 = 8
⇒ 3x + 100 = 160
⇒ 3x = 60
⇒ x = 20 km
∴ The distance travelled on foot is 20 km.

Use of Abacus in Class II does not help the students to write the numeral equivalent of numbers given in words 

From the given information given in the figure:
The number of cubical blocks = ?
Now, the one-centimetre cubical boxes placed horizontally = 5
Number of boxes vertically = 3
Number of cubical box slides = 3
Total number of cubical boxes =5×3×3=45

Piaget's work is based on heredity as well as variations in source, nature, and limitations of knowledge. According to Piaget, cognitive development takes place at different rates at different stages of development depending upon the understanding of how children acquire knowledge, and the nature of intelligence which can be summaries as follows:

• Sensorimotor stage: birth to 2 years
• Preoperational stage: ages 2 to 7
• Concrete operational stage: ages 7 to 11
• Formal operational stage: ages 12 and up

Teaching mathematics by mastery activity involves charts, diagrams, activities, etc.

Piaget believed that learning results from social institutions. 
So, the teacher should ask students to make group projects and take part in the group discussion. 
Because by using the group discussion and group projects methods the many students with different minds present their opinion about any lesson or topic as these are under the social institutions.

Mathematics is a study of patterns, numbers, geometrical objects, data, and information. It deals with data analysis, integration of various fields of knowledge, involves proofs, deductive - inductive reasoning, and generalizations.

• The teaching of mathematics should be done in the way, in which a student learns the best i.e., following the child-centered approach by engaging students actively in the learning.

Side of the square = 80/4 = 20 cm
Area of the square = 20 x 20 = 400 sq.cm
Length of the rectangle = 20 x 2 = 40 cm
Breadth of the rectangle = 20 cm
Area of the rectangle = 20 x 40 = 800 sq.cm
The area of rectangle exceeds the area of square by (800 - 400) = 400 sq.cm

Dividend = divisor × quotient + remainder
Given, divisor is 8 times quotient and 6 times remainder.
Given, remainder = 28
∴ Divisor = 6 × 28 = 168
Quotient = divisor/8
⇒ Quotient = 168/8 = 21
Dividend = 168 × 21 + 28
⇒ Dividend = 3556

To understand the two-dimensional shapes we need to understand their properties based on their dimensions, and then we need to develop an intuitive approach to understand the properties. So the process must begin with sorting of the different 2-d shapes followed by observing the different sides and corners and similarities & dissimilarities between them. Then we should count the sides, diagonals, etc of the different shapes given to us. Then we need to develop an intuitive approach to understand the properties and visualize the shape accordingly.
Hence, the correct statements are, 'III, I, IV, II.'

Let the first number be x.
Therefore, the other four numbers will be x+1, x+2, x+3 and  x+4.
Now, according to the question,

Therefore, the numbers will be 12, 13, 14, 15 and 16.
Hence, the mean of the smallest and the largest numbers,
m = (12+16)/2
= 28/2
= 14.

As per the question,
10 thousand = 10000
10 tens = 100
10 ones = 10×1 = 10
Now, add them:
= 10000 + 100 + 10
= 10110
Hence, the correct answer is 10110

Perimeter of rectangle = 10 cm
Area of rectangle = 4 cm2
Formula used:
Perimeter of rectangle = 2(l + b)
Area of rectangle = l × b
Where, l = length and b = breadth

The emergent phase development presents an early or novice level as a simple and tangible activity. The learner encounters an aspect of at least one essential application that is novel to them.

The NCF-2005 stated that having children develop a positive attitude towards, and a liking for Mathematics at the primary stage is as important as developing cognitive skills and concepts. General tactics of problem-solving can be taught progressively during the different stages of school: abstraction, quantification, analogy, case analysis, reduction to simpler situations.
The importance of mathematics in relation to other sciences, education, and research can not be overstressed. So, widening the skills and scopes throughout different stages and also relating it with other subjects is critical in succeeding in mathematics.
Hence, the correct answer is "Widening  the scope  of  mathematics and relating it to other subjects".

Mathematics is a subject that has numbers, patterns, shapes, objects, and statistical data as its main content. It basically deals with the complex abstractions of our daily life.​

• It is the responsibility of a teacher to connect mathematical knowledge to the real world by touching every aspect of a student's life i.e., cultural, economic, and historical, etc. so that they can learn in an effective manner.

From the above diagram, it is clear that in the year 2004, the school gives the highest percent of 95%.

By remembering the things and their patterns and the completion the creativity of the students enhances. The recognition of patterns helps students to observe and understand the properties of numbers and the operation in mathematics. They can make their own problems and patterns.

Given
Number of items = 50
Mean = 50
Formula used
Mean = sum of observation/Number of observation
Calculation
Sum of observation = 50 × 24
⇒ 1200
correct mean = (Sum of observation - wrong item included + right item)/Number of items
correct mean = (1200 - 83 - 17 + 38 + 77)/50
⇒ 1215/50
⇒ 24.3
∴ The correct mean is 24.3

In concrete operational stage, students use an object or a diagram to solve any question.

Firstly, the teacher wants the students to learn the place-value system. So the teacher starts from the system concept. Then the teacher taught the rules of subtraction and the set of rules to be followed in calculations or problem-solving operations. So by explaining this, the teacher uses the algorithm, and then the teacher taught the application of subtraction on a number that is an operation of subtraction. So, the sequence of the lesson is: 
From system concept→algorithm→operations

13 + 53 + 33 = 153
163 + 503 + 333 = 165033
1663 + 5003 + 3333 = 166500333
According to this pattern
16663 + 50003 + 33333 = 166650003333

The important role of a Mathematics teacher in a class is to act as a facilitator and help the children learn the concept.

Let us first fold the numbers to form a cube so that we can add and see whether we are getting the result as 7 or not. Starting with the first one the cube forms in the way that 3 is the opposite of 4, 1 is the opposite of 6, and 5 is the opposite of 2. Adding 3 and 4 we get 7, 1 and 6 we get 7 and also when we add 5 and 2 we get the result as 7.

Word problems in mathematics are those questions that are given in the form of statements, which, after comprehension, are solved using mathematical operations. Word problems help to develop the ability to convert real-life problems into mathematical problems and find out a solution.

The essential steps in educational diagnosis are:
i) Identifying the students who are having trouble or need help. 
ii) Locating the errors or learning difficulties. 
iii) Discovering the causal factors of slow learning.

Hundredths of 26 = 26/100 = 0.26
Now, the required sum = 26+0.26
⇒ 26.26
Hence, the correct answer is 26.26

In educational parlance, evaluation is usually considered an activity concerned with ascertaining the extent to which pupils' learning has taken place.

• Recording a pupil’s progress is an essential step to knowing the amount and pace of learning. Not only it helps us to assess pupils’ achievement but also provides information about the effectiveness of teaching methods and teaching-learning material used.