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ML Aggarwal Class 6 Solutions Chapter 10 Basic Geometrical Concept Ex 10.3 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 10 Basic Geometrical Concept Ex 10.3

Question 1.
Draw rough diagrams to illustrate the following:
(i) open simple curve
(ii) closed simple curve
(iii) open curve that is not simple
(iv) closed curve that is not simple.
Solution:

Question 2.
Consider the given figure and answer the following questions:
(i) Is it a curve?
(ii) Is it a closed curve?
(iii) Is it a polygon?

Solution:

Question 3.
Draw a rough sketch of a triangle ABC. Mark a point P in its interior and a point Q in its exterior. Is the point A in its exterior or in its interior?
Solution:

Question 4.
Draw a rough sketch of a quadrilateral PQRS. Draw its diagonals. Name them.
Solution:

Question 5.
In context of the given figure:
(i) Is it a simple closed curve?
(ii) Is it a quadrilateral?
(iii) Draw its diagonals and name them.
(iv) State which diagonal lies in the interior and which diagonal lies in the exterior of the quadrilateral.

Solution:

Question 6.
Draw a rough sketch of a quadrilateral KLMN. State,
(i) two pairs of opposite sides
(ii) two pairs of opposite angles
(iii) two pairs of adjacent sides
(iv) two pairs of adjacent angles.

Solution:

ML Aggarwal Class 6 Solutions Chapter 10 Basic Geometrical Concept Ex 10.2 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 10 Basic Geometrical Concept Ex 10.2

Question 1.
How many angles are shown in the following figure? Name them.

Solution:

Question 2.
In the given figure, name the point(s)
(i) In the interior of ∠DOE
(ii) In the exterior of ∠EOF
(iii) On ∠EOF

Solution:

Question 3.
Draw rough diagrams of two angles such that they have
(i) One point in common.
(ii) Two points in common.
(iii) One ray in common.
Solution:

ML Aggarwal Class 6 Solutions Chapter 10 Basic Geometrical Concept Ex 10.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 10 Basic Geometrical Concept Ex 10.1

Question 1.
How many lines can be drawn through a given point?
Solution:

Question 2.
How many lines can be drawn through two distinct given points?
Solution:

Question 3.
How many lines can be drawn through three collinear points?
Solution:

Question 4.
Mark three non-collinear points A, B and C in your note-book. Draw lines through these points taking two at a time and name these lines. How many such different lines can be drawn?
Solution:

Question 5.
Use the figure to name :
(i) Five point
(ii) Aline
(iii) Four rays
(iv) Five line segments

Solution:

Question 6.
Use the figure to name:

(i) Line containing point E.
(ii) Line passing through A.
(iii) Line on which point O lies.
(iv) Two pairs of intersecting lines.
Solution:

Question 7.
From the given figure, write

(i) collinear points
(ii) concurrent lines and their points of concurrence.
Solution:

Question 8.
In the given figure, write

(i) all pairs of parallel lines.
(ii) all pairs of intersecting lines,
(iii) concurrent lines.
(iv) collinear points.
Solution:

Question 9.
Count the number of line segments drawn in each of the following figures and name them:

Solution:

Question 10.
(i) Name all the rays shown in the following figure whose initial points are A, B and C respectively.

(ii) Is ray AB different from ray AD?
(iii) Is ray CA different from ray CE?
(iv) Is ray BA different from ray CA?
(v) Is ray ED different from ray DE?
Solution:

Question 11.
Consider the following figure of line \(\overleftrightarrow { MN } \). Says whether following statements are true or false in context of the given figure.

(i) Q, M, O, N and P are points on the line
\(\overleftrightarrow { MN } \).
(ii) M, O and N are points on a line segment
\(\overline{\mathrm{MN}}\).
(iii) M and N are end points of line segment
\(\overline{\mathrm{MN}}\) .
(iv) O and N are end points of line segment
\(\overline{\mathrm{OP}}\).
(v) M is a point on the ray \(\overline{\mathrm{OP}}\).
(vi) M is one of the end points of line segment
\(\overline{\mathrm{QO}}\).
(vii) Ray \(\overrightarrow { OP } \) is same as ray
\(\overrightarrow { OM } \).
(viii)Ray \(\overrightarrow { OM } \) is not opposite to ray
\(\overrightarrow { OP } \).
(ix) Ray \(\overrightarrow { OP } \) is different from ray
\(\overrightarrow { QP } \).
(x) O is not an initial point of ray \(\overrightarrow { OP } \).
(xi) N is the initial point of \(\overrightarrow { N } \) and
\(\overrightarrow { NM } \).
Solution:

ML Aggarwal Class 6 Solutions Chapter 9 Algebra Objective Type Questions for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 9 Algebra Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) In algebra, we use …………… to represent variables (generalized numbers).
(ii) A symbol or letter which can be given various numerical values is called a ……………
(iii) If Jaggu’s present age is x years, then his age 7 years from now is ……………
(iv) If one pen costs ₹X x, then the cost of 9 pens is ……………
(v) An equation is a statement that the two expressions are ……………
(vi) Trial an error is one of methods to obtain …………… of an equation.
(vii) 7 less than thrice a number y is ……………
(viii) If 3x + 4 = 19, then the value of x is ……………
(ix) The number of pencils bought for ₹ x at the rate of ₹2 per pencil is ……………
(x) In the expression (-7)⁵, base = …………… and exponent = ……………
(xi) If base = 6 and exponent = 5, then the exponential form = …………… .
Solution:

Question 2.
State whether the following statements are ture (T) or false (F):
(i) If x is variable then 5x is also variable.
(ii) If y is variable then y – 5 is also variable.
(iii) The number of angles in a triangle is a variable.
(iv) The value of an algebraic expression changes with the change in the value of the variable.
(v) If the length of a rectangle is twice its breadth, then its area is a constant.
(vi) An equation is satisfied only for a definite value of the variable.
(vii) If x toffees are distributed equally among 5 children, then each child gets 5x toffees.
(viii) t minutes are equal to 60 t seconds.
(ix) If x is a negative integer, then -x is a positive integer.
(x) x = 5 is a solution of the equation 3x + 2 = 13.
(xi) 2y- 7 > 13 is an equation.
(xii) ‘One third of a number x added to itself gives 8’ can be expressed as \(\frac{x}{3}\) + 8 = x.
(xiii)The difference between the ages of two sisters Lata and Asha is a variable.
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 19):
Question 3.
I think of a number x, add 5 to it. The result is then multiplied by 2 and the final result is 24. The correct algebraic statement is
(a) x + 5 × 2 = 24
(b) (x + 5) × 2 = 24
(c) 2 × x + 5 = 24
(d) x + 5 = 2 × 24
Solution:

Question 4.
Which of the following is an equation?
(a) x + 5
(b) 7x
(c) 2y + 3 = 11
(d) 2p < 1
Solution:

Question 5.
If each matchbox contains 48 matchsticks, then the number of matchsticks required to fill n such boxes is
(i) 48 + n
(b) 48 – n
(c) 48 ÷ n
(d) 48n
Solution:

Question 6.
If the perimeter of a regular hexagon is x metres, then the length of each of its sides is
(a) (x + 6) metres
(b) (x – 6) metres
(c) (x ÷ 6) metres
(d) (6 ÷ x) metres
Solution:

Question 7.
x = 3 is the solution of the equation
(a) x + 7 = 4
(b) x + 10 = 7
(c) x + 7 = 10
(d) x + 3 = 7
Solution:

Question 8.
The solution of the equation 3x – 2 = 10 is
(a) x = 1
(b) x = 2
(c) x = 3
(d) x = 4
Solution:

Question 9.
The operation not involved in forming the expression 5x + \(\frac{5}{x}\) from the variable x and number 5 is
(a) addition
(b) subtraction
(c) multiplication
(d) division
Solution:

Question 10.
The quotient of x by 3 added to 7 is written as

Solution:

Question 11.
If there are x chairs in a row, then the number of persons that can be seated in 8 rows are
(a) 64
(b) x + 8
(c) 8x
(d) none of these
Solution:

Question 12.
If Arshad earns ₹ x per day and spends ₹ y per day, then his saving for the month of March is
(a) ₹(31x – y)
(b) ₹31(x – y)
(c) ₹31 (x + y)
(d) ₹31 (y – x)
Solution:

Question 13.
If the length of a rectangle is 3 times its breadth and the breadth is x units, then its perimeter is
(a) 4x units
(b) 6x units
(c) 8x units
(d) 10x units
Solution:

Question 14.
Rashmi has a sum of ₹ x. She spend ₹800 on grocery, ₹600 on cloths and ₹500 on education and received as ₹200 as a gift. How much money (in ₹) is left with her?
(a) x – 1700
(b) x – 1900
(c) x + 200
(d) x – 2100
Solution:

Question 15.
For any two integers a and b, which of the following suggests that the operation of addition is commutative?
(a) a × b = b × a
(b) a + b = b + a
(c) a – b = b – a
(d) a + b > a
Solution:

Question 16.
In \(\left(\frac{3}{4}\right)^{5}\), the base is
(a) 3
(b) 4
(c) 5
(d) \(\frac{3}{4}\)
Solution:

Question 17.
a × a × b × b × b can be written as
(a) a²b³
(b) a³b²
(c) a³b³
(d) a⁵b⁵
Solution:

Question 18.
(-5)² × (-1)³ is equal to
(a) 25
(b) -25
(c) 10
(d) -10
Solution:

Question 19.
(-2)³ × (-3)² is equal to
(a) 6⁵
(b) (-6)⁵
(c) 72
(d) -72
Solution:

ML Aggarwal Class 6 Solutions Chapter 9 Algebra Ex 9.5 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 9 Algebra Ex 9.5

Question 1.
State which of the following are equations with a variable. In case of an equation with a variable, identify the variable.
(i) 17 + x = 5
(ii) 2b – 3 = 7
(iii) (y – 7) > 5
(iv) \(\frac{9}{3}=3\)
(v) 7 × 3 – 19 = 2
(vi) 5 × 4 – 8 = 31
(vii) 2p < 15
(viii) 7 = 11 × 5 – 12 × 4
(ix) \(\frac{3}{2} q=5\)
Solution:

Question 2.
Solve each of the following equations :
(i) x + 6 = 8
(ii) 2 – x = 5
(iii) 4x = -6
(iv) \(\frac{x}{2}=5\)
(v) 2y – 3 = 2
(vi) 4 – 5y = 2
Solution:

Question 3.
Solve the following linear equations:
(i) 5(x + 1) = 25
(ii)2(3x – 1) = 10
(iii) \(\frac{3 x-1}{4}=11\)
Solution:

Question 4.
Solve the following linear equations:

Solution:

Question 5.
Solve the following equations and verify your answers:
(i) 3(x + 7) = 18
(ii) 2(x- 1) = x + 2
(iii) \(3 x-\frac{1}{3}=2\left(x-\frac{1}{2}\right)+5\)
(iv) 4(2x – 1) -2(x – 5) = 5(x + 1) + 3
Solution: