Page 113 - Math_Genius_V1.0_C7_Flipbook

E:\Working\Focus_Learning\Math_Genius-7_(12-11-2024)\Open_File\05_Chapter\05_Chapter
\ 28-Jan-2025 Surender Prajapati Proof-5 Reader’s Sign _______________________ Date __________

2. Express the following statements mathematically.

(a) 5 more than y (b) 3 less than z
(c) product of 4 and x (d) dividing 6 by n
(e) 4 times of z (f) 4 is added to 3 times x
(g) 11 is subtracted from the sum of y and z (h) Product of x and the sum of 7 and y

(i) Difference of 5 times of x and 4 times y (j) Quotient of the sum of z and 4 by 3
(k) Divide the product of a and b by the sum of c and 2
(l) Quotient of x by y is added to the product of y and z

(m) y is multiplied by (–8) and then 5 is added to the result
3. Translate each of the following algebraic expressions into statements.
7
(a) 3x + y (b) 4 × (a + b) (c) 100 – 2xy (d)
a 5 − x
(e) 11 (f) b – 4ac
2
b
4. Change the following statements using expressions into statements in ordinary language.
(For example, Salim scores r runs in a cricket match, Nalin scores (r + 15) runs. In ordinary language
– Nalin scores 15 runs more than Salim.)

(a) A notebook costs `p. A book costs `3p.
(b) Tony puts q marbles on the table. He has 8q marbles in his box.
(c) Our class has n students. The school has 20n students.
(d) Jaggu is z years old. His uncle is 4z years old and his aunt is (4z – 3) years old.

(e) In an arrangement of dots there are r rows. Each row contains 5 dots.
5. Sneha scored 85 marks in Maths, x marks in Science and y marks in English. If she gets 350 marks
in four subjects, then how many marks did she get in Hindi?
6. The perimeter of an equilateral triangle is given as ‘3 × length of its each side’. If the length of each
side of an equilateral triangle is a units, and the perimeter of the triangle is denoted by P, then write
the rule for the perimeter of the equilateral triangle.

7. The diameter of a circle is given as ‘2 × radius of the circle’. If the radius of circle is r units, and the
diameter of the circle is denoted by D, then write the rule for the diameter of the circle.

8. Perimeter of a triangle is found by the formula P = a + b + c, where a, b and c are the sides of the
triangle. Write the rule that is expressed by this formula in words.

9. The side of a regular hexagon is denoted by l. Express the perimeter of the hexagon using l.
10. A cube is a three-dimensional figure. It has six faces and all of them are identical squares. The length
of an edge of the cube is given by l. Find the formula for the total length of the edges of a cube.
11. Take Ruhi’s present age to be x years.

(a) What will be her age after 5 years from now?
(b) What was her age 3 years back?
(c) Ruhi’s grandfather is 6 times her age. What is the age of her grandfather?
(d) Grandmother is 2 years younger than grandfather. What is grandmother’s age?

(e) Ruhi’s father’s age is 5 years more than 3 times Ruhi’s age. What is her father’s age?

111 Introduction to Algebra