Algebra quiz

The number of matchsticks needed to make n copies of the letter L is:

The expression for "5 less than x" is:

Which of the following is an equation?

The solution of the equation x + 8 = 15 is:

The perimeter of an equilateral triangle of side l is:

If n = 6, the value of 4n - 5 is:

The number of matchsticks needed to make n copies of the letter C is:

"Three times y added to 7" is written as:

The solution of 4p = 36 is:

The rule a x b = b x a for any two numbers is called the:

Write the expression for the number of matchsticks needed to make n copies of the letter F, and find the number needed for 8 copies. (2 marks)

A box has x pencils. Write expressions for the number of pencils in (i) 7 such boxes (ii) 7 boxes and 4 loose pencils. (2 marks)

Write the following expressions in words: (i) y + 9 (ii) 3m - 4. (2 marks)

Check whether the value given in brackets is a solution of the equation: (i) n + 5 = 19 (n = 14) (ii) 7n + 5 = 19 (n = 2). (2 marks)

The cost of one notebook is Rs t. Write an expression for the cost of 6 notebooks and 3 pens if one pen costs Rs 10. (2 marks)

Give two examples of rules from geometry that are written using variables, stating what each variable stands for. (2 marks)

Explain why x + 4 = 9 has only one solution among the whole numbers by testing x = 4, 5 and 6. (2 marks)

Mother has a box of n laddus. She gives 5 laddus to Sharad and 3 to Meena. Write an expression for the number of laddus left. (2 marks)

Write an equation for the statement "Twice a number decreased by 4 is 10" and find the number by trial and error. (2 marks)

Write the distributive property of multiplication over addition using variables a, b and c, and verify it for a = 3, b = 4, c = 5. (2 marks)

Solve by trial and error, showing your table of values: (i) y - 7 = 12 (ii) 3x = 27 (iii) z/5 = 8. (3 marks)

The side of a regular pentagon is s cm. Write the rule for its perimeter. Find the perimeter when s = 6 cm, and find s when the perimeter is 45 cm. (3 marks)

Find the values of the expressions when x = 3 and y = 2: (i) 5x - 2y (ii) x + y + 10 (iii) 4xy - 7. (3 marks)

A teacher distributes pencils so that each student gets 5 pencils and 3 pencils are left with her. (i) Write an expression for the total pencils if there are s students. (ii) If she had 128 pencils, form an equation and find s. (3 marks)

The number of girls in a class is 3 more than the number of boys b. (i) Write an expression for the number of girls. (ii) Write an expression for the total number of students. (iii) If the class has 41 students, find b. (3 marks)

Read the passage and answer the questions. Appu and Sarita were making patterns with matchsticks. Appu made a row of triangles joined side by side so that neighbouring triangles shared one matchstick. One triangle needed 3 matchsticks, two joined triangles needed 5 and three joined triangles needed 7. (i) How many matchsticks will four joined triangles need? (ii) Write the rule for the number of matchsticks for n joined triangles. (iii) How many joined triangles can Appu make with 41 matchsticks? (5 marks)

Read the passage and answer the questions. A shopkeeper sells biscuits in packets. Each packet holds 12 biscuits. On Monday he sold p packets and also 7 loose biscuits from an opened packet. On Tuesday he sold twice as many packets as on Monday and no loose biscuits. (i) Write an expression for the number of biscuits sold on Monday. (ii) Write an expression for the number of packets sold on Tuesday and the number of biscuits in them. (iii) If 79 biscuits were sold on Monday, form an equation and find p. (5 marks)

Read the passage and answer the questions. Raju is the son of Bala. Raju's age is r years and his father is 30 years older than him. His grandfather is twice as old as his father. (i) Write expressions for the father's age and grandfather's age. (ii) What was Raju's age 4 years ago in terms of r? (iii) If the grandfather is 80 years old, form an equation and find Raju's age. (5 marks)

Read the passage and answer the questions. The school canteen sells idli plates at Rs 15 each and dosa plates at Rs 25 each. On a particular day, x idli plates and y dosa plates were sold. (i) Write an expression for the money collected from idli plates and from dosa plates. (ii) Write an expression for the total money collected. (iii) Find the total collection if x = 20 and y = 12. (5 marks)

Read the passage and answer the questions. A rectangular garden has length that is 5 m more than its breadth. The breadth is b metres. A fence is to be built all around the garden. (i) Write an expression for the length of the garden. (ii) Write the rule for the perimeter of the garden in terms of b. (iii) If the length of fencing used is 50 m, find the breadth and length by trial and error. (5 marks)

Draw matchstick patterns of 1, 2 and 3 copies of the letter H. Count the matchsticks in each and write the rule for n copies. Use the rule to find the matchsticks needed for 9 copies, and find how many copies can be made with 54 matchsticks. Explain why the number of matchsticks is a variable while the number needed for one letter is a constant. (6 marks)

Draw a square of side l and a rectangle of length l and breadth b. Write the rules for the perimeter of each. Find the perimeter of each when l = 8 cm and b = 5 cm. If the perimeter of the square is 36 cm, form an equation for l and solve it. Explain how variables help us write a single rule for all squares. (6 marks)

Explain the difference between an expression and an equation with two examples each. Form equations for the following and solve each by trial and error: (i) the sum of a number and 12 is 20 (ii) one-third of a number is 6 (iii) 4 times a number minus 3 is 25. (6 marks)

Draw dot patterns forming rows of squares where the first figure has 4 dots, the second has 6 dots, and the third has 8 dots (two rows of dots growing by one column each time). Write the rule for the number of dots in the nth figure, find the dots in the 20th figure, and find which figure has 50 dots. (6 marks)

Write the following properties of numbers using variables: commutative property of addition, commutative property of multiplication, associative property of addition and distributive property of multiplication over addition. Verify each property for the numbers 2, 3 and 6. Explain why writing properties with variables is better than writing them with particular numbers. (6 marks)