Punjab Board Class 9 Mathematics — Flashcards for Quick Revision

A: Yes, zero is a rational number. We can write it as 0/1, 0/2, 0/3, etc., where p = 0 and q ≠ 0. Since zero can be expressed as the ratio of two integers, it satisfies the definition of a rational numbe

A: Method: Write 3 and 4 with denominator 6 (5+1): 3 = 18/6 and 4 = 24/6. The five numbers between them are: 19/6, 20/6 = 10/3, 21/6 = 7/2, 22/6 = 11/3, 23/6. Simplified answers: 19/6, 10/3, 7/2, 11/3, 2

A: Method 1 - Midpoint method: Between 3/5 and 4/5, find (3/5 + 4/5)/2 = 7/10. Between 3/5 and 7/10, find (3/5 + 7/10)/2 = (6/10 + 7/10)/2 = 13/20. Between 7/10 and 4/5, find (7/10 + 4/5)/2 = (7/10 + 8/1

A: Step 1: Substitute x = 2 into p(x) Step 2: p(2) = 2(2)² + 5(2) - 3 Step 3: p(2) = 2(4) + 10 - 3 Step 4: p(2) = 8 + 10 - 3 Step 5: p(2) = 15 Answer: The value of the polynomial at x = 2 is 15

A: Step 1: Substitute x = -1 into p(x) Step 2: p(-1) = (-1)³ - 3(-1)² + 2(-1) - 5 Step 3: p(-1) = -1 - 3(1) - 2 - 5 Step 4: p(-1) = -1 - 3 - 2 - 5 Step 5: p(-1) = -11 Answer: The polynomial equals -11 w

A: Step 1: Substitute x = 3 into p(x) Step 2: p(3) = (3)² - 5(3) + 6 Step 3: p(3) = 9 - 15 + 6 Step 4: p(3) = 0 Conclusion: Since p(3) = 0, x = 3 IS a zero of the polynomial. Note: This means (x - 3) i

A: Step 1: Identify the x-coordinate - distance from y-axis along x-axis = 5 (positive, since right of y-axis) Step 2: Identify the y-coordinate - distance from x-axis along y-axis = 3 (positive, since a

A: Step 1: Check x-coordinate = -4 (negative) → 4 units to the LEFT of y-axis Step 2: Check y-coordinate = +2 (positive) → 2 units ABOVE x-axis Step 3: Determine quadrant: (-,+) = Quadrant II Answer: Poi

A: The origin is the point where the x-axis and y-axis intersect. Step 1: Distance from x-axis = 0 Step 2: Distance from y-axis = 0 Step 3: x-coordinate = 0, y-coordinate = 0 Answer: The coordinates of o