Algebra Class 10

Problem 1

• Ratio of smaller square area to large square area is 1/2
• Diagram shows a circle and two squares, with the smaller square inside the larger square and the circle inscribed within the larger square.

Problem 2

• If a cosine graph is 90 degrees out of phase with a sine graph, and the cosine of 0 degrees is 1, then the cosine of 90 degrees must be zero.
• The correct statement is "sin 90 - cos 90"

Problem 3

• Quadratic equation: sum of roots = 0 and product of roots = -16
• The equation is x² - 16 = 0

Problem 4

• Different outfits possible: 5 x 5 x 5 = 125
• The woman has five pairs of shoes, five skirts and five shirts.
• One pair of shoes is black and one shirt is brown.

Problem 7

• Function: y = 0.2x/(x+1)
• For x ≥ 1, the range of the function is 0.1 ≤ y ≤ 0.2.

Problem 8

• If a + b = s, and a - b = t, then the value of ab is given by (s² - t²)/4
• The variables are a and b

Problem 9

• Range of f(x) = x² - 14x + 43 is y ≥ -6
• The range is all values of y greater than or equal to -6

Problem 10

• Overall percentage increase over four years is approximately 73%, rounded to the nearest 1%.
• Increase in the first year = 25%
• Increase in the second year = 20%
• Decrease in the third year = 20%
• Increase in the fourth year = 50%

Problem 11

• x = -2 + sqrt(3)
• x² + 4x + 7= 10

Problem 12

• Starting passenger number = 48
• Passengers on the bus from the terminal = 15

Problem 13

• The diagonal of the square, given the radius of inscribed circle r is r(2+sqrt(2))

Problem 14

• Given x + y = x² - 2xy + y². Value of (24)8 is 12

Problem 15

• Total surface area of cylindrical tube = 201.5pi

Problem 16

• Answer = 1

Problem 17

• Shaded area is 24 - 6Pi cm²
• Semi-circular shape cut-out from a rectangle

Problem 18

• The set of values for k such that y=x² crosses or touches the curve y = x² + kx + 2 is 3≤k≤5

Problem 19

• Solve the inequality x(2x+6)≤8. The answer is x≤ -4 or -1≤ x ≤ 1

Problem 20

• Area of quadrilateral AMCK is 1.25
• ABCD is a square

Problem 21

• (410^-11)(8.110^6) = 3.24*10^-4

Problem 22

• Answer is 135

Problem 23

• Area of the octagon is 9

Problem 24

• The height of the solid, which is in terms of the volume V is equal to {3V/4}, which matches option (C)

Problem 25

• The correct inequality is a < d, b < c, and a + b + c + d > 0 (I, II, and III)

Problem 26

• Area of the shape = 200

Problem 27

• Distance from school =4.5 km

Problem 28

• x = 1.0 (1.5 is one of the options, but it does not match the provided answer)

Problem 29

• Area of quadrilateral AMCK = 7/2cm² or 2.5 cm²

Problem 30

• Length of one small triangle = 5

This quiz covers various algebraic concepts including ratios, quadratic equations, functions, and trigonometric identities. Test your knowledge on the application of formulas and the analysis of graphical relationships. Perfect for students in 10th grade who are studying algebra.