Statistics – Mathematical Tools (Line Equation, Slope) Quiz - ICSE Class 11 Economics

Free practice quiz: Statistics – Mathematical Tools (Line Equation, Slope) (ICSE Class 11 Economics). 50 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

Sample questions

1. If a linear demand curve is represented by the equation P = 100 - 2Q, where P is price and Q is quantity, what is the slope of the demand curve?

   1. 2
   2. -2
   3. 100
   4. -100
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   Answer: B. -2

   The equation is given in the form P = mQ + c, where 'm' is the slope. Rearranging the given equation P = 100 - 2Q, we can see that the coefficient of Q is -2. Therefore, the slope of the demand curve is -2.

2. For the line segment connecting points A(1, 2) and B(5, 10), what is the equation of the line passing through these points?

   1. y = 2x
   2. y = 2x + 0
   3. y = 2x + 1
   4. y = x + 1
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   Answer: A. y = 2x

   First, calculate the slope: m = (10 - 2) / (5 - 1) = 8 / 4 = 2. Using the point-slope form y - y1 = m(x - x1) with point A(1, 2): y - 2 = 2(x - 1) => y - 2 = 2x - 2 => y = 2x. Alternatively, using the slope-intercept form y = mx + c and point A(1, 2): 2 = 2(1) + c => 2 = 2 + c => c = 0. Thus, y = 2x.

3. The equation of a total revenue function is TR = 10Q - 0.2Q^2. What is the marginal revenue when Q=10?

   1. 10
   2. 8
   3. 6
   4. 2
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   Answer: C. 6

   Marginal Revenue (MR) is the derivative of the Total Revenue (TR) function with respect to quantity (Q). MR = d(TR)/dQ = d(10Q - 0.2Q^2)/dQ = 10 - 0.4Q. At Q=10, MR = 10 - 0.4(10) = 10 - 4 = 6.

4. A linear curve is given by y = -5x + 20. If x increases by 3 units, what is the change in y?

   1. 15
   2. -15
   3. 3
   4. -3
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   Answer: B. -15

   The slope of the line is -5. The change in y is the slope multiplied by the change in x. Change in y = (-5) * 3 = -15.

5. The marginal cost of production is MC = 10 + 2Q. If the marginal cost at Q=5 is $20, what is the marginal cost at Q=10?

   1. 20
   2. 30
   3. 40
   4. 50
   Show answer

   Answer: B. 30

   The marginal cost function is MC = 10 + 2Q. We are given that at Q=5, MC = 10 + 2(5) = 10 + 10 = 20, which is consistent. Now, we need to find MC at Q=10. MC at Q=10 = 10 + 2(10) = 10 + 20 = 30.

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