WEEK 1	Set Theory - Number system, Sets and their operations, Relations and functions - Relations and their types, Functions and their types
WEEK 2	Rectangular coordinate system, Straight Lines - Slope of a line, Parallel and perpendicular lines, Representations of a Line, General equations of a line, Straight-line fit
WEEK 3	Quadratic Functions - Quadratic functions, Minima, maxima, vertex, and slope, Quadratic Equations
WEEK 4	Algebra of Polynomials - Addition, subtraction, multiplication, and division, Algorithms, Graphs of Polynomials - X-intercepts, multiplicities, end behavior, and turning points, Graphing & polynomial creation
WEEK 5	Functions - Horizontal and vertical line tests, Exponential functions, Composite functions, Inverse functions
WEEK 6	Logarithmic Functions - Properties, Graphs, Exponential equations, Logarithmic equations
WEEK 7	Sequence and Limits - Function of One variable - • Function of one variable • Graphs and Tangents • Limits for sequences • Limits for function of one variable • Limits and Continuity
WEEK 8	Derivatives, Tangents and Critical points - • Differentiability and the derivative • Computing derivatives and L’Hˆopital’s rule • Derivatives, tangents and linear approximation • Critical points: local maxima and minima
WEEK 9	Integral of a function of one variable - • Computing areas, Computing areas under a curve, The integral of a function of one variable • Derivatives and integrals for functions of one variable
WEEK 10	Graph Theory - Representation of graphs, Breadth-first search, Depth-first search, Applications of BFS and DFS; Directed Acyclic Graphs - Complexity of BFS and DFS, Topological sorting
WEEK 11	Longest path, Transitive closure, Matrix multiplication Graph theory Algorithms - Single-source shortest paths, Dijkstra’s algorithm, Bellman-Ford algorithm, All-pairs shortest paths, Floyd–Warshall algorithm, Minimum cost spanning trees, Prim’s algorithm, Kruskal’s algorithm
WEEK 12	Revision

Quiz 1 (Qualifier Stage)

Week 1

Question 1

Topic: Number Systems

Which of the following are irrational numbers?

$(8 + 2) (12 - 3)$
$(8 - 2) (18 + 2)$
$\frac{6 + 3}{6 - 3}$
$\frac{8 + 2}{8 - 2}$

Answer: Options 1 and 3.

$(8 + 2) (12 - 3)$

$\frac{6 + 3}{6 - 3}$

Question 2

Topic: Functions, Domain, and Set Theory

Suppose $f : D ⟶ R$ is a function defined by $f (x) = \frac{x ^{2} - 16}{x + 4}$ , where $D \subset Z$ . Let $A$ be the set of integers which are not in the domain of $f$ , then find the cardinality of the set $A$ .

Answer: 8

Question 3

Topic: Set Theory and Relations

Consider the set $S = {a ∣ a \in N, a \leq 33}$ . Let $R_{1} and R_{2}$ be relations from $S$ to $S$ defined as $R_{1} = {(x, y) ∣ x, y \in S, y = 3 x}$ and $R_{2} = {(x, y) ∣ x, y \in S, y = x^{2}}$ . Find the cardinality of the set $R_{1} ∖ (R_{1} \cap R_{2})$ .

Answer: 10

Question 4

Topic: Set Theory and Venn Diagrams

In a Zoo, there are 6 Bengal white tigers and $6$ Bengal royal tigers. Out of these tigers, 5 are males and 10 are either Bengal royal tigers or males. Find the number of female Bengal white tigers in the Zoo.

Answer: 2

Question 5

Topic: Relations and their Properties

A survey was conducted on pollution of 525 ponds across some cities. It was found that 230 ponds are polluted by fertilisers $(F)$ , 245 ponds are polluted by pesticides $(P)$ and 257 ponds are polluted by pharmaceutical products $(P h)$ . 100 ponds are polluted by fertilisers and pesticides, 82 ponds are polluted by fertilisers and pharmaceutical products, 77 ponds are polluted by pesticides and pharmaceutical products. Define a relation on the set of 525 ponds such that two ponds are related if both are polluted by fertilisers and pharmaceutical products. Which of the following is/are true?

Relation is reflexive.
Relation is transitive.
Relation is symmetric.
This is an equivalence relation.

Answer: Options 2 and 3.

Relation is transitive.

Relation is symmetric.

Question 6

Topic: Functions (Bijective, Injective, Surjective)

Consider the table of materials and their dielectric constants. We can think of this as a function $f$ from the set of materials to the set of dielectric constant values ${1, 2, 3, 8, 7, 13}$ . Pick the correct statement.

$f$ is neither one to one nor onto.
$f$ is one to one but not onto.
$f$ is onto but not one to one.
$f$ is bijective.

Answer: Option 4.

$f$ is bijective.

Question 7

Topic: Set Operations and Cardinality

Consider the sets:

$A = {x \in N ∣ x mod 2 = 0 and 1 \leq x \leq 10}$
$B = {x \in N ∣ x mod 5 = 0 and 6 \leq x \leq 25}$
$C = {x \in N ∣ x mod 7 = 0 and 7 \leq x \leq 29}$

What is the cardinality of $(A ∖ (B \cup C)) \cup (B ∖ (C \cup A)) \cup (C ∖ (B \cup A))$ ?

Answer: 11

Question 8

Topic: Relations and Family Trees

Mahesh has four sons (Shubh, Rabi, Mahendra, and Rajat). Shubh has two sons (Yashubh and Navrtna). Rabi has two sons (Rathi and Rakesh). Let $M$ be the collection of all family members. Define two relations:

$R := {(A, B) ∣ A and B are cousins}$ .
$S := {(A, B) ∣ A is son of B}$ .

If $m = ∣ R ∣$ and $n = ∣ S ∣$ , find $m + n$ .

Answer: 16

Question 9

Topic: Functions (Injective and Surjective)

Define a function $f : Q \to Z$ , such that $f (p / q) = p - q$ , where $g c d (p, q) = 1$ . Which of the following is true?

$f$ is one to one but not onto
$f$ is neither one to one nor onto.
$f$ is onto but not one to one.
$f$ is a bijective function.

Answer: Option 3.

$f$ is onto but not one to one.

Question 10

Topic: Domain of Functions

Suppose $f_{1} (x)$ and $f_{2} (x)$ are functions defined on domains $D_{1} \subset R$ and $D_{2} \subset R$ respectively. What is the domain of the function $f_{1} (x) + f_{2} (x)$ ?

$D_{1} \cup D_{2}$
$D_{1} ∖ D_{2}$
$D_{2} ∖ D_{1}$
$D_{1} \cap D_{2}$

Answer: Option 4.

$D_{1} \cap D_{2}$

Week 2

Question 1

Topic: Coordinate Geometry (Lines and Intersection)

A bird is flying along the straight line $2 y - 6 x = 6$ . In the same plane, an aeroplane starts to fly in a straight line from the origin and passes through the point $(4, 12)$ . If the bird and plane collide, enter the answer as 1, and if not, then 0. (Note: Bird and aeroplane can be considered to be of negligible size.)

Answer: 0

Question 2

Topic: Calculus (Rates of Change) & Geometry (Circles)

A rock is thrown in a pond and creates circular ripples whose radius increases at a rate of 0.2 meters per second. What will be the value of $\frac{A}{π}$ , where $A$ is the area (in square meters) of the circle after 5 seconds? (Hint: The area of a circle = $π r^{2}$ , where $r$ is the radius of the circle.)

Answer: 1.0

Question 3

Topic: Coordinate Geometry (Reflection and Equations of Lines)

A ray of light passing through the point $A (1, 2)$ is reflected at a point $B$ on the X-axis and then passes through the point $(5, 3)$ . What is the equation of the straight line segment $A B$ ?

$5 x + 4 y = 13$
$5 x - 4 y = - 3$
$4 x + 5 y = 14$
$4 x - 5 y = - 6$

Answer: Option 1.

$5 x + 4 y = 13$

Question 4

Topic: Coordinate Geometry (Properties of Parallelograms)

Let $A BC D$ be a parallelogram with vertices $A (x_{1}, y_{1})$ , $B (x_{2}, y_{2})$ , and $C (x_{3}, y_{3})$ . Which of the following always denotes the coordinate of the fourth vertex $D$ ?

$(x_{1} + x_{2} + x_{3}, y_{1} + y_{2} + y_{3})$
$(x_{1} - x_{2} + x_{3}, y_{1} - y_{2} + y_{3})$
$(x_{1} + x_{2} - x_{3}, y_{1} + y_{2} - y_{3})$
$(x_{1} - x_{2} - x_{3}, y_{1} - y_{2} - y_{3})$

Answer: Option 2.

$(x_{1} - x_{2} + x_{3}, y_{1} - y_{2} + y_{3})$

Question 5

Topic: Algebra & Coordinate Geometry (Systems of Equations)

Find the y-coordinate of the point of intersection of straight lines represented by (1) and (2), given:

$a x + b y + c = E$ --- (1)
$b x + cy + d^{2} = F$ --- (2) And it is given that:
$E = F = 0$
Arithmetic mean of $a$ and $b$ is $c$ .
Geometric mean of $a$ and $b$ is $d$ .

$(\frac{2 a ^{2} b - ab - b ^{2}}{2 b ^{2} - a ^{2} - ab})$
$(\frac{a ^{2}}{a - b} - 1)$
$(\frac{2 b ^{2} b - ab - b ^{2}}{2 b ^{2} - b ^{2} - ab})$
$(\frac{b ^{2}}{a - b} - 1)$

Answer: Option 1.

$(\frac{2 a ^{2} b - ab - b ^{2}}{2 b ^{2} - a ^{2} - ab})$

Question 6

Topic: Linear Models & Cost Analysis

Lalith wants to buy a new mobile and needs 200 minutes of calls per month. He has two options:

Company Offer: Mobile and a 1-year Astron Network plan (unlimited calls) for ₹34000.
Separate Purchase: Buy only the mobile for ₹22000 and choose a network provider.

The available network providers have the following monthly charges:

Network Provider	Fixed Charge (Per month)	Per minute Charge
Astron	₹100	₹2
Proton	₹200	₹0.5

How much will Lalith save per year if he chooses the best option (buying separately and picking the cheaper network) compared to the company’s offer?

Answer: 8400

Questions 7 & 8

Topic: Coordinate Geometry (Shortest Distance from a Point to a Line)

The government wants to connect a town to a national highway. The national highway is a straight line connecting points $(2, 1)$ and $(10, 7)$ . There are 3 possible locations in the town to build the connecting road from: A(3,8), B(5,7), and C(6,9). The connecting road must be the shortest possible path. (Note: 1 unit = 100 meters).

Question 7: Which location (A, B, or C) should be selected to build the road?

A
B
C
None

Answer: Option 2.

B

Question 8: What is the minimum length of road (in meters) required?

Answer: 300

Questions 9 & 10

Topic: Linear Regression & Data Interpretation

A fitness trainer models a client’s weight loss with the equation $W = - 8 t + 98$ , where $W$ is weight in Kg and $t$ is time in months. The actual data is in the table below:

Time (months)	Weight (Kgs)
0	98
1	90
2	82
3	74
4	66
5	57
6	49

Question 9: An equation is a “good fit” if its Sum of Squared Errors (SSE) is less than 5. Is the trainer’s equation, $W = - 8 t + 98$ , a good fit for the data?

True
False

Answer: Option 1.

True

Question 10: Assuming the trainer’s weight loss rate (-8 kg/month) is accurate, how many days are required to lose weight from 100 kg to 72 kg? (Note: 1 month = 30 days).

Answer: 105

Question 11

Topic: Curve Fitting (Minimizing SSE)

A function $f (x) = - (x - 1)^{2} (x - 3) (x - 5) (x - 7) + c$ is the best fit for the data in the table. What is the value of $c$ that minimizes the Sum of Squared Error (SSE)?

x	y
1	4
2	18
3	4
4	-24
5	3

Answer: 3.4

Question 12

Topic: Coordinate Geometry (Intersection of Lines)

A bird is flying along the straight line $2 y - 6 x = 6$ . An aeroplane follows a straight line path with a slope of 2 and passes through the point $(4, 8)$ . Let $(α, β)$ be the point where the bird and aeroplane collide. Find the value of $α + β$ .

Answer: -9

Question 13

Topic: Coordinate Geometry (Area of a Triangle, Section Formula)

Consider a triangle $△ A BC$ with coordinates $A (- 3, 3)$ , $B (1, 7)$ , and $C (2, - 2)$ . Point $M$ divides the line $A B$ in the ratio $1 : 3$ , point $N$ divides the line $A C$ in the ratio $2 : 3$ , and point $O$ is the midpoint of $BC$ . Find the area of $△ MNO$ (in sq. units).

Answer: 4.5

Questions 14 & 15

Topic: Coordinate Geometry (Equations of Lines, Intersection, Angle between Lines)

Suppose $L_{1}$ and $L_{2}$ are lines in the plane. The x-intercepts of $L_{1}$ and $L_{2}$ are 2 and -1, respectively. The y-intercepts are -3 and 2, respectively.

Question 14: Choose the point where $L_{1}$ and $L_{2}$ intersect.

(10, 18)
(5, 8)
(-10, -18)
(6, 6)

Answer: Option 3.

(-10, -18)

Question 15: If $θ$ is the angle between $L_{1}$ and $L_{2}$ , then $tan θ$ is equal to:

$\frac{1}{8}$
$\frac{1}{6}$
$\frac{3}{8}$
$\frac{1}{4}$

Answer: Option 1.

$\frac{1}{8}$

Questions 16 & 17

Topic: Coordinate Geometry (Area of a Triangle)

Consider two triangles, $△ A BC$ and $△ P A B$ , with coordinates $A (4, 3)$ , $B (2, 2)$ , $C (8, 3)$ , and $P (k, k)$ . The area of $△ A BC$ is 4 times the area of $△ P A B$ .

Question 16: What is the area of $△ A BC$ ?

Answer: 2

Question 17: Choose all the possible options for point P.

(0, 0)
(2, 4)
(-2, 4)
(-1, 1)

Answer: Option 4.

(-1, 1)

Question 18

Topic: Linear Regression (Sum of Squared Errors)

Radhika is tracking her monthly expenses ( $y$ ) versus the number of outings ( $x$ ). She fits a best-fit line to her data and gets the equation $y = 4 x + 2$ . What is the value of the SSE (Sum of Squared Errors) for this line and the data below?

Amount spent (y)	6	14	24	29	39	45
Number of outings (x)	1	3	5	7	9	11

Answer: 7

Week 3

Question 1

Topic: Parabolas & Calculus (Derivatives)

If the slope of the parabola $y = a x^{2} + b x + c$ (where $a, b, c \in R ∖ {0}$ ) at points $(3, 2)$ and $(2, 3)$ are $32$ and $2$ respectively, find the value of $a$ .

Answer: 15

Question 2

Topic: Word Problems & Quadratic Equations

A class of 140 students is arranged in rows such that the number of students in a row is one less than thrice the number of rows. Find the number of students in each row.

Answer: 20

Question 3

Topic: Number Theory

The product of two consecutive odd natural numbers is 143. Find the largest number among them.

Answer: 13

Question 4

Topic: Parabolas & Calculus (Derivatives)

The slope of a parabola $y = 3 x^{2} - 11 x + 10$ at a point $P$ is 1. Find the y-coordinate of the point $P$ .

Answer: 0

Question 5

Topic: Parabolas & Coordinate Geometry (Intersection of Curves)

Two parabolas, $y = x^{2} + 3 x + 2$ and $y = - x^{2} - 5 x - 4$ , intersect at points $A$ and $B$ ( $A$ is not on the X-axis). A line $ℓ_{1}$ passes through $A$ with a slope equal to the slope of $y = - x^{2} - 5 x - 4$ at $A$ . Lines $ℓ_{2}$ and $ℓ_{3}$ pass through $B$ with slopes equal to the slopes of $y = x^{2} + 3 x + 2$ and $y = - x^{2} - 5 x - 4$ at $B$ , respectively. Which of the following is/are true?

$ℓ_{1}$ and $ℓ_{2}$ are parallel.
$ℓ_{1}$ and $ℓ_{3}$ are parallel.
$ℓ_{1}$ and $ℓ_{3}$ are intersecting at point (-2, 3).
$ℓ_{2}$ and $ℓ_{3}$ are intersecting at point (-1, 0).
$ℓ_{2}$ and $ℓ_{3}$ are parallel.

Answer: Options 1, 3, and 4.

$ℓ_{1}$ and $ℓ_{2}$ are parallel.

$ℓ_{1}$ and $ℓ_{3}$ are intersecting at point (-2, 3).

$ℓ_{2}$ and $ℓ_{3}$ are intersecting at point (-1, 0).

Question 6

Topic: Kinematics & Word Problems

To cover a fixed distance of 48 km, two vehicles start from the same place. The faster one takes 2 hours less and has a speed 4 km/hr more than the slower one. What is the time (in hours) taken by the faster one?

Answer: 4

Question 7

Topic: Quadratic Functions (Properties)

The maximum value of a quadratic function $f$ is $- 3$ , its axis of symmetry is $x = 2$ , and its value at $x = 0$ is $- 9$ . What is the coefficient of $x^{2}$ in the expression for $f$ ?

$- 1$
1
$- 1.5$
$- 0.5$

Answer: Option 3.

$- 1.5$

Question 8

Topic: Quadratic Functions (Projectile Motion)

A water fountain’s stream follows a parabolic arc given by the equation $h (t) = - 0.5 t^{2} + 4 t + 1$ , where $h (t)$ is the height in meters and $t$ is the time in seconds. How long does it take for the water to reach its maximum height?

Answer: 4

Question 9

Topic: Coordinate Geometry (Intersection of Curve and Line)

Find the intersection points of the curve $y = 4 x^{2} + x + 6$ and the straight line passing through the points $(1, 6)$ and $(4, 5)$ .

$(\frac{- 1}{2}, \frac{13}{2})$
$(\frac{1}{6}, \frac{113}{18})$
$(0, 6)$
The curve and the straight line do not intersect.

Answer: Options 1 and 2.

$(\frac{- 1}{2}, \frac{13}{2})$

$(\frac{1}{6}, \frac{113}{18})$

Question 10

Topic: Parabolas & Calculus (Derivatives)

The slopes of the parabola $y = A x^{2} + B x + C$ at points $(3, 2)$ and $(2, 3)$ are 16 and 12, respectively. Calculate the value of $A$ .

Answer: 2

Questions 11, 12 & 13

Topic: Quadratic Functions (Projectile Motion)

A ballistic missile is launched from a fighter jet at a height of 40 m. It hits a tank on the ground. Its height is given by the function $h (t) = - 8 t^{2} + 32 t + 40$ , where $h$ is in meters and $t$ is in seconds.

Question 11: What is the maximum height (in meters) attained by the missile?

Answer: 72

Question 12: How long (in seconds) does it take for the missile to hit the tank?

Answer: 5

Question 13: An air defense system at the origin fires a missile along the path $h (t) = 10 t$ . At what height will it destroy the ballistic missile?

40 m
12.5 m
4 m
1.25 m

Answer: Option 1.

40 m

Question 14

Topic: Polynomials & Quadratic Functions

The polynomial $p (x) = a (x - 4) (x - 6) (x - 8) (x - 10)$ passes through the vertex of the quadratic function $q (x) = - (x - 7)^{2} - 9$ . Calculate the value of $a$ .

Answer: -1

Week 4

Question 1

Topic: Polynomial Functions & Calculus (Turning Points, Increasing/Decreasing Intervals)

Let $f (x) = x^{3} - 8 x^{2} + 7$ and $g (x) = - 2 f (x)$ . Choose the correct option(s).

$f$ has two turning points and there are no turning points with negative y-coordinate.
$f$ is strictly increasing in $[10, \infty)$ .
$g$ has two turning points and the y-coordinate of only one turning point is negative.
$g$ has two turning points and there are no turning points with positive y-coordinate.

Answer: Options 2 and 3.

$f$ is strictly increasing in $[10, \infty)$ .

$g$ has two turning points and y-coordinate of only one turning point is negative.

Question 2

Topic: Polynomial Functions (Behavior in Intervals)

Which of the following functions first increases and then decreases in all the intervals $(- 4, - 3)$ , $(- 1, 2)$ , and $(5, 6)$ ?

$\frac{1}{10000} (x + 1)^{2} (x - 2) (x + 3)^{2} (x + 4) (x - 5) (x - 6)^{2}$
$\frac{1}{10000} (x + 1)^{2} (x - 2) (x + 3) (x + 4) (x - 5)^{2} (x - 6)^{2}$
$\frac{- 1}{10000} (x + 1)^{2} (x - 2) (x + 3)^{2} (x + 4)^{2} (5 - x) (x - 6)^{2}$
$\frac{1}{10000} (x + 1)^{2} (x - 2) (x + 3) (x + 4) (x - 5)^{2} (x - 6)^{2} (x + 7)$

Answer: Options 1 and 3.

$\frac{1}{10000} (x + 1)^{2} (x - 2) (x + 3)^{2} (x + 4) (x - 5) (x - 6)^{2}$

$\frac{- 1}{10000} (x + 1)^{2} (x - 2) (x + 3)^{2} (x + 4)^{2} (5 - x) (x - 6)^{2}$

Question 3

Topic: Polynomial Functions (Turning Points & Intervals)

Consider the polynomial function $p (x) = - (x^{2} - 16) (x - 3)^{2} (2 - x)^{2} (x + 9)$ . Choose the correct options.

$p (x)$ is strictly increasing when $x \in (- \infty, - 9)$ .
The total number of turning points of $p (x)$ is 6.
$p (x)$ first increases then decreases in the interval $(2, 3)$ .
The total number of turning points of $p (x)$ is 7.

Answer: Options 2 and 3.

Total number of turning points of $p (x)$ are 6.

$p (x)$ first increases then decreases in the interval $(2, 3)$ .

Question 4

Topic: Polynomials (Roots / x-intercepts)

An ant needs to find food, located at the x-intercepts of the function $f (x) = (x^{2} - 23) ((x - 10)^{3} - 1)$ . What is the sum of the x-coordinates of all the food locations?

Answer: 11

Question 5

Topic: Polynomials (Intersection & Roots)

Two roads, $r_{1}$ and $r_{2}$ , follow the polynomial curves $f (x) = (x - 9) (x - 7)^{2}$ and $g (x) = - (x - 9) (x - 7)$ , respectively. The roads connect aspirational districts located at their intersection points and x-intercepts. If the first two districts are at the x-intercepts of $f (x)$ and $g (x)$ , what is the x-coordinate of the third district (intersection point)?

Answer: 6

Question 6

Topic: Polynomial Functions (Constructing Equations)

A polynomial function $f (x)$ of degree 4 intersects the X-axis at $x = 2, x = - 3,$ and $x = - 4$ . Also, $f (x) < 0$ when $x \in (1, 2)$ , and $f (x) > 0$ when $x \in (- 1, 1)$ . Find the equation of the polynomial.

$a (x - 2)^{2} (x^{2} + 7 x + 12), a > 0$
$a (x^{4} + 4 x^{3} - 7 x^{2} - 22 x + 24), a > 0$
$a (x - 2)^{2} (x^{2} + 2 x - 8), a > 0$
$a (x^{4} - 5 x^{3} - 7 x^{2} - 50 x - 24), a > 0$

Answer: Option 2.

$a (x^{4} + 4 x^{3} - 7 x^{2} - 22 x + 24), a > 0$

Question 7

Topic: Polynomial Operations

Given $P (x) = x^{4} + 4 x^{3} + x + 10$ and $Q (x) = x^{3} + 2 x^{2} - 6$ . Let $M (x)$ be the line passing through $(2, Q (2))$ with a slope of 3. Find the equation of $P (x) + M (x) Q (x)$ .

$4 x^{4} + 14 x^{3} + 8 x^{2} - 17 x - 14$
$4 x^{4} + 14 x^{3} - 6 x^{2} - 19 x - 34$
$4 x^{4} + 2 x^{3} + 8 x^{2} - 17 x - 14$
$4 x^{4} + 2 x^{3} + 8 x^{2} - 18 x - 34$

Answer: Option 1.

$4 x^{4} + 14 x^{3} + 8 x^{2} - 17 x - 14$

Question 8

Topic: Polynomials (End Behavior, Turning Points, Division)

Consider the polynomials $p (x) = - x^{5} + 5 x^{4} - 7 x - 2$ and $q (x) = - x^{5} + 5 x^{4} - x^{2} - 2$ . Which of the following options is/are true?

$q (x) \to \infty$ as $x \to \infty$ .
$p (x) \to - \infty$ as $x \to \infty$ .
$p (x)$ has at most 4 turning points.
The quotient obtained when dividing $q (x)$ by $p (x)$ is a constant.

Answer: Options 2, 3, and 4.

$p (x) \to - \infty$ as $x \to \infty$ .

$p (x)$ has at most 4 turning points.

The quotient obtained while dividing $q (x)$ by $p (x)$ is a constant.

Question 9

Topic: Polynomial Functions (Application)

Ritwik’s score in mock test $n$ (where $n \in {1, 2, ..., 12}$ ) is given by $M (n) = - (\frac{n ^{2}}{1000}) (n^{3} - 15 n^{2} + 50 n) + 40$ . A passing score is 40 or above. How many mock tests did Ritwik pass?

Answer: 6

Question 10

Topic: Polynomial Functions (Behavior in Intervals)

The height of a roller coaster is modeled by $h (t) = (- 0.01 t^{3} + 0.35 t^{2} - 3.5 t + 10) (t + 5)^{2} (t - 5) (t + 1) (2 - t)^{3}$ . Which statements are true?

The roller coaster will first go up and then go down in the interval $(- 5, - 1)$ .
The roller coaster will first go down and then go up in the interval $(10, 20)$ .
The roller coaster will first go up and then go down in the interval $(- 1, - 2)$ .
The roller coaster will first go up and then go down in the interval $(2, 5)$ .

Answer: Options 1, 2, and 4.

The roller coaster will first go up and then go down in the interval $(- 5, - 1)$ .

The roller coaster will first go down and then go up in the interval $(10, 20)$ .

The roller coaster will first go up and then go down in the interval $(2, 5)$ . will first go up and then go down in the interval $(2, 5)$ .

🧠 IIT Madras Notes

Explorer

Maths 1 Assignments

Quiz 1 (Qualifier Stage)

Week 1

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Week 2

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Questions 7 & 8

Questions 9 & 10

Question 11

Question 12

Question 13

Questions 14 & 15

Questions 16 & 17

Question 18

Week 3

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Questions 11, 12 & 13

Question 14

Week 4

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Quiz 2 (Week 5 to 8)

Week 5

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