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CBSE Class 11 Maths starter questions: weeks 35–45

33 short questions to open a lesson for CBSE Class 11 Mathematics, weeks 35–45 of the teaching year, three or four a week. Each question is shown as an image with its text underneath; the answers and mark schemes are free on the free weekly starters page, to show or project in class.

Week 35

Question 1: Rules and standard derivatives
If f(x) = 3x² - 5x + 2, then f'(1) is (a) 1 (b) 0 (c) 6 (d) -5
Question 2: Rules and standard derivatives
The derivative of sin xcos x is (a) -sin 2x (b) cos 2x (c) cos² x (d) -sin xcos x
Question 3: Coordinates of a point
A point (4, -3, 2) is projected straight down onto the xy-plane. Where does it land? (a) (4, 0, 2) (b) (0, -3, 2) (c) (4, -3, 0) (d) (0, 0, 2)

Week 36

Question 1: Variance and standard deviation
The variance of 1, 2, 3, 4, 5 is (a) 3 (b) √2 (c) 2 (d) 10
Question 2: Dispersion and range
The range of the data 12, 7, 19, 3, 15 is (a) 22 (b) 19 (c) 12 (d) 16
Question 3: Factorial
The value of (10!)/(8! 2!) is (a) 45 (b) 90 (c) 5 (d) 5/4

Week 37

Question 1: Events
Two dice are thrown. The probability that the sum is 7 or both dice show the same number is (a) 1/6 (b) 11/36 (c) 1/3 (d) 5/18
Question 2: Variance and standard deviation
If every observation of a data set is multiplied by 3, its standard deviation is (a) multiplied by 3 (b) unchanged (c) multiplied by 9 (d) increased by 3
Question 3: The binomial theorem
The term independent of x in the expansion of (x + 1/x)⁴ is (a) 6 (b) 4 (c) 1 (d) 12

Week 38

Question 1: Random experiments and sample spaces
A coin is tossed three times. The number of outcomes in the sample space is (a) 3 (b) 6 (c) 8 (d) 9
Question 2: Dispersion and range
The range of the data 45, 32, 57, 29, 61, 40 is (a) 61 (b) 28 (c) 32 (d) 16
Question 3: Arithmetic mean
Two arithmetic means are inserted between 4 and 19. The larger of them is (a) 15 (b) 9 (c) 14 (d) 11.5

Week 39

Question 1: Axiomatic probability
A sample space is ω_1, ω_2, ω_3. Which assignment of probabilities is valid? (a) 0.5, 0.6, -0.1 (b) 0.2, 0.3, 0.5 (c) 0.4, 0.4, 0.4 (d) 1, 1, 0
Question 2: Mean deviation
The mean deviation about the mean of 2, 4, 6, 8, 10 is (a) 2 (b) 2.4 (c) 6 (d) 0
Question 3: Angle between two lines
The acute angle between two lines with slopes 1 and 0 is (a) 60° (b) 30° (c) 45° (d) 90°

Week 40

Question 1: Counting with combinations
Two cards are drawn at random from a pack of 52. The probability that both are red is (a) 25/102 (b) 1/4 (c) 1/2 (d) 26/51
Question 2: Hyperbola
The foci of the hyperbola (y²)/9 - (x²)/16 = 1 are (a) (0, ±√7) (b) (± 5, 0) (c) (0, ± 5) (d) (0, ± 3)
Question 3: Distance between two points
The distance of (3, 4, 12) from the origin is (a) 13 (b) 19 (c) 5 (d) √19

Week 41

Question 1: Axiomatic probability
A sample space has three outcomes. Which of these is NOT a valid assignment of probabilities to them? (a) 0.2, 0.3, 0.5 (b) 1/3, 1/3, 1/3 (c) 0, 0.4, 0.6 (d) 0.6, 0.5, -0.1
Question 2: Comparing spread
Two series have equal means and standard deviations 4 and 6. The series that is more consistent is the one with standard deviation (a) it cannot be decided (b) 6 (c) both are equally consistent (d) 4
Question 3: The number i
Simplify 1/(i³), where i = √(-1). (a) -i (b) i (c) 1 (d) -1

Week 42

Question 1: Random experiments and sample spaces
A coin is tossed until a head appears, or until it has been tossed three times. The number of outcomes in the sample space is (a) 8 (b) 4 (c) 3 (d) 6
Question 2: Systems and double inequalities
The number of integers satisfying both 5x - 3 < 2x + 9 and 3x + 4 ≥ x - 2 is (a) 7 (b) 6 (c) 8 (d) 5
Question 3: Factorial
Work out 5! - 3! (using n! = 1 × 2 × … × n). (a) 120 (b) 2! (c) 114 (d) 20

Week 43

Question 1: Pascal's triangle
Add up all the numbers in the row of Pascal's triangle for n = 8. The total is (a) 256 (b) 128 (c) 64 (d) 72
Question 2: Arithmetic mean
If 2k - 1 is the arithmetic mean of 5 and 13, then k is (a) 5 (b) 9 (c) 4 (d) 9/2
Question 3: Angle between two lines
Two non-vertical lines have slopes m and -1/m. The lines are (a) coincident (b) parallel (c) inclined at 45° (d) perpendicular

Week 44

Question 1: Hyperbola
The hyperbola with foci (±5, 0) and vertices (±3, 0) is (a) (x²)/9 - (y²)/16 = 1 (b) (x²)/9 - (y²)/25 = 1 (c) (x²)/25 - (y²)/9 = 1 (d) (x²)/9 + (y²)/16 = 1
Question 2: Distance between two points
The distance between (1, -2, 3) and (4, 2, 3) is (a) √7 (b) 7 (c) 5 (d) 25
Question 3: Polynomial and rational functions
Factorise x³ - 8 to find the value of lim_x → 2(x³ - 8)/(x - 2). (a) 0 (b) 4 (c) 8 (d) 12

Week 45

Question 1: Comparing spread
The coefficient of variation of a distribution with mean 50 and standard deviation 10 is (a) 5% (b) 20% (c) 500% (d) 40%
Question 2: Random experiments and sample spaces
A die is thrown and a coin is tossed. The number of outcomes in the sample space is (a) 8 (b) 12 (c) 6 (d) 36
Question 3: Modulus and conjugate
The modulus of (1 + i)(2 + 3i) is (a) √26 (b) √15 (c) 5 (d) 26

More starter questions

Other weeks: Weeks 1–19 · Weeks 20–34 · Weeks 35–45. Answers and mark schemes, free for everyone, are on the free weekly starters page.

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