Pure Maths With Statistics 1 · Government Bilingual High School Yaounde · April 2021 · Mock GCE · Advanced Level
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Exercices, méthodes & corrigés (50)
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Question 1
Polynômes
1. Given that the polynomials x³ + 4x² - 2x + 1 and x³ + 3x² - x + 7 leave the same remainder when divided by x - p the possible values of p are A 2,3 B -2,-3 C -2,3 D 2,-3
Question 10
Dérivation
10. Given that (cosx) dy/dx = ysinx, then A y = |ln secx| + K B y = sec²x + K C lny = sec²x + K D lny = |ln secx| + K
Question 11
Question 12
Dénombrement
12. The first, second and third prizes are to be awarded to a class of 20 pupils. In how many ways can this be done A 3800 B 6840 C 3040 D 3000
Question 13
Logarithme et exponentielle
13. Given that 2 logᵧ x + 2 logₓ y = 5, then the values of logᵧ x are A 1/2, 2 B 2,4 C 5/2, 1/2 D 2,-2
Question 14
Nombres complexes
14. z = x + yi and P is the point (x, y) on an argand diagram. Given that |z| = 14, the equation of the locus of P is A r=9 B r = 14 C x² + y² = 14 D argz = π
Question 15
Question 16
Équations et inéquations
16. If p is the statement 'Peter is eating' and q is the statement 'Peter is playing', then the proposition ~q → p is A If Peter is eating then he is playing B If Peter is eating then he is not playing C If Peter does not play then he will not eat D If Peter is not playing then he is eating
Question 17
Dénombrement
17. The number of ways of forming a committee of six members from 2 girls and 4 boys is A 15 B 14 C 42 D 1
Question 18
Dérivation
18. A curve has gradient 2x + 3 at every point on the curve. Given that the curve passes through the point (1,2) then the equation is A y = x² + 1 B y = x² + 3x C y = 2x² + 3x - 3 D y = x² + 3x - 3
Question 19
Polynômes
19. Given that the equation x² + 2x - k = 0 has exactly one root between 1 and 2, then A k(3-k) < 0 B k²-3k < 0 C k(3-k) > 0 D (3-k)(8-k) < 0
Question 2
Question 20
Trigonométrie
20. Given that α and ß are acute angles such that sinα = 3/5 and sinß = 5/13, then the exact value of tan(α - ß) is A 1/3 B 16/63 C 1/6 D 1/2
Question 21
Question 22
Fonctions
22. The domain of the function f where f(x) = (3x) / (x²-2x) may be defined as A ]-∞,-1[ U ]-1,2[ U ]2, +∞[ B ]-∞,-1] U [-1,2] U [2, +∞[ C ]-∞,-1[ U ]-1, -2[ U ]-2, +∞[ D ]-∞, -1] U [-1,2[ U ]2, +∞[
Question 23
Limites et continuité
23. The value of the constant k for which the function h is defined by h(x) = { 4, 1<x≤2 ; k(x-1), 2<x≤3 is continuous in the interval 1 ≤ x ≤ 3 is A 1 B 3 C 2 D 1/2
Question 24
Question 25
Question 26
Question 27
Logarithme et exponentielle
27. The variables x and y are related by the law y = a²bˣ. Reducing this law to linear form gives A log y = xlog b + log a B log y = blog x + + 2log a C log y = 2xlog b + log a D log y = xlog b + 2log a
Question 28
Dérivation
28. If sin(x + y) = x then dy/dx A 1-cos(x+y) B cos(x+y)+2 / cos(x+y) C cos(x+y) / cos(x+y)-1 D cos(x+y)
Question 29
Question 3
Dérivation
3. The function y = f(x) is defined by the parametric equations x = eᵗ and y = sint, d²y/dx² in terms of t is A -sint-cost / e²t B -sintcost / e²t C -2sint / e²t D e-2tsin2t
Question 30
Dérivation
30. The curve y = x³ – 9x² + 27x-5 has A a point of inflexion B a minimum turning point C a vertical asymptote D a maximum turning point
Question 31
Fonctions
31. A function f defined on x ∈ R is bijective iff (i) f is a one-to-one mapping (ii) Codomain of f = Range of f (iii) Domain of f⁻¹ = Domain of f A (i) and (ii) only B (i) and (iii) only C (i) only D (iii)only
Question 32
Nombres complexes
32. If z = (1+2i) / (3-4i) in the form a + bi, then z = A z = 2/5 + 1/5i B z = 1/5 + 2/5i C z = -1/5 - 2/5i D z = 1/5
Question 33
Vecteurs
33. The position vectors of the points OA = 2i + j - 4k and OB = -4i + 3j - 2k. A vector equation passing through A and B A r = 2i+j- 4k + μ(4i + 3j + 2k) B r = -4i-3j + 2k + μ(2i + j + 2k) C r = 2i + j − 4k + μ(-4i + 3j + 2k) D r = -4i+3j – 2k + μ(2i + j-4k)
Question 34
Primitives et intégrales
34. The x coordinate of the centre of gravity of a uniform lamina bounded by y = x, the x-axis and the line x = 4 is A 2 B 8/3 C 2/3 D 1
Question 35
Dénombrement
35. The number of different permutations of the letters INSECT in a line, if the vowels must be together is A 48 B 120 C 720 D 240
Question 36
Statistiques
36. Consider the result of a final exam taken by 120 students, as given in the following relative frequency distribution: Grade: Less than 50, 50-59, 60-69, 70-79, 80-89, 90-100 Cumulative frequency: 15%, 10%, 56%, 25%, 15%, 5% How many students received at least a 70 on this exam? A 54 B 45 C 25 D 30
Question 37
Statistiques
37. This question is based on the following sample of ages (in months) of 18 children at a day care: 36, 42, 18, 32, 22, 22, 25, 29, 30, 31, 19, 24, 35, 29, 26, 36, 24, and 28. The median age of the children is A 29 B 28.2 C 30.5 D 28.5
Question 38
Probabilités
38. Suppose the respective probabilities are 0.7, 0.2, and 0.1 that a person applying for a driver's license in Saskatchewan will require 1, 2, or 3 attempts in order to obtain a license. Let X be a random variable, the number of attempts in order to obtain a license. Find the mean (expected value) of X. A 0.63 B 2 C 1 D 1.4
Question 39
Question 4
Équations et inéquations
4. The range of values for which (x-3)(x-2) / (x+1) > 0 is A {x: -1 < x < 2 U x > 3} B {x:x <-1 U 2 < x < 3} C {x: -1 < x <2U2 < x <3} D {x: x < -1 U x > 3}
Question 40
Question 41
Probabilités
41. A discrete random variable Y has the following probability distribution: y: 0, 1, 2, 3, 4 P(Y = y): 0.12, 0.08, β, 0.34, 0.14 The value of β is: A 0.32 B 0.23 C 1 D 0.36
Question 42
Probabilités
42. Two events A and B are such that P(B) = 1/3, P(A ∩ B) = 1/4 and P(B/A) = 1/3. P(A/B) = A 1/5 B 8/45 C 5/8 D 3/8
Question 43
Probabilités
43. The probability distribution of a discrete random variable, X, is as shown below: X = x: 1, 2, 3, 4, 5 P(X = x): 1/24, 5/24, 1/2, 5/24, 1/24 E(3X - 4) = A 2 B 5 C 3 D 9
Question 44
Probabilités
44. The probability density of a continuous random variable X is defined as follows: f(x) = { 1/9x², 0 ≤ x ≤ 3 ; 0, otherwise P(X ≤ 1)= A 1/12 B 1/27 C 1/9 D 1/3
Question 45
Probabilités
45. The Random variable X has probability density function f defined by f(x) = { ax(2 – x), 0 ≤ x ≤ 2 ; 0, otherwise The value of a = A 3/4 B 56/3 C 42/3 D 4/3
Question 46
Dénombrement
46. In a class, 25 students offer Economics or Geography or both. If 12 students offer Economics and 17 students offer Geography, the number of students offering both subjects is A 2 B 4 C 5 D 6
Question 47
Statistiques
47. The regression lines of y on x and x on y are y = 0.64x + 2.5 and x = 0.36y – 1.8 respectively. The product moment correlation coefficient for this data is A 0.84 B 0.48 C 0.60 D 0.68
Question 48
Statistiques
48. The mean of five numbers 2, 3, 5, 6, 8 is 4.8. What is the standard deviation? A 14.4 B 17.48 C 2.14 D 2.21
Question 49
Probabilités
49. A fair die is rolled once. Given that the score is an even number, the probability that it is a prime number is A 1/3 B 1/2 C 2/3 D 1/6
Question 5
Géométrie dans le plan
5. Which of the following is NOT an equation of a circle A x² + (y - 2)² – 9 = 0. B x² + y² + 2x + 3xy = 4 C x² + 2x + y² - 2y - 2 = 0 D x²+9-6x – 2y² - 8y = 3
Question 50
Probabilités
50. The random variable X,is such that X~Bin(50, 0.2). Using the normal approximation to the binomial distribution, A X~N(10,√8) B X~N (10,4) C X~N(10,8²) D X~N (10,8)
Question 6
Polynômes
6. Given that α and ß arethe roots of the equation 2x² - 4x + 1, then the equation whose roots are α² and ß² is A 4x² - 12x + 1 = 0 B 2x² - 4x + 1 = 0 C 4x²-2x + 1 = 0 D 4x² 3x + 1 = 0
Question 7
Trigonométrie
7. If θ is very small and measured in radians then the approximate value of (1+cosθ) / (2+sinθ) is A (1+2θ) / (2(1+θ)) B (2-θ) / 2 C (1+θ²) / (4-θ²) D (1+θ²) / (4+θ²)
Question 8
Polynômes
8. The numerical value of the term independent of x in the expansion of (x + 2/x)² is A 48 B 64 C 16 D 32
Question 9
Suites numériques
9. The sum of the first n terms of a sequence is 2n² + n. The nth term of the sequence is A 2n-1 B 3n-1 C 4n-1 D 4n-3
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