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Advanced mathematics
FAST · ریاضی · 41 سوالات
نام: ____________________ تاریخ: ____________
The derivative of x³ with respect to x is:
- A 3x
- B x⁴ ÷ 4
- C 3x²
- D x²
The integral of 2x with respect to x is:
- A 2 + c
- B x² + c
- C 2x² + c
- D x + c
The roots of x² − 5x + 6 = 0 are:
- A −1 and 6
- B 2 and 3
- C 1 and 6
- D −2 and −3
The sum of the first 10 terms of an arithmetic progression with first term 2 and common difference 3 is:
- A 160
- B 150
- C 155
- D 145
The value of log₂ 32 is:
- A 16
- B 4
- C 6
- D 5
The value of sin 30° is:
- A 1/2
- B √2/2
- C 1
- D √3/2
The determinant of the matrix with rows (2, 3) and (1, 4) is:
- A −5
- B 11
- C 5
- D 8
The slope of the line through (1, 2) and (3, 8) is:
- A 6
- B 3
- C 4
- D 2
The limit of (sin x) ÷ x as x approaches 0 is:
- A 1
- B ∞
- C −1
- D 0
The number of different arrangements of 4 distinct letters is:
- A 12
- B 24
- C 8
- D 16
The sum to infinity of the geometric series 1 + 1/2 + 1/4 + … is:
- A 3/2
- B 1
- C 2
- D 4
The distance between the points (0, 0) and (6, 8) is:
- A 14
- B 10
- C 7
- D 12
The derivative of cos x with respect to x is:
- A −sin x
- B tan x
- C −cos x
- D sin x
The integral of 3x² with respect to x is:
- A x³ + c
- B 6x + c
- C x² + c
- D 3x³ + c
The limit of (x² − 4) ÷ (x − 2) as x approaches 2 is:
- A 0
- B ∞
- C 2
- D 4
Which expression equals cos 2θ?
- A 1 − 2 sin²θ
- B 1 + 2 sin²θ
- C 2 sin θ cos θ
- D sin²θ − cos²θ
The 12th term of an arithmetic progression with first term 5 and common difference 4 is:
- A 45
- B 53
- C 48
- D 49
The 8th term of the geometric progression 3, 6, 12, … is:
- A 192
- B 96
- C 768
- D 384
The value of log₁₀ 1000 is:
- A 10
- B 100
- C 3
- D 2
If log₃ x = 4, then x is:
- A 81
- B 12
- C 64
- D 7
If A has rows (1, 2) and (0, 1), then A² has rows:
- A (1, 4) and (0, 1)
- B (1, 2) and (0, 1)
- C (2, 4) and (0, 2)
- D (1, 4) and (0, 2)
The inverse of the matrix with rows (2, 1) and (1, 1) has rows:
- A (1, 1) and (1, 2)
- B (2, −1) and (−1, 1)
- C (1, −1) and (−1, 2)
- D (−1, 1) and (1, −2)
The distance of the point (3, 4) from the origin is:
- A 5
- B 25
- C 7
- D 12
The midpoint of (2, 4) and (6, 10) is:
- A (4, 7)
- B (3, 5)
- C (4, 6)
- D (8, 14)
The equation of the circle with centre at the origin and radius 5 is:
- A x + y = 25
- B x² − y² = 25
- C x² + y² = 25
- D x² + y² = 5
The focus of the parabola y² = 8x is:
- A (8, 0)
- B (4, 0)
- C (0, 2)
- D (2, 0)
The number of diagonals of a hexagon is:
- A 15
- B 12
- C 9
- D 6
The value of 6C3 is:
- A 18
- B 10
- C 20
- D 30
The probability that the sum of two dice is 7 is:
- A 7/36
- B 1/12
- C 1/7
- D 1/6
Two fair coins are tossed. The probability of at least one head is:
- A 3/4
- B 1/4
- C 1/2
- D 2/3
The modulus of the complex number 3 + 4i is:
- A 5
- B √7
- C 7
- D 25
The product (2 + 3i)(2 − 3i) is:
- A −5
- B 4 + 9i
- C −13
- D 13
The discriminant of x² − 6x + 9 = 0 is:
- A −36
- B 36
- C 18
- D 0
The product of the roots of 2x² − 5x + 3 = 0 is:
- A 2/3
- B −3/2
- C 3/2
- D 5/2
The solution of |x| < 3 is:
- A x > −3
- B −3 < x < 3
- C x < 3
- D x < −3 or x > 3
The sum of the coefficients in the expansion of (1 + x)⁴ is:
- A 8
- B 32
- C 16
- D 4
The dot product of (1, 2, 3) and (4, −5, 6) is:
- A 12
- B 0
- C 21
- D −12
The sum of the integers from 1 to 20 is:
- A 210
- B 420
- C 200
- D 190
The value of the integral of x from 0 to 1 is:
- A 0
- B 1/2
- C 1
- D 2
The derivative of e²ˣ with respect to x is:
- A e²ˣ ÷ 2
- B 2xe²ˣ
- C e²ˣ
- D 2e²ˣ
The angle in radians equal to 180° is:
- A π
- B 2π
- C π/2
- D π/4
جوابی کلید
1. C, 2. B, 3. B, 4. C, 5. D, 6. A, 7. C, 8. B, 9. A, 10. B, 11. C, 12. B, 13. A, 14. A, 15. D, 16. A, 17. D, 18. D, 19. C, 20. A, 21. A, 22. C, 23. A, 24. A, 25. C, 26. D, 27. C, 28. C, 29. D, 30. A, 31. A, 32. D, 33. D, 34. C, 35. B, 36. C, 37. A, 38. A, 39. B, 40. D, 41. A
The power rule gives 3x² for x³.
Integrating 2x gives x² plus a constant.
The equation factors as (x − 2)(x − 3) = 0.
S = (10 ÷ 2)(2 × 2 + 9 × 3) = 5 × 31 = 155.
2⁵ = 32, so the logarithm is 5.
This is a standard value.
The determinant is 2 × 4 − 3 × 1 = 5.
Slope = (8 − 2) ÷ (3 − 1) = 3.
This is a standard limit.
4! = 4 × 3 × 2 × 1 = 24.
The sum is a ÷ (1 − r) = 1 ÷ (1/2) = 2.
The distance is √(36 + 64) = √100 = 10.
This is a standard derivative.
The power rule gives x³ for 3x².
The expression simplifies to x + 2, which is 4 at x = 2.
This is one of the double angle identities.
a + 11d = 5 + 44 = 49.
The term is 3 × 2⁷ = 384.
10³ = 1000.
x = 3⁴ = 81.
Multiplying the matrix by itself gives 1×2 + 2×1 = 4 in the top right.
The determinant is 1, and the inverse swaps the diagonal and changes the other signs.
The distance is √(9 + 16) = 5.
The midpoint is the mean of each coordinate.
The equation is x² + y² = r².
For y² = 4ax, the focus is (a, 0), and here 4a = 8.
The number is n(n − 3) ÷ 2 = 6 × 3 ÷ 2 = 9.
6C3 = 6! ÷ (3! × 3!) = 20.
Six of the 36 outcomes give a sum of 7.
Only tail and tail has no head, so the probability is 1 − 1/4.
The modulus is √(9 + 16) = 5.
The product is 4 − 9i² = 4 + 9 = 13.
b² − 4ac = 36 − 36 = 0, so the roots are equal.
The product of the roots is c ÷ a.
The distance of x from zero must be less than 3.
Put x = 1 to get 2⁴ = 16.
The product is 4 − 10 + 18 = 12.
The sum is 20 × 21 ÷ 2 = 210.
The antiderivative is x²/2, which is 1/2 at 1.
The chain rule gives a factor of 2.
A half turn is π radians.