FURTHER MATHEMATICS SECOND TERM EXAMINATION SS 1

Part A

Objectives

1. The derivative of x^3 with respect to x is ____. a) 3x^2 b) 2x c) x^2 d) 3x
2. The integral of 2x with respect to x is ____. a) x^2 + C b) x^3 + C c) x + C d) 2x^2 + C
3. The point of intersection of a curve and its tangent is called a ____. a) maximum point b) minimum point c) stationary point d) critical point
4. The turning point of a curve occurs where the derivative changes from ____ to ____. a) positive, negative b) negative, positive c) increasing, decreasing d) decreasing, increasing
5. In calculus, the product rule is used to differentiate ____. a) sums b) differences c) products d) quotients
6. The second derivative of a function gives information about its ____. a) concavity b) slope c) intercept d) maximum value
7. A matrix with the same number of rows and columns is called a ____ matrix. a) square b) rectangular c) diagonal d) identity
8. In matrix multiplication, the number of columns in the first matrix must equal the number of ____ in the second matrix. a) rows b) columns c) elements d) diagonals
9. The determinant of a 2×2 matrix [[a, b], [c, d]] is calculated as ____. a) ad – bc b) ac – bd c) ab – cd d) bc – ad
10. The rank of a matrix is determined by the number of ____ rows or columns. a) zero b) non-zero c) positive d) negative
11. The equation of a circle with center (h, k) and radius r is given by ____. a) (x – h)^2 + (y – k)^2 = r b) (x + h)^2 + (y + k)^2 = r c) (x – h)^2 – (y – k)^2 = r d) (x + h)^2 – (y + k)^2 = r
12. The equation of a parabola in vertex form is ____. a) y = ax^2 + bx + c b) y = a(x – h)^2 + k c) y = a(x + h)^2 + k d) y = a(x – h)(x + k)
13. The focus of a parabola is located ____ the vertex along the axis of symmetry. a) above b) below c) to the left of d) to the right of
14. In trigonometry, sin(x) = opposite/hypotenuse in a ____ triangle. a) right-angled b) isosceles c) equilateral d) obtuse
15. The trigonometric identity tan(x) = sin(x)/cos(x) is true for angles in a ____ triangle. a) right-angled b) isosceles c) equilateral d) acute
16. The period of a trigonometric function is the ____ of one complete cycle. a) amplitude b) wavelength c) height d) width
17. The equation of a sine wave is given by y = A sin(Bx + C) + D, where A represents the ____. a) amplitude b) period c) phase shift d) vertical shift
18. The probability of an event E occurring is denoted as P(E) and lies between ____. a) 0 and 1 b) -1 and 1 c) 1 and ∞ d) -∞ and ∞
19. In probability, mutually exclusive events have a probability of ____ occurring simultaneously. a) 0 b) 1 c) 0.5 d) 0 or 1
20. The mean of a data set is calculated by summing all values and dividing by the ____. a) range b) mode c) median d) number of values
21. The median of a data set is the middle value when the data is ____. a) arranged in ascending order b) arranged in descending order c) randomly distributed d) grouped in classes
22. The mode of a data set is the value that ____. a) occurs most frequently b) occurs least frequently c) is the average value d) is the largest value
23. The standard deviation measures the ____ of a data set from its mean. a) spread b) center c) mode d) median
24. In coordinate geometry, the distance between two points (x1, y1) and (x2, y2) is given by the formula ____. a) √((x2 – x1)^2 + (y2 – y1)^2) b) √((x2 + x1)^2 + (y2 + y1)^2) c) (x2 – x1)(y2 – y1) d) (x2 + x1)(y2 + y1)
25. The equation of a line passing through two points (x1, y1) and (x2, y2) is given by ____. a) y = mx + b b) y – y1 = m(x – x1) c) y = ax^2 + bx + c d) y = a(x – h)^2 + k
26. An arithmetic sequence is characterized by a common ____ between consecutive terms. a) ratio b) sum c) difference d) product
27. The nth term of an arithmetic sequence is given by the formula ____. a) an = a + (n – 1)d b) an = a * (n – 1)d c) an = a + nd d) an = a * nd
28. A geometric sequence is characterized by a common ____ between consecutive terms. a) ratio b) sum c) difference d) product
29. The sum of the first n terms of a geometric sequence is given by the formula ____. a) Sn = a * (1 – r^n) / (1 – r) b) Sn = a + r^n c) Sn = n * (a + l) / 2 d) Sn = n * a
30. The formula for the area of a trapezium with bases �1b1​ and �2b2​ and height $h$ is given by ____. a) 12(�1+�2)ℎ21​(b1​+b2​)h b) 12(�1−�2)ℎ21​(b1​−b2​)h c) 12(�1�2)ℎ21​(b1​b2​)h d) 12(�1×�2)ℎ21​(b1​×b2​)h
31. In a right triangle, the side opposite the right angle is called the ____. a) hypotenuse b) base c) adjacent side d) opposite side
32. The angle of elevation is measured ____ the horizontal line of sight. a) above b) below c) parallel to d) perpendicular to
33. The complementary angle to 30 degrees is ____ degrees. a) 30 b) 45 c) 60 d) 90
34. The derivative of a constant term in calculus is always ____. a) zero b) one c) undefined d) negative
35. The definite integral of a function represents the area ____ the curve and the x-axis. a) above b) below c) tangent to d) parallel to
36. The inverse of a matrix A is denoted as ____. a) A’ b) A^T c) A^-1 d) A^2
37. In matrix addition, matrices must have the same ____. a) number of elements b) number of rows c) number of columns d) number of diagonals
38. A parabola opens upward if the coefficient of �2x2 is ____. a) positive b) negative c) zero d) one
39. A tangent to a circle at a given point is ____ to the radius at that point. a) perpendicular b) parallel c) equal in length d) longer

Part B

1. Define the derivative of a function.
2. Explain what is meant by the integral of a function.
3. What is the relationship between a curve and its tangent at a point?
4. Define the rank of a matrix.
5. Explain what is meant by the determinant of a matrix.
6. Define the equation of a circle.
7. What is the vertex form of a parabola?
8. Define the period of a trigonometric function.
9. Explain the concept of probability.
10. Define the mean of a data set.
11. What is the median of a data set?
12. Define the mode of a data set.
13. Explain what is meant by standard deviation.
14. Define the distance formula in coordinate geometry.
15. What is the equation of a line passing through two points?
16. Define an arithmetic sequence.
17. Explain what is meant by a geometric sequence.
18. Define the area of a trapezium.
19. What is the angle of elevation?
20. Explain the concept of the inverse of a matrix.

Part C

Fill in the gap

1. The integral of 3x^2 with respect to x is ____.
2. The determinant of a 3×3 matrix is calculated by expanding along a ____.
3. The equation of a line in slope-intercept form is y = mx + ____.
4. The sum of the angles in a triangle is ____ degrees.
5. The nth term of an arithmetic sequence is given by ____.
6. In trigonometry, cos(x) = ____/hypotenuse in a right-angled triangle.
7. The formula for the area of a circle is ____.
8. The turning point of a quadratic function is also called the ____.
9. The probability of an event E not occurring is denoted as P(E’) and is equal to ____.
10. The inverse of a 2×2 matrix [[a, b], [c, d]] is calculated using the formula ____