FURTHER MATHEMATICS SECOND TERM EXAMINATION SS 1

Part A

Objectives

The integral of 2x with respect to x is ____. a) x^2 + C b) x^3 + C c) x + C d) 2x^2 + C
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
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

In calculus, the product rule is used to differentiate ____. a) sums b) differences c) products d) quotients
The second derivative of a function gives information about its ____. a) concavity b) slope c) intercept d) maximum value
A matrix with the same number of rows and columns is called a ____ matrix. a) square b) rectangular c) diagonal d) identity

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
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
The rank of a matrix is determined by the number of ____ rows or columns. a) zero b) non-zero c) positive d) negative

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
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)
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

In trigonometry, sin(x) = opposite/hypotenuse in a ____ triangle. a) right-angled b) isosceles c) equilateral d) obtuse
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
The period of a trigonometric function is the ____ of one complete cycle. a) amplitude b) wavelength c) height d) width

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
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 ∞
In probability, mutually exclusive events have a probability of ____ occurring simultaneously. a) 0 b) 1 c) 0.5 d) 0 or 1

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
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
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

The standard deviation measures the ____ of a data set from its mean. a) spread b) center c) mode d) median
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)
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

An arithmetic sequence is characterized by a common ____ between consecutive terms. a) ratio b) sum c) difference d) product
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
A geometric sequence is characterized by a common ____ between consecutive terms. a) ratio b) sum c) difference d) product

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
The formula for the area of a trapezium with bases $b_{1}$ and $b_{2}$ and height $h$ is given by ____. a) $2 1 (b_{1} + b_{2}) h$ b) $2 1 (b_{1} - b_{2}) h$ c) $2 1 (b_{1} b_{2}) h$ d) $2 1 (b_{1} \times b_{2}) h$
In a right triangle, the side opposite the right angle is called the ____. a) hypotenuse b) base c) adjacent side d) opposite side

The angle of elevation is measured ____ the horizontal line of sight. a) above b) below c) parallel to d) perpendicular to
The complementary angle to 30 degrees is ____ degrees. a) 30 b) 45 c) 60 d) 90
The derivative of a constant term in calculus is always ____. a) zero b) one c) undefined d) negative

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
The inverse of a matrix A is denoted as ____. a) A’ b) A^T c) A^-1 d) A^2
In matrix addition, matrices must have the same ____. a) number of elements b) number of rows c) number of columns d) number of diagonals

A parabola opens upward if the coefficient of $x^{2}$ is ____. a) positive b) negative c) zero d) one
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

Part C

Fill in the gap

The formula for the area of a circle is ____.
The turning point of a quadratic function is also called the ____.
The probability of an event E not occurring is denoted as P(E’) and is equal to ____.

The inverse of a 2×2 matrix [[a, b], [c, d]] is calculated using the formula ____

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