HomeSS 1Further MathematicsSS1 Further Maths Second Term Examination

SS1 Further Maths Second Term Examination

SS1 Further Maths Second Term Examination

Part A

Objectives

  1. A linear inequality has a degree of ____. a) 1 b) 2 c) 3 d) 0
  2. In a linear inequality, the sign ≤ represents ____. a) less than b) greater than c) less than or equal to d) greater than or equal to
  3. The solution to a linear inequality is represented on a number line using ____. a) circles b) squares c) arrows d) crosses
  4. In mapping, each element in the domain is paired with exactly ____ element(s) in the range. a) one b) two c) three d) four
  5. A function assigns exactly one ____ for each element in the domain. a) range b) value c) variable d) function
  6. The x-intercepts of a quadratic equation are also known as its ____. a) roots b) maximum points c) minimum points d) turning points
  7. The quadratic formula is used to find the ____ of a quadratic equation. a) roots b) coefficients c) discriminants d) inequalities
  8. In trigonometry, sin(x) = opposite/hypotenuse in a ____ triangle. a) right-angled b) isosceles c) equilateral d) obtuse
  9. The tangent of an angle in a right-angled triangle is equal to ____ divided by ____. a) opposite, adjacent b) hypotenuse, adjacent c) adjacent, hypotenuse d) opposite, hypotenuse
  10. The reciprocal of sin(x) is ____. a) cos(x) b) tan(x) c) sec(x) d) csc(x)
  11. The formation of a quadratic equation involves the use of ____. a) two variables b) one variable c) three variables d) no variables
  12. The solution set of a linear inequality is usually expressed using ____ notation. a) set b) fraction c) decimal d) mixed number
  13. In mapping, a function can be represented as a set of ____. a) ordered pairs b) fractions c) decimals d) percentages
  14. The discriminant of a quadratic equation is found using the formula ____. a) b^2 – 4ac b) 4ab – c^2 c) a^2 + b^2 – c^2 d) b^2 + 4ac
  15. The range of a function is the set of ____ values. a) x b) y c) z d) w
  16. The roots of a quadratic equation can be ____ or ____. a) real, imaginary b) positive, negative c) whole numbers, fractions d) integers, decimals
  17. A linear inequality is represented graphically by shading the region ____ the boundary line. a) above b) below c) left of d) right of
  18. In trigonometry, cos(x) = ____/hypotenuse in a right-angled triangle. a) adjacent b) opposite c) hypotenuse d) tangent
  19. The standard form of a quadratic equation is ____. a) ax^2 + bx + c = 0 b) x^2 + y^2 = r^2 c) y = mx + c d) y = ax^2 + bx + c
  20. The reciprocal of cos(x) is ____. a) sin(x) b) tan(x) c) sec(x) d) csc(x)
  21. The maximum number of solutions for a linear inequality is ____. a) one b) two c) infinite d) zero
  22. The domain of a function consists of all possible ____ values. a) x b) y c) z d) w
  23. A quadratic equation can have ____ real roots. a) one b) two c) three d) none
  24. The ratio of tan(x) to sin(x) is ____. a) adjacent/opposite b) opposite/adjacent c) opposite/hypotenuse d) hypotenuse/adjacent
  25. The discriminant of a quadratic equation determines the nature of its ____. a) roots b) coefficients c) domain d) range
  26. The range of a quadratic function that opens upward is ____. a) all real numbers b) only positive numbers c) only negative numbers d) zero
  27. A linear inequality is solved by identifying the ____ region on a graph. a) shaded b) unshaded c) intersecting d) parallel
  28. The angle of elevation is measured ____ the horizontal line of sight. a) above b) below c) parallel to d) perpendicular to
  29. The roots of a quadratic equation can be found using the ____ formula. a) linear b) quadratic c) discriminant d) trigonometric
  30. In mapping, a function is represented using ____ notation. a) set b) decimal c) fraction d) percent

SS 1 FIRST TERM LESSON NOTE FURTHER MATHEMATICS

Part B

Theory

  1. Define a linear inequality and give an example.
  2. Explain what mapping is and why it is used in mathematics.
  3. Describe how to form a quadratic equation from given roots.
  4. What are the primary trigonometric ratios, and how are they defined?
  5. Explain the difference between a linear equation and a linear inequality.
  6. Define a function and explain its importance in mathematics.
  7. How do you determine the discriminant of a quadratic equation?
  8. Describe the process of solving a linear inequality graphically.
  9. What is the significance of the vertex in a quadratic function?
  10. How do you determine the range of a function?
  11. Explain how to find the roots of a quadratic equation using the quadratic formula.
  12. Describe the relationship between the angle of elevation and trigonometric ratios.
  13. What are the conditions for a system of linear inequalities to have a solution?
  14. How do you identify the domain of a function?
  15. Explain the concept of reciprocal trigonometric ratios.
  16. Describe how to graph a linear inequality on a coordinate plane.
  17. What is the difference between the domain and range of a function?
  18. Explain how to find the equation of a quadratic function given its vertex and another point.
  19. Describe the properties of the discriminant in quadratic equations.
  20. How do you determine whether a quadratic function opens upward or downward from its equation?

 

MID TERM TEST FIRST TERM FURTHER MATHS SS 2

 

 

Part C

Fill in the gaps

  1. A linear inequality has a degree of ____.
  2. In mapping, each element in the domain is paired with exactly ____ element(s) in the range.
  3. The quadratic formula is used to find the ____ of a quadratic equation.
  4. The reciprocal of cos(x) is ____.
  5. The discriminant of a quadratic equation determines the nature of its ____.
  6. The range of a quadratic function that opens upward is ____.
  7. The roots of a quadratic equation can be found using the ____ formula.
  8. The angle of elevation is measured ____ the horizontal line of sight.
  9. A linear inequality is solved by identifying the ____ region on a graph.
  10. In trigonometry, sin(x) = ____/hypotenuse in a right-angled triangle

Part A: Multiple-Choice Questions with Explanations

  1. A linear inequality has a degree of ____.
    Answer: (a) 1

    • A linear inequality involves variables raised to the first power (degree 1), such as 2x + 3 > 5.

  2. In a linear inequality, the sign ≤ represents ____.
    Answer: (c) less than or equal to

    • The symbol ≤ means the value on the left is either less than or exactly equal to the right-hand value.

  3. The solution to a linear inequality is represented on a number line using ____.
    Answer: (c) arrows

    • Arrows indicate an infinite range of values that satisfy the inequality.

  4. In mapping, each element in the domain is paired with exactly ____ element(s) in the range.
    Answer: (a) one

    • A function ensures each input (domain) maps to only one unique output (range).

  5. A function assigns exactly one ____ for each element in the domain.
    Answer: (b) value

    • The definition of a function states that each input has one unique output.

  6. The x-intercepts of a quadratic equation are also known as its ____.
    Answer: (a) roots

    • The x-intercepts are the points where the quadratic function touches the x-axis, also called solutions or roots.

  7. The quadratic formula is used to find the ____ of a quadratic equation.
    Answer: (a) roots

    • The quadratic formula: x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}
      • It finds the values of x that satisfy the quadratic equation.

  8. In trigonometry, sin(x) = opposite/hypotenuse in a ____ triangle.
    Answer: (a) right-angled

    • The Sine rule applies only in a right-angled triangle.

  9. The tangent of an angle in a right-angled triangle is equal to ____ divided by ____.
    Answer: (a) opposite, adjacent

    • tan(θ) = opposite / adjacent.

  10. The reciprocal of sin(x) is ____.
    Answer: (d) csc(x)

  • The cosecant function (csc x) is the reciprocal of sine: csc(x)=1sin⁡(x)csc(x) = \frac{1}{\sin(x)}
  1. The formation of a quadratic equation involves the use of ____.
    Answer: (b) one variable
  • Quadratic equations have one variable raised to the second power (e.g., x² + 3x – 5 = 0).
  1. The solution set of a linear inequality is usually expressed using ____ notation.
    Answer: (a) set
  • Example: {x | x > 2} represents values greater than 2.
  1. In mapping, a function can be represented as a set of ____.
    Answer: (a) ordered pairs
  • A function is often written as (x, y) pairs, e.g., (2, 4), (3, 9).
  1. The discriminant of a quadratic equation is found using the formula ____.
    Answer: (a) b² – 4ac
  • The discriminant determines the nature of roots:
    • > 0 → Two real roots
    • = 0 → One real root
    • < 0 → Complex roots
  1. The range of a function is the set of ____ values.
    Answer: (b) y
  • The range is the set of possible output values (y-values).
  1. The roots of a quadratic equation can be ____ or ____.
    Answer: (a) real, imaginary
  • If the discriminant b² – 4ac < 0, the roots are imaginary.
  1. A linear inequality is represented graphically by shading the region ____ the boundary line.
    Answer: (a) above
  • If y > an expression, shade above; if y <, shade below.
  1. In trigonometry, cos(x) = ____/hypotenuse in a right-angled triangle.
    Answer: (a) adjacent
  • cos(θ) = adjacent/hypotenuse.

  1. The standard form of a quadratic equation is ____.
    Answer: (a) ax² + bx + c = 0

  2. The reciprocal of cos(x) is ____.
    Answer: (c) sec(x)

  • sec(x) = 1/cos(x).
  1. The maximum number of solutions for a linear inequality is ____.
    Answer: (c) infinite
  • Linear inequalities have an infinite set of solutions.

  1. The domain of a function consists of all possible ____ values.
    Answer: (a) x

  2. A quadratic equation can have ____ real roots.
    Answer: (b) two

  • Discriminant > 0 means two distinct real roots.
  1. The ratio of tan(x) to sin(x) is ____.
    Answer: (a) adjacent/opposite
  • tan(x)/sin(x) = cos(x).

  1. The discriminant of a quadratic equation determines the nature of its ____.
    Answer: (a) roots

  2. The range of a quadratic function that opens upward is ____.
    Answer: (b) only positive numbers

  • If a > 0, the range is y ≥ the minimum value.

  1. A linear inequality is solved by identifying the ____ region on a graph.
    Answer: (a) shaded

  2. The angle of elevation is measured ____ the horizontal line of sight.
    Answer: (a) above

  3. The roots of a quadratic equation can be found using the ____ formula.
    Answer: (b) quadratic

  4. In mapping, a function is represented using ____ notation.
    Answer: (a) set

Part B: Theory Questions with Explanations

  1. Define a linear inequality and give an example.

    • A linear inequality is an algebraic expression that compares two expressions using inequality symbols.
    • Example: 3x – 2 < 7.

  2. Explain what mapping is and why it is used in mathematics.

    • Mapping shows how elements in the domain relate to elements in the range.

  3. Describe how to form a quadratic equation from given roots.

    • If roots are r₁ and r₂, the equation is: (x−r1)(x−r2)=0(x – r₁)(x – r₂) = 0

  4. What are the primary trigonometric ratios, and how are they defined?

    • Sine: sin(θ) = opposite/hypotenuse
    • Cosine: cos(θ) = adjacent/hypotenuse
    • Tangent: tan(θ) = opposite/adjacent

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