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Excel AS Pure Mathematics terms and their correct answers for 2024 candidates, Exams of Mathematics

Excel AS Pure Mathematics terms and their correct answers for 2024 candidates

Typology: Exams

2023/2024

Available from 06/07/2024

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Excel AS Pure Mathematics terms
and their correct answers for 2024
candidates
1. Domain - Correct Answers the set of possible inputs for a function.
2. Range - Correct Answers the set of possible outputs of a function.
3. Discriminant - Correct Answers b² - 4ac > 0 then two distinct real
roots.
4. b² - 4ac = 0 then one repeated real root.
5. b² - 4ac < 0 then a quadratic function has no real roots.
6. Types of Lines for Regions - Correct Answers If y < f(x) or y > f(x)
then the curve y = f(x) is not included in the region, and is
represented by a dotted line.
7. If y ≤ f(x) or y ≥ f(x) then the curve y = f(x) is included in the region,
and is represented by a solid line.
8. Graph Translations - Correct Answers y = f(x) + a is a translation of
the graph y = f(x) by an upwards.
9. y = f(x + a) is a translation of the graph y = f(x) by a to the left.
10. Graph Stretches - Correct Answers y = aft(x) is a stretch of the
graph y = f(x) by a scale factor of a in the vertical direction.
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Excel AS Pure Mathematics terms

and their correct answers for 2024

candidates

  1. Domain - Correct Answers the set of possible inputs for a function.
  2. Range - Correct Answers the set of possible outputs of a function.
  3. Discriminant - Correct Answers b² - 4ac > 0 then two distinct real roots.
  4. b² - 4ac = 0 then one repeated real root.
  5. b² - 4ac < 0 then a quadratic function has no real roots.
  6. Types of Lines for Regions - Correct Answers If y < f(x) or y > f(x) then the curve y = f(x) is not included in the region, and is represented by a dotted line.
  7. If y ≤ f(x) or y ≥ f(x) then the curve y = f(x) is included in the region, and is represented by a solid line.
  8. Graph Translations - Correct Answers y = f(x) + a is a translation of the graph y = f(x) by an upwards.
  9. y = f(x + a) is a translation of the graph y = f(x) by a to the left.
  10. Graph Stretches - Correct Answers y = aft(x) is a stretch of the graph y = f(x) by a scale factor of a in the vertical direction.
  1. y = f (ax) is a stretch of the graph y = f(x) by a scale factor of 1/a in the horizontal direction.
  2. Graph Reflections - Correct Answers y = -f(x) is a reflection of the graph of y = f(x) in the x-axis.
  3. y = f (-x) is a reflection of the graph of y = f(x) in the y-axis.
  4. Gradient of Equation - Correct Answers m = (y₂ - y₁) ÷ (x₂ - x₁)
  5. Equation of a Line - Correct Answers y - y₁ = m(x - x₁)
  6. with cords (x₁, y₁)
  7. Distance Formula - Correct Answers √((x₂ - x₁)² + (y₂ - y₁)²)
  8. from (x₁, y₁) to (x₂, y₂)
  9. Perpendicular Bisector - Correct Answers -1/m
  10. where m is original gradient
  11. Standard Equation of a Circle - Correct Answers (x - a)² + (y - b)² = r²
  12. with center (a, b) and radius r
  13. Equation of a Circle (fog) - Correct Answers x² + y² + 2fx + 2gy
    • c = 0
  14. with center (-f, -g) and radius √(f² + g² - c)
  15. Circle Theorems - Correct Answers • Tangent to a circle is perpendicular to the radius of the circle at the point of intersection.
    • Perpendicular bisector of a chord will go through the circle center.
    • If triangle forms across the circle, its diameter is the hypotenuse of the right-angled triangle.
  1. Sine Rule Solutions - Correct Answers Sometimes produces two possible solutions for a missing angle:
  2. sin(θ) = sin(180 - θ)
  3. Sine Graph - Correct Answers
  4. Cosine Graph - Correct Answers
  5. Tangent Graph - Correct Answers
  6. CAST Diagram - Correct Answers
  7. Trigonometry - Correct Answers
  8. Trig Triangles (30, 60, 90) - Correct Answers
  9. Trig Triangles (45, 90) - Correct Answers
  10. Principal Value - Correct Answers When you use the inverse trig function on your calculator, the angle you get is the principal value.
  11. Sine and Cosine Formulae - Correct Answers sin²(θ) + cos²(θ) = 1
  12. tan(θ) = sin(θ) ÷ cos(θ)
  13. Triangle Law for Vector Addition - Correct Answers A→B + B→C = A→C
  14. If A→B = a, B→C = b and A→C = c, then a + b = c
  15. Vector Rules - Correct Answers • P→Q = R→S, then line segments PQ and RS are equal in length and are parallel.
    • A→B = -(B→A)
    • Any vector parallel to the vector a may be written as a
  16. Vector Magnitude - Correct Answers a = xi + in → |a| = √(x² + y²)
  1. Unit Vector - Correct Answers In the direction of a, unit vector is
  2. a ÷ |a|
  3. Position Vector - Correct Answers O→P = pi + qi
  4. A→B = O→B - O→A
  5. First Derivative Formula - Correct Answers
  6. Differentiation Formula - Correct Answers die/dx = andⁿ⁻¹
  7. Function's Gradient - Correct Answers Increasing on the interval [a, b] if f'(x) ≥ 0 for all values of a < x < b.
  8. Decreasing on the interval [a, b] if
  9. F'(x) ≤ 0 for all values of a < x < b.
  10. Stationary Point - Correct Answers Any point on the curve y = f(x) where f'(x) = 0.
    • If f’’ (a) > 0, the point is a local minimum.
    • If f’’ (a) < 0, the point is a local maximum.
  11. Integration Formula - Correct Answers y = k/(n+1) x xⁿ⁺¹ + c
  12. Area of a Triangle - Correct Answers ½ x ab x sin(C)
  13. Differentiating eel - Correct Answers y = eᵏˣ → die/dx = keᵏˣ
  14. Logarithm Format - Correct Answers
  15. Logarithm Laws - Correct Answers
  16. Natural Log (y = ln x) - Correct Answers the graph of y = ln(x) is a reflection of the graph y = eel in the line y = x.
  17. eelⁿ⁽ˣ⁾ = ln(eel) = x