math

• What is the total mark for the National 5 Mass 2024 paper one?

  40 marks
• What are the two ways to evaluate $3\frac{1}{2} - 1\frac{1}{4}?$


  Subtracting whole numbers and fractions separately or converting to a common denominator
• What is the step-by-step method to evaluate $3\frac{1}{2} - 1\frac{1}{4}$ using a common denominator?


  1. Convert mixed fractions to improper fractions:

  • $3\frac{1}{2} =$$\frac{7}{2}$
  • $1\frac{1}{4} =$$\frac{5}{4}$

  
  

  1. Find a common denominator for $\frac{7}{2}$ and $\frac{5}{4}:$

  • The common denominator is 4

  
  

  1. Rewrite the fractions with the common denominator:

  • $\frac{7}{2} =$$\frac{14}{4}$
  • $\frac{5}{4}$ remains the same

  
  

  1. Subtract the numerators:

  • $\frac{14}{4} - \frac{5}{4} =$$\frac{9}{4}$

  
  

  1. Convert back to a mixed fraction:

  • $\frac{9}{4} =$$2\frac{1}{4}$
• How do you find the median of a set of ordered numbers?

  The median is the middle value when the numbers are arranged in order
• What is the interquartile range (IQR)?

  The interquartile range is the difference between the upper quartile and the lower quartile of a dataset. It represents the range containing the middle 50% of the data
• What are the steps to find the interquartile range?

  1. Order the data from least to greatest
  2. Find the median
  3. The lower quartile is the median of the lower half of the data
  4. The upper quartile is the median of the upper half of the data
  5. Calculate the difference between the upper and lower quartiles: IQR = Upper Quartile - Lower Quartile
• What are two valid comments about the median and interquartile range of the camera prices?

  Median:

  • On average, camera prices are higher in shops than online

  
  

  Interquartile Range:

  • The prices of cameras vary more online than in shops
• How do you simplify $\sqrt{75} - \sqrt{3}?$


  1. Factorize 75: $75 =$$25 \times 3$
  2. Simplify the square root of 75: $\sqrt{75} =$$\sqrt{25 \times 3} =$$\sqrt{25} \times \sqrt{3} =$$5\sqrt{3}$
  3. Combine the terms: $5\sqrt{3} - \sqrt{3} =$$4\sqrt{3}$
• What are the properties of tangents to a circle?

  • A tangent meets a radius at right angles
  • Two tangents from the same external point are equal in length
  • The angle formed by two tangents drawn from the same external point to the circle is twice the angle subtended at the center by the arc between the tangents
• If AC is a tangent to the circle at B, what is the relationship between angle BAC and angle ABC?

  Angle BAC and angle ABC are alternate angles and are equal
• In the given circle, if angle FOD = 125°, what is the measure of the shaded angle?

  62.5°
• What equation is used to represent the relationship between distance (d) and time (t)?

  \(d = -2t + 32\)
• What axes are used in the distance-time graph?

  The axes are D and T.
• What is the meaning of the equation \(d = -2t + 32\)?

  The equation shows that the distance from the finishing line decreases by 2 units for every unit of time.
• What are the main circle geometry rules mentioned?

  • A tangent meets a radius at right angles
  • Angles on a straight line add to \(180^{\circ}\)
  • Two radii make an isosceles triangle
• How do you find the shaded angle in the diagram?

  By applying circle geometry rules about tangents, radii, and angles in triangles and straight lines.
• How do angles around a point sum up?

  Angles around a point add up to \(360^{\circ}\).
• What rule about right angles relates to tangents and radii in the diagram?

  A tangent makes a radius at right angles.
• Why is the shaded angle calculated by subtracting the sum of angles around the point from \(360^{\circ}\)?

  Because angles around a point total \(360^{\circ}\), subtracting known angles gives the remaining angles, which sum to the shaded angle.
• How do you find the angles in a four-sided shape?

  Angles in a four-sided shape add up to \(360^{\circ}\).
• What is the process of completing the square?

  1. Half the coefficient of the x term
  2. Take away the square of that term
  3. Add the constant term
• What is the general form of completing the square for a quadratic expression?

  \(x^2 - 6x + 8 = (x - e)^2 + B\)
• What are the coordinates of the turning point of a quadratic graph?

  (3, -1).
• If \(x = 0\), what is the y-intercept of \(y = x^2 - 6x + 8\)?

  8.
• How do you find the x-intercepts of a quadratic equation?

  • Set the equation to zero: \(x^2 - 6x = 0\)
  • Factorize: \(x(x - 6) = 0\)
  • Solve for x: \(x = 0\) and \(x = 6\)
• What is the sum of the powers when multiplying terms with the same base?

  Add the powers.
• What does \(x^0\) equal?


  1.
• What does it mean when two triangles are similar?

  • Corresponding angles are equal
  • Corresponding sides are proportional
• How do you use scale factors with similar triangles to find missing side lengths?

  Multiply the scale factor by a known side length to find an unknown corresponding side length.
• Area of a Circle

  A = π x R²
• Volume of a Cylinder


  V = π x R² x H
• Circumference


  C = π x D
• simultaneous equations


  A pair of linear equations in which the variable appears in each equation, and the solution involves solving for the intersection point of the two lines.
• percentage increase


  A percentage increase is calculated by finding the amount of an increase as a fraction of the original value, then multiplying by 100.
• surd


  A value in the form of an expression containing a square root (e.g., √2, 3 + √2).
• 1. intercept


  The point where a graph of a linear equation intersects the x-axis, giving the value of x when y is equal to zero.
• gradient


  The rate of change of a linear equation, calculated by dividing the difference in y-values by the difference in x-values.
• quadratic formula


  A formula used to solve quadratic equations in the form ax^2 + bx + c = 0, given by x = (-b ± √(b^2 - 4ac)) / 2a.
• gradient formula


  m = (y2 - y1) / (x2 - x1), where m is the gradient and (x1, y1) and (x2, y2) are two points on the line.