Maths

• How do you convert mixed numbers into improper fractions?

  Multiply the whole number by the denominator and add the numerator.
• What is the process for dividing fractions?


  Multiply by the reciprocal of the second fraction.
• How do you convert an improper fraction to a mixed number?


  Divide the numerator by the denominator to find the whole number and the remainder.
• What does it mean to shade in the circle on a number line for inequalities?


  It indicates that the value is included in the solution.
• What is the modal class in a frequency table?


  The class with the highest frequency.
• How do you find the median from a frequency table with 60 students?


  Count up the frequencies until you reach the middle value, which is the 30.5th person.
• What is the interval that contains the median for 60 students based on the frequencies given?


  20 to 30
• What is the final part of the question asking for in terms of estimating the mean?


  It asks for an estimate based on the frequency distribution.
• What is the modal class in the given data?


  The modal class is 10 to 20.
• How do you determine the modal class from a frequency table?


  You identify the class with the highest frequency.
• How do you find the interval that contains the median when there are 60 students?


  You calculate the position of the median as $\frac{60 + 1}{2} =$$30.5$.
• What do you do after calculating the median position of 30.5?


  You count the cumulative frequencies until you exceed 30.5.
• What is the interval that contains the median for the given data?


  The interval is 20 to 30.
• How do you estimate the mean time spent revising from a frequency table?


  • Calculate midpoints for each class interval.
  • Multiply midpoints by their corresponding frequencies.
  • Sum the results to get total time.
  • Divide by the total number of students.
• What is the mean time spent revising if the total time is 1,470 for 60 students?


  The mean time is $\frac{1470}{60} =$$24.5$.
• What is the first step to input a calculation into a calculator as described?

  Press the fraction button.
• How do you round a number to three significant figures?


  You identify the first three non-zero digits and round based on the next digit.
• What is the rounded value of 2.746 to three significant figures?


  The rounded value is 2.75.
• What are the steps to construct an angle bisector using compasses?


  1. Place the compass point at the angle vertex.
  2. Draw an arc across both lines of the angle.
  3. Mark the intersection points of the arc with the lines.
  4. Draw arcs from each intersection point.
  5. Connect the vertex to the intersection of the arcs.
• How do you draw the graph of the equation $y =$$3x +$$2$?


  1. Create a table of values for <latex>x</text{ from -2 to 3}.
  2. Calculate corresponding $y$ values using the equation.
  3. Plot the points on a graph.
  4. Connect the points with a straight line.
• What is the $y$ value when $x =$$0$ in the equation $y =$$3x +$$2$?


  The $y$ value is 2.
• What is the $y$ value when $x =$$1$ in the equation $y =$$3x +$$2$?


  The $y$ value is 5.
• What is the $y$ value when $x =$$2$ in the equation $y =$$3x +$$2$?


  The $y$ value is 8.
• What is the $y$ value when $x =$$3$ in the equation $y =$$3x +$$2$?


  The $y$ value is 11.
• How do you determine if a point lies on the line represented by the equation $y =$$3x +$$2$?


  You substitute the $x$ value into the equation and check if the resulting $y$ matches.
• Does the point (25, 77) lie on the line $y =$$3x +$$2$?


  Yes, it lies on the line.
• How do you estimate calculations by rounding to one significant figure?


  • Round each number to one significant figure.
  • Perform the calculation using the rounded numbers.
• What is the estimated value of $\frac{699}{0.21}$ when rounded to one significant figure?


  The estimated value is 105,000.
• What is the perimeter of an equilateral triangle with side length 8?


  The perimeter is 24.
• How do you calculate the circumference of a circle that is 20% greater than the perimeter of a triangle?


  You multiply the perimeter by 1.2.
• What is the circumference of the circle if the perimeter of the triangle is 24?


  The circumference is 28.8.
• What formula is used to find the diameter of a circle from its circumference?

  The formula is $Diameter =$$\frac{Circumference}{\pi}$.
• How do you find the radius from the diameter?


  You divide the diameter by 2.
• What is the area of a circle with radius approximately 4.58?


  The area is $\pi \times (4.58)^2$.
• What is the rounded area of the circle to three significant figures?


  The rounded area is 66.0.
• How do you find the Mth term of a sequence?


  • Identify the pattern in the sequence.
  • Use the pattern to express the Mth term mathematically.
• What is the Mth term of the sequence for triangular tiles starting from 6?


  The Mth term is $2n +$$4$.
• If Rich uses 88 total tiles, what equation represents the total tiles in terms of pattern number?


  The equation is $4n +$$4 =$$88$.
• What is the value of $n$ if $4n +$$4 =$$88$?


  The value of $n$ is 21.
• How many square tiles are used in pattern number 21?


  There are 42 square tiles.