GCSE MATHS EXAM WITH VERIFIED
QUESTIONS AND ANSWERS
Construct a 60 degree angle - ANSWER--Keep compass the same length
-Draw one large arc with the needle on the end of the line
-Draw another arc with the needle where the first one crosses the given line
-Draw line through where they cross
Construct a 90 degree angle - ANSWER--Put needle on one point on the line
-Draw two arcs on either side of the line
-Make compass a bit bigger
-Place needle on each arc and draw two pairs of arcs on either side of the line
-Join up
Construct a perpendicular line from a point - ANSWER--Keep compass same
length
-Place needle on point
-Draw two arcs on either side of line
-Place needle on each arc
-Draw two arcs that cross over
-Join up arc and point
How do you find a bearing? - ANSWER--Draw a North line
-Measure a clockwise angle
,How should bearings be given? - ANSWER-As three figures e.g. 045°
What do you use when two angles and any side are given? - ANSWER-Sine
rule
What do you use when two sides and a non-enclosed angle are given? -
ANSWER-Sine rule
What do you use when an angle enclosed by two given sides is given? -
ANSWER-Cosine rule
What do you use when all three sides are given but no angles? - ANSWER-
Cosine rule
How do you calculate the longest diagonal of a cuboid? - ANSWER--Use
Pythagoras to calculate the diagonal of the bottom face
-Use this diagonal and one vertical side to calculate the long diagonal
How do you use 3D Trig to calculate angles? - ANSWER--Draw a right angled
triangle in
-Draw a 2D sketch of this triangle
-Use Pythagoras and trig to find the angle
How do you calculate the frequency density an area will have on a histogram? -
ANSWER-Frequency density = Frequency / class width
How can you smooth out seasonality in a time series / line graph? - ANSWER-
A moving average
, How do you find a 2 point moving average? - ANSWER--Find the mean of the
1st and 2nd values and plot it
-Find the mean of the 2nd and 3rd values and plot it
-Continue
What do you need to remember when comparing box plots? - ANSWER--Give
the context of the data
-A larger spread means the values are less consistent
-A higher median means generally higher results
-A small IQR shows more consistent results
How can you calculate an average from a histogram? - ANSWER-Work
backwards to calculate frequency (f), the mid-intervals (x) and fx
Compound Interest Formula - ANSWER-
Density - ANSWER-
Speed - ANSWER-
Area of a triangle (trig) - ANSWER-
Sine rule - ANSWER-
Cosine rule for a - ANSWER-
Cosine rule for CosA - ANSWER-
QUESTIONS AND ANSWERS
Construct a 60 degree angle - ANSWER--Keep compass the same length
-Draw one large arc with the needle on the end of the line
-Draw another arc with the needle where the first one crosses the given line
-Draw line through where they cross
Construct a 90 degree angle - ANSWER--Put needle on one point on the line
-Draw two arcs on either side of the line
-Make compass a bit bigger
-Place needle on each arc and draw two pairs of arcs on either side of the line
-Join up
Construct a perpendicular line from a point - ANSWER--Keep compass same
length
-Place needle on point
-Draw two arcs on either side of line
-Place needle on each arc
-Draw two arcs that cross over
-Join up arc and point
How do you find a bearing? - ANSWER--Draw a North line
-Measure a clockwise angle
,How should bearings be given? - ANSWER-As three figures e.g. 045°
What do you use when two angles and any side are given? - ANSWER-Sine
rule
What do you use when two sides and a non-enclosed angle are given? -
ANSWER-Sine rule
What do you use when an angle enclosed by two given sides is given? -
ANSWER-Cosine rule
What do you use when all three sides are given but no angles? - ANSWER-
Cosine rule
How do you calculate the longest diagonal of a cuboid? - ANSWER--Use
Pythagoras to calculate the diagonal of the bottom face
-Use this diagonal and one vertical side to calculate the long diagonal
How do you use 3D Trig to calculate angles? - ANSWER--Draw a right angled
triangle in
-Draw a 2D sketch of this triangle
-Use Pythagoras and trig to find the angle
How do you calculate the frequency density an area will have on a histogram? -
ANSWER-Frequency density = Frequency / class width
How can you smooth out seasonality in a time series / line graph? - ANSWER-
A moving average
, How do you find a 2 point moving average? - ANSWER--Find the mean of the
1st and 2nd values and plot it
-Find the mean of the 2nd and 3rd values and plot it
-Continue
What do you need to remember when comparing box plots? - ANSWER--Give
the context of the data
-A larger spread means the values are less consistent
-A higher median means generally higher results
-A small IQR shows more consistent results
How can you calculate an average from a histogram? - ANSWER-Work
backwards to calculate frequency (f), the mid-intervals (x) and fx
Compound Interest Formula - ANSWER-
Density - ANSWER-
Speed - ANSWER-
Area of a triangle (trig) - ANSWER-
Sine rule - ANSWER-
Cosine rule for a - ANSWER-
Cosine rule for CosA - ANSWER-
