34 self-marking GCSE and IGCSE practice questions on Construction, written specifically for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1) across Foundation and Higher tier. Instant marking with full worked solutions on every question.
A few of the 34 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.
Question 12 marksGrade 4-5
The points V(0,0), A(4,0) and B(0,4)
Quick answers about Construction
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There are 34 self-marking GCSE and IGCSE Maths questions on Construction, written for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1) across Foundation and Higher tier. Each one is marked instantly and has a full worked solution.
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are shown on the grid, forming angle
AVB
. Using only the circle and line tools, construct the bisector of angle
AVB
. (Draw an arc centred at
V
crossing both arms, then two more equal-radius arcs centred on those crossing points, and draw a line from
V
through where the new arcs intersect.)
On the practice page you draw or plot the answer on screen.
Show the worked solution
Draw an arc centred at V that crosses both arm VA and arm VB. From each of those two crossing points, draw an arc of equal radius into the angle so the arcs intersect. The line from V through that intersection point bisects angle AVB. Since AVB is a right angle here, the bisector runs along y=x. M1A1
Question 22 marksGrade 4-5
The line BC has been drawn for you, where BC=6 cm. Using a ruler and compasses, construct triangle ABC, where AB=3 cm and AC=5 cm. You must show all your construction lines.
On the practice page you draw or plot the answer on screen.
Show the worked solution
Set your compasses to a radius of 3 cm and draw an arc centred at B.
Set your compasses to a radius of 5 cm and draw an arc centred at C.
The two arcs intersect at the point A - this is the third vertex of the triangle. M1
Join B to A
Question 32 marksGrade 4-5
The points A(−2,0) and B(2,0) are shown on the grid. Using only the circle and line tools, construct the perpendicular bisector of AB. (Draw a circle centred at A and a circle centred at B, both passing through the other point, then draw a line through the two points where the circles cross.)
On the practice page you draw or plot the answer on screen.
Question 42 marksGrade 4-5
The line through L1(−4,0) and L2(4,0) is shown, along with the point P(2,3), which is not on the line. Using only the circle and line tools, construct the perpendicular from P to the line. (Draw a circle centred at P that crosses the line at two points, then two more equal-radius arcs centred on those crossing points on the opposite side, and draw a line through P and where the new arcs intersect.)
On the practice page you draw or plot the answer on screen.