Mastery

Playing with Constructions — Mastery

30 questions 30 min Full-chapter mastery

Q1. The artwork shown in Fig. 8.1 — joined circles, concentric circles, a mouse face — is included in the chapter mainly to
- A. Motivate students to use compass and ruler by promising they can recreate these figures
- B. Show that constructions are only useful for art
- C. Test whether students can draw freehand without instruments
- D. Show that circles cannot be drawn freehand at all
Q2. For drawing the basic figures of this chapter, the chapter pairs the compass with which other instrument?
- A. Ruler (also called scale)
- B. Set square only
- C. Divider only
- D. Eraser and pencil sharpener
Q3. Priya draws a curve of points she thinks are 4 cm from P. To verify her curve is actually a circle of radius 4 cm, she should
- A. Measure the length of the curve from end to end
- B. Compare the curve with a freehand curve made by her friend
- C. Count the number of points she marked
- D. Pick a few points on the curve and check whether each is 4 cm from P
Q4. Which of the following is the most accurate description of an arc, as used in this chapter?
- A. A straight line segment connecting two points
- B. A part of a circle drawn with the compass at a fixed centre and radius
- C. Any curved line drawn freehand on paper
- D. A full circle of small radius
Q5. In rectangle ABCD the side opposite to AB is
- A. AD
- B. BC
- C. AC
- D. CD
Q6. A square has corners labelled (clockwise) W, X, Y, Z. Which is a valid name for this square?
- A. WXZY
- B. WYXZ
- C. XZYW
- D. ZYXW
Q7. Rectangle ABCD and rectangle BCDA refer to
- A. Two different rectangles of the same size
- B. The same rectangle, named starting from different corners
- C. Two rectangles that are mirror images
- D. Only valid if A, B, C, D are written in alphabetical order
Q8. In STEP 3 (Method 1) of the 6 cm square PQRS construction, the point S is marked such that
- A. S is the midpoint of PQ
- B. PS = 6 cm, measured on the perpendicular at P with a ruler
- C. PS = 3 cm so that the figure looks balanced
- D. S is any point on the perpendicular
Q9. In Method 2 of the 6 cm square construction , once S has been located on the perpendicular at P using the compass, the next point R is located by
- A. Measuring RS = 6 cm with a ruler only
- B. Joining S directly to Q without any tools
- C. Drawing a fresh perpendicular at Q and using the same compass setting to mark R at 6 cm from Q
- D. Drawing a circle of radius 12 cm with centre P
Q10. Asha has just finished constructing a rectangle of sides 2 cm and 10 cm. The chapter asks her to check whether it 'satisfies both rectangle properties'. The two properties to check are
- A. Both diagonals equal and one angle 90°
- B. All sides equal (S1) and all angles 90° (S2)
- C. Opposite sides equal (R1) and all angles 90° (R2)
- D. Sides equal in pairs and angles in pairs summing to 360°
Q11. To construct a rectangle ABCD with AB = 6 cm and BC = 4 cm, Priya starts by drawing AB and then needs perpendiculars to AB at both A and B. The reason both perpendiculars are needed is
- A. Because the figure must look symmetric on paper
- B. So that R1 (opposite sides equal) holds automatically
- C. Because rectangle property R2 requires the angles at A and B both to be 90°
- D. Because the compass cannot reach further otherwise
Q12. In the solved example for constructing a rectangle from one side and a diagonal , the very first step is
- A. Drawing the base CD of length 5 cm
- B. Drawing the diagonal of length 7 cm
- C. Drawing a circle of radius 7 cm
- D. Drawing a perpendicular at any point
Q13. After drawing the 5 cm base DC and the perpendicular l at C, a student wants to locate B using just an arc instead of a full 7 cm circle. The arc must be drawn
- A. Centred at C with radius 5 cm
- B. Centred at any point on l with radius 7 cm
- C. Centred at the midpoint of DC with radius 6 cm
- D. Centred at D with radius 7 cm, passing near where l is expected to be cut
Q14. In rectangle PQRS, the two diagonals are
- A. PR and QS
- B. PQ and RS
- C. PS and QR
- D. PQ and PR
Q15. After constructing rectangle PQRS, Ravi measures PR and QS. He should find that
- A. PR is longer than QS
- B. QS is longer than PR
- C. PR = QS (the two diagonals are equal)
- D. PR is exactly twice QS
Q16. While locating roof-point A of the House, the circle of radius 5 cm centred at B contains exactly
- A. Only one point that is 5 cm from B
- B. All points that are 5 cm from B, including the future A
- C. Only points that are also 5 cm from C
- D. Only points lying on the line BC
Q17. The chapter notes that finding point A (5 cm from both B and C) with only a ruler is possible but inefficient because
- A. A ruler cannot draw straight lines
- B. Rulers cannot reach above the line BC
- C. A ruler is too short for 5 cm
- D. It needs trial and error — measuring repeatedly until both distances come out 5 cm
Q18. The first task in the House construction is to
- A. Decide the colour of the roof
- B. Draw the curved roof line before anything else
- C. Buy a new compass with a longer reach
- D. Identify the sequence in which lines and curves will be drawn
Q19. In the House construction, STEP 1 builds the lower part — a rectangle-like base BCDE with all sides 5 cm and a small door of 2 cm × 1 cm. The order of building this base is best described as
- A. Draw the door first, then build the rectangle around it
- B. Draw all four sides simultaneously
- C. Draw the diagonal of BCDE first, then the sides
- D. Draw the base DE, then perpendiculars at D and E for sides DB and EC, then close BC
Q20. After locating A, the two roof sides AB and AC are drawn as
- A. Two curved arcs from B and C meeting at A
- B. Half circles based on BC
- C. Two perpendiculars from BC meeting at A
- D. Two straight line segments joining A to B and A to C, using a ruler
Q21. Asha wants a rectangle that can be divided into three identical squares. Which pair of side lengths works?
- A. 6 cm × 2 cm
- B. 6 cm × 6 cm
- C. 7 cm × 2 cm
- D. 5 cm × 2.5 cm
Q22. In the rough figure small tick marks ('|') on segments are used to represent
- A. The starting point of construction
- B. Right angles at the corners
- C. Sides that are equal in length
- D. The midpoint of each side
Q23. In the 'Falling Squares' figure (each square of side 4 cm), the chapter notes that the squares are aligned such that
- A. Each square's lower-left corner touches the upper-right corner of the square below it
- B. Each square sits on top of the previous one with no overlap
- C. All squares share a single common corner
- D. Squares are stacked vertically, all of side 4 cm overlapping fully
Q24. The 'A Person' figure has two distinct components, which are
- A. A circle (head) and a body that includes a curved 'collar' formed by an arc
- B. Two circles of different radii placed side by side
- C. A square and a rhombus joined at a corner
- D. Three concentric circles
Q25. A Class 6 student keeps producing wobbly circles because, while drawing, he lets the pencil end stay fixed and moves the metal tip across the page. The most useful correction is to
- A. Re-teach the hint — keep the tip fixed and move only the pencil — and demonstrate with his own compass
- B. Tell him to draw faster so the wobble averages out
- C. Tell him to switch to a freehand drawing
- D. Replace the compass with a longer ruler
Q26. Three teachers each introduce the side + diagonal rectangle construction. Which approach is most aligned with the chapter's stated method?
- A. Teacher A asks students to start drawing immediately and fix mistakes as they appear
- B. Teacher B asks students to first sketch a rough figure of the final rectangle (labelling 5 cm and 7 cm) and plan the order of steps before construction begins
- C. Teacher C dictates each step orally without any rough sketch
- D. Teacher D shows only the finished figure and asks students to copy by eye
Q27. Mrs Pillai wants her class to understand why two 5 cm arcs from B and C intersect to give a single point A. Which classroom move best uses the predict–observe–explain (POE) idea?
- A. Skip the question and tell students directly that two arcs always intersect at one point
- B. Ask each student to first predict whether the arcs will meet and where, then draw and observe, then explain why the intersection is 5 cm from both centres
- C. Show a video of the finished figure without student drawing
- D. Have the brightest student draw on the board while others copy
Q28. Mr Khan is designing a 10-mark task to assess his Class 6 students on a 6 cm square construction (Method 2). Which set of criteria best assesses real construction skill rather than just neatness?
- A. 10 marks for clean lines, regardless of measurements
- B. Marks for (i) correct base PQ length, (ii) correct perpendiculars at P and Q, (iii) correct compass setting for the side length, (iv) PS = QR = 6 cm verified, (v) RS = 6 cm and all angles 90°
- C. 10 marks only if the figure is exactly above another correct figure
- D. Full marks for any rectangle drawn, regardless of method or side length
Q29. The 'Square with more Holes' figure shows four equal circular holes inside one square. To construct this, the most efficient plan is
- A. Divide the square into four equal smaller squares, then draw a circle inside each smaller square at its centre
- B. Draw four circles freehand without measuring
- C. Place all four circles at one corner of the big square
- D. Draw a single large circle and then four tangent lines
Q30. Several students drawing a 6 cm square keep reading 80° from the inner scale of the protractor when they intend a 90° angle, because they align the 0° on the wrong side. Which response best handles this common error?
- A. Ask them to predict where 90° should be (perpendicular to PQ), measure with both scales and check which gives 90°, and then re-do the step
- B. Tell them their squares look fine and move on to the next topic
- C. Tell them to always use the outer scale, even when the base is on the right
- D. Switch the class to a different construction

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