Geometry and measures, Year 7: more practice：全部卡片
整套按顺序列出——孩子看到之前，您可以先通读一遍。
- When you measure an angle with a protractor, where must its centre mark be placed?
On the vertex (the corner) of the angle
提示It goes where the two arms meet.
为什么The baseline of the protractor must also lie along one arm, so the other arm points to the reading on the scale.
- An angle is clearly acute but one protractor scale reads 125°. What is the angle, and why?
55° — read the other scale (180° − 125°)
提示An acute angle is less than 90°.
为什么Protractors have two scales running in opposite directions. Start from 0° on the arm you are lined up with; 125° is the reading from the other end, and 180° − 125° = 55°.
- You construct a triangle with sides 5 cm, 6 cm and 7 cm. Which instrument finds where the two longer sides meet?
Compasses, drawing two arcs
提示Draw the 7 cm base first, then you need two curves that cross.
为什么From one end of the base draw an arc of radius 5 cm, and from the other end an arc of radius 6 cm. They cross at the third vertex.
- A triangle is drawn from two sides and the angle between them. What is this called, using letters?
SAS (side, angle, side)
提示The known corner sits between the two lengths.
为什么SAS fixes one triangle only. The angle must lie between the two known sides; a given angle that is not between them can give two different triangles.
- A cuboid has volume 60 cm³, length 5 cm and width 4 cm. What is its height in cm? (number only)
3
提示Volume is length × width × height, so work backwards by dividing.
为什么The base area is 5 × 4 = 20 cm², and 60 ÷ 20 = 3. Check: 5 × 4 × 3 = 60.
- Does a parallelogram that is not a rectangle or a rhombus have any lines of symmetry?
No, it has none
提示Imagine folding it along a diagonal or through the midpoints of opposite sides.
为什么Folding along a diagonal makes the two halves match in size but the corners do not land on each other. It does have rotational symmetry of order 2.
- What is the order of rotational symmetry of a rectangle that is not a square?
2
提示Count how many positions in a full turn look exactly the same.
为什么A rectangle fits onto itself after a half turn and after a full turn, so its order is 2.
- Point (3, 2) is reflected in the y-axis. What are the coordinates of its image?
(−3, 2)
提示The y-axis is vertical: which way does the point move, and does its height change?
为什么The image is the same distance from the mirror line on the other side, and 2 up as before. Reflecting in the y-axis changes the sign of x.
- A pencil measures 14.6 cm on a ruler. How long is it in millimetres? (number only)
146
提示One centimetre is split into ten small divisions on a ruler.
为什么1 cm = 10 mm, so 14.6 × 10 = 146 mm. The 0.6 cm is six of the small divisions.
- What is the name of a straight line that joins two points on a circle but does not have to pass through the centre?
A chord
提示It is not a radius or a diameter.
为什么A chord joins any two points on the circumference. The longest chord passes through the centre and is a diameter.
1★ KS3-MATH-GEO-0094
2★ KS3-MATH-GEO-0095
3★ KS3-MATH-GEO-0096
4★ KS3-MATH-GEO-0097
5★ KS3-MATH-GEO-0098
6★ KS3-MATH-GEO-0099
7★ KS3-MATH-GEO-0100
8★ KS3-MATH-GEO-0101
9★ KS3-MATH-GEO-0102
10★ KS3-MATH-GEO-0103