Worksheet

Worksheet: National Evaluation, Subject II

Published · by

Open PDF The PDF is in Romanian.

Summary

Subject II of the National Evaluation tests plane and solid geometry with six items that come with figures: segments, angles, triangles and quadrilaterals, the circle, areas and solids. The worksheet has five items of each type, each with its own drawing. You pick the letter of the correct answer and check it on the page.

Press “Check” next to an exercise. Your answers stay on this device.

Circle the letter of the correct answer. Each item has exactly one correct answer.

Collinear points and segments

  1. In the figure, the points $A$, $B$ and $C$ are collinear, in this order, $AB = 9$ cm and $BC = 5$ cm. The point $M$ is the midpoint of the segment $AC$. The length of the segment $BM$ is:

    A line with the points A, M, B and C, in this order; the segments AM and MC are marked equal
    • a) $7$ cm
    • b) $2$ cm
    • c) $4$ cm
    • d) $4,5$ cm

  2. In the figure, the points $A$, $B$, $C$ and $D$ are collinear, in this order, with $AB = BC = CD$ and $AD = 15$ cm. The length of the segment $AC$ is:

    The collinear points A, B, C and D, with the segments AB, BC and CD marked equal
    • a) $5$ cm
    • b) $7,5$ cm
    • c) $10$ cm
    • d) $12$ cm

  3. In the figure, $AB = 16$ cm, the point $M$ is the midpoint of the segment $AB$, and the point $N$ is the midpoint of the segment $MB$. The length of the segment $AN$ is:

    The collinear points A, M, N and B, with the segments MN and NB marked equal
    • a) $12$ cm
    • b) $8$ cm
    • c) $4$ cm
    • d) $10$ cm

  4. In the figure, the points $A$, $B$ and $C$ are collinear, in this order, $AB = 3 \cdot BC$ and $AC = 20$ cm. The length of the segment $BC$ is:

    The collinear points A, B and C, in this order
    • a) $15$ cm
    • b) $4$ cm
    • c) $10$ cm
    • d) $5$ cm

  5. In the figure, $O$ is the midpoint of the segment $AB$, $AB = 9$ cm, and the point $P$ lies on the ray $OB$, beyond $B$, so that $OP = 7$ cm. The length of the segment $BP$ is:

    The collinear points A, O, B and P, with the segments AO and OB marked equal
    • a) $11,5$ cm
    • b) $2,5$ cm
    • c) $4,5$ cm
    • d) $3$ cm

Angles

  1. In the figure, the lines $a$ and $b$ are parallel, and the line $c$ is a transversal. The value of $x$ is:

    The parallel lines a and b cut by the transversal c; a 58° angle at line a and the angle x at line b, on the same side of the transversal, between the parallels
    • a) $58{^\circ}$
    • b) $122{^\circ}$
    • c) $32{^\circ}$
    • d) $132{^\circ}$

  2. In the figure, the points $A$, $O$ and $C$ are collinear, and $\sphericalangle AOB = \sphericalangle BOC + 40{^\circ}$. The angle $BOC$ measures:

    The collinear points A, O and C and the ray OB, forming the angles AOB and BOC
    • a) $70{^\circ}$
    • b) $110{^\circ}$
    • c) $40{^\circ}$
    • d) $20{^\circ}$

  3. In the figure, the ray $OM$ is the bisector of the angle $AOB$ and $\sphericalangle AOM = 38{^\circ}$. The angle $AOB$ measures:

    The angle AOB with the bisector OM; the angle AOM is 38°
    • a) $19{^\circ}$
    • b) $52{^\circ}$
    • c) $76{^\circ}$
    • d) $142{^\circ}$

  4. In the figure, the angles $AOB$, $BOC$ and $COA$ are around the point $O$, $\sphericalangle AOB = 130{^\circ}$ and $\sphericalangle BOC = 110{^\circ}$. The angle $COA$ measures:

    The rays OA, OB and OC around the point O; the angle AOB is 130° and the angle BOC is 110°
    • a) $100{^\circ}$
    • b) $60{^\circ}$
    • c) $140{^\circ}$
    • d) $120{^\circ}$

  5. An angle measures $\frac{2}{3}$ of its complement. The measure of the angle is:

    • a) $54{^\circ}$
    • b) $45{^\circ}$
    • c) $36{^\circ}$
    • d) $60{^\circ}$

Triangles and quadrilaterals

  1. A picture frame has the shape of a rectangle with the dimensions shown in the figure. The length of the frame is:

    A rectangle with sides of 0,8 m and 50 cm
    • a) $1,3$ m
    • b) $2,6$ m
    • c) $1,6$ m
    • d) $4$ m

  2. In the figure, the triangle $ABC$ is isosceles, with $AB = AC$, and $\sphericalangle B = 65{^\circ}$. The angle $A$ measures:

    The isosceles triangle ABC, with the sides AB and AC marked equal and the angle B of 65°
    • a) $65{^\circ}$
    • b) $115{^\circ}$
    • c) $50{^\circ}$
    • d) $25{^\circ}$

  3. In the figure, $ABCD$ is a parallelogram with $AB = 2 \cdot BC$ and a perimeter of $42$ cm. The length of the side $AB$ is:

    The parallelogram ABCD
    • a) $7$ cm
    • b) $14$ cm
    • c) $21$ cm
    • d) $10,5$ cm

  4. In the figure, the triangle $ABC$ is a right triangle with the right angle at $A$, $AB = 5$ cm and $AC = 12$ cm. The length of the hypotenuse $BC$ is:

    The triangle ABC with the right angle at A, AB = 5 cm and AC = 12 cm
    • a) $17$ cm
    • b) $7$ cm
    • c) $15$ cm
    • d) $13$ cm

  5. In the figure, $M$ is the midpoint of the side $AB$, $N$ is the midpoint of the side $AC$, and $BC = 18$ cm. The length of the segment $MN$ is:

    The triangle ABC, with M the midpoint of AB, N the midpoint of AC and the segment MN
    • a) $9$ cm
    • b) $6$ cm
    • c) $18$ cm
    • d) $36$ cm

The circle

  1. In the figure, $AB$ is a diameter of the circle with centre $O$ and $AB = 10$ cm. The area of the disc is:

    The circle with centre O and the diameter AB
    • a) $100\pi$ cm²
    • b) $10\pi$ cm²
    • c) $25\pi$ cm²
    • d) $5\pi$ cm²

  2. In the figure, $AB$ is a diameter of the circle with centre $O$, the point $C$ lies on the circle and $\sphericalangle BAC = 35{^\circ}$. The angle $ABC$ measures:

    The circle with centre O, the diameter AB and the point C on the circle; the angle BAC is 35°
    • a) $55{^\circ}$
    • b) $35{^\circ}$
    • c) $90{^\circ}$
    • d) $45{^\circ}$

  3. The figure shows a circle with centre $O$ and radius $OA = 6$ cm. The circumference of the circle is:

    The circle with centre O and the radius OA
    • a) $6\pi$ cm
    • b) $36\pi$ cm
    • c) $24\pi$ cm
    • d) $12\pi$ cm

  4. In the figure, the points $A$, $B$ and $C$ lie on the circle with centre $O$, and $\sphericalangle ACB = 40{^\circ}$. The angle $AOB$ measures:

    The circle with centre O, the points A, B and C on the circle, the chords CA and CB and the radii OA and OB; the angle ACB is 40°
    • a) $40{^\circ}$
    • b) $80{^\circ}$
    • c) $20{^\circ}$
    • d) $140{^\circ}$

  5. In the figure, the circle with centre $O$ has a radius of $5$ cm, the line $PT$ is tangent to the circle at the point $T$ and $OP = 13$ cm. The length of the segment $PT$ is:

    The circle with centre O, the tangent PT at the point T and the segment OP; the angle OTP is a right angle
    • a) $8$ cm
    • b) $\sqrt{194}$ cm
    • c) $12$ cm
    • d) $18$ cm

Areas

  1. In the figure, the rectangle $ABCD$ has an area of $54$ cm² and $BC = 6$ cm. The perimeter of the rectangle is:

    The rectangle ABCD, with BC = 6 cm
    • a) $30$ cm
    • b) $15$ cm
    • c) $60$ cm
    • d) $108$ cm

  2. In the figure, $AD\bot BC$, $D \in BC$, $BC = 12$ cm and $AD = 7$ cm. The area of the triangle $ABC$ is:

    The triangle ABC, with the altitude AD perpendicular to BC
    • a) $84$ cm²
    • b) $42$ cm²
    • c) $19$ cm²
    • d) $38$ cm²

  3. In the figure, $ABCD$ is a trapezoid with the bases $AB = 13$ cm and $CD = 7$ cm, and the height of the trapezoid is $5$ cm. The area of the trapezoid is:

    The trapezoid ABCD, with the bases AB and CD and the height drawn from D
    • a) $100$ cm²
    • b) $45$ cm²
    • c) $50$ cm²
    • d) $65$ cm²

  4. In the figure, $ABCD$ is a rhombus with the diagonals $AC = 14$ cm and $BD = 9$ cm. The area of the rhombus is:

    The rhombus ABCD, with the diagonals AC and BD meeting at O
    • a) $126$ cm²
    • b) $23$ cm²
    • c) $31,5$ cm²
    • d) $63$ cm²

  5. In the figure, the triangle $ABC$ is equilateral, with a side of $6$ cm. The area of the triangle is:

    The equilateral triangle ABC, with all sides marked equal
    • a) $18\sqrt{3}$ cm²
    • b) $9\sqrt{3}$ cm²
    • c) $36$ cm²
    • d) $6\sqrt{3}$ cm²

The cube and the rectangular cuboid

  1. The figure shows the cube $ABCDA'B'C'D'$. The sum of the lengths of all the edges of the cube is $60$ cm. The volume of the cube is:

    The cube ABCDA′B′C′D′, with the hidden edges dashed
    • a) $25$ cm³
    • b) $150$ cm³
    • c) $125$ cm³
    • d) $75$ cm³

  2. The figure shows the rectangular cuboid $ABCDA'B'C'D'$, with $AB = 5$ cm, $BC = 3$ cm and $AA' = 2$ cm. The total surface area of the cuboid is:

    The rectangular cuboid ABCDA′B′C′D′, with AB = 5 cm
    • a) $62$ cm²
    • b) $30$ cm²
    • c) $31$ cm²
    • d) $50$ cm²

  3. The figure shows the cube $ABCDA'B'C'D'$. The number of edges of the cube that are parallel to the edge $AB$ (not counting $AB$) is:

    The cube ABCDA′B′C′D′, with the edge AB drawn thicker
    • a) $2$
    • b) $3$
    • c) $4$
    • d) $1$

  4. The figure shows the cube $ABCDA'B'C'D'$, with an edge of $5$ cm. The length of the diagonal $AC$ of the face $ABCD$ is:

    The cube ABCDA′B′C′D′, with the diagonal AC of the face ABCD
    • a) $5\sqrt{3}$ cm
    • b) $10$ cm
    • c) $25$ cm
    • d) $5\sqrt{2}$ cm

  5. A box has the shape of a rectangular cuboid, with the dimensions shown in the figure. The greatest number of cubes with an edge of $2$ cm that fit in the box is:

    A box shaped like a rectangular cuboid, with dimensions of 10 cm, 6 cm and 4 cm
    • a) $30$
    • b) $240$
    • c) $60$
    • d) $15$

Frequently asked questions

What does Subject II of the National Evaluation ask for?

Six multiple-choice geometry items worth 5 points each, usually with a figure next to them: collinear points and segments, angles, triangles and quadrilaterals, the circle, areas and a solid. You use the data in the statement and in the figure together.

How do I use the figure in a geometry item?

Mark every piece of data from the statement on the figure: lengths, angles, midpoints, right angles. Then look for a configuration you recognise, such as a right triangle, a midline or an inscribed angle. Do not measure on the drawing: the figure is not to scale, so the result is calculated, not read off.