Annual Examination – Set 1 വാർഷിക പരീക്ഷ

The height of an equilateral triangle of side 2 cm is

To divide a line AB into 5 equal parts using parallel lines, how many equal steps should be marked on the slanted line drawn from A?

The product of two numbers is 300 and their sum is 40. The product of the numbers that are each 1 less than these numbers is

True or false? Give the reason:   10½ × 4½ = 40¼

√5 × √20 =

A point at 4 on the number line moves 9 units to the left. Its new position is

Using regular polygons of 96 sides, who showed that 31071 < π < 317?

The circumference of a circle of radius 3.5 cm is cm. (Take π = 227.)

Pick the odd one out and give the reason:   √9,  −4,  0.25,  √6,  ¾

The side of a square is (x + 3) cm. Its area, written as a polynomial, is

Five years ago a mother was 7 times as old as her daughter. Five years from now she will be 3 times as old as her daughter. Find their present ages.

The perpendicular sides of a right triangle are 1 m and 3 m. (a) Find the length of the hypotenuse. (b) Find the perimeter of the triangle correct to a centimetre. (Use √10 ≈ 3.162.)

In the figure, the lines l, m, n are parallel. AB = BC = 2.5 cm and PQ = 3.2 cm. (a) Find QR. Give the reason. (b) Are the lines l, m, n equally spaced? Why?

A rectangle has sides √8 cm and √18 cm. Find (a) its area (b) its perimeter, in simplest form.

In the triangles ABC and PQR, ∠A = ∠P and ∠B = ∠Q (figure). AB = 4 cm, BC = 6 cm, CA = 5 cm and PQ = 6 cm. Find QR and PR.

Take x = −3, y = 5, z = −4. (a) Show that x − (y − z) = (x − y) + z. (b) Is x − (y − z) equal to x − y − z for these numbers?

On the number line, find (a) the distance between −2¾ and 3½ (b) the midpoint of −2¾ and 3½.

Each edge of a cube of edge 2 cm is increased by x cm. Write the volume v(x) of the new cube as a polynomial. What is its degree?

(a) Show that (3½)² − (2½)² = 6. (b) Use this to draw a line of length √6 cm with ruler and compass, and draw a square of area 6 sq cm on it. Write the steps. (c) 2.4² = 5.76 and 2.5² = 6.25. Between which two tenths does √6 lie?

Construct a square of perimeter 13 cm. Write the steps of construction and say why the method gives equal parts. What is the length of a side of the square?

The perpendicular sides of a right triangle are √45 cm and √80 cm. (a) Write these lengths in simplest form. (b) Find the hypotenuse in simplest form. (c) Find the perimeter and the area of the triangle.

A KSRTC bus runs on a straight east–west road. Positions are measured in kilometres from the bus stand O, east as positive and west as negative. The bus starts 4 km west of O. It goes 7 km east, then 10 km west, then 2 km east. (a) Write each move as an addition and find the position after the second move. (b) Find the final position and say where it is. (c) What single change of position would take the bus from its start straight to the same place?

Consider the numbers −3,  2/5,  √7,  0,  −√16,  π,  1.6. (a) Which of them are integers? Which are rational and which are irrational? (b) Arrange them in increasing order. (c) Write the numbers x with |x + 1| < 3 in the form “between … and …” and show them on a number line. Which of the given numbers satisfy it?

A photo 15 cm long and 10 cm wide is put in a frame of the same width x cm all round (figure). (a) Write the outer length and breadth, and the outer perimeter p(x) as a polynomial. (b) Write the area a(x) of the frame alone as a polynomial. What is its degree? (c) Find a(2) and check it with the outer measures.

At the Nehru Trophy boat race in Alappuzha, the gallery sells adult tickets and child tickets. One family paid ₹1300 for 3 adult and 2 child tickets. Another family paid ₹1100 for 2 adult and 3 child tickets. (a) Write two equations, taking the prices of an adult ticket and a child ticket as ₹x and ₹y. (b) Find the price of each ticket. (c) A school group bought 50 tickets in all and paid ₹10000. How many adult and how many child tickets did they buy?

Anu’s family has a rectangular vegetable plot in the courtyard, x m long and y m wide. Its area is 120 sq m and its perimeter is 46 m. Without finding x and y first: (a) Using (x + 1)(y + 1) = xy + x + y + 1, find the area if the length and the breadth are each increased by 1 m (figure). (b) Find the area if each is increased by ½ m instead. (c) Using (x − y)² = (x + y)² − 4xy, find the length and the breadth. (d) Check your answers to (a) and (b) with these sides.

Before a Vallam Kali boat race, the organisers want the width of the river. T is a tree on the far bank and A is the point on the near bank just opposite it (TA is perpendicular to the bank). Rahul walks 50 m along the bank from A to B, puts a stick at B, and walks 10 m more to C. From C he walks at right angles to the bank, away from the river, until the stick B and the tree T are in one line with him; this point is D, and CD = 12 m (figure). (a) Show that the triangles TAB and DCB have the same angles. (b) Write the ratios of the sides opposite the equal angles. (c) Find the width TA of the river. (d) If Rahul had walked only 5 m beyond B, how far from C would D have been?

The walking track round a panchayat playground has two straight parts of 66 m each, joined at the ends by two semicircles of diameter 28 m (figure). Take π = 227. (a) Find the length of one semicircular end. (b) Find the length of one round of the track. (c) Manu rides a bicycle once round the track. The diameter of its wheel is 70 cm. How many times does the wheel turn? (d) A second track runs 1 m outside the first all round (straight parts still 66 m, semicircles of diameter 30 m). How much longer is one round of it?