Annual Examination – Set 2 വാർഷിക പരീക്ഷ
A full annual-examination paper covering all ten chapters (Part 1 and Part 2). Print it on A4 paper and give it to the student with a timer; the answer key is printed separately.
ANNUAL EXAMINATION · MODEL PAPER · SET 2
Standard IX · MATHEMATICS ഗണിതം
Name:Roll No.:Division:
- The first 15 minutes is cool-off time. Use it to read the questions and plan your answers; do not write during this time.
- Answer all the questions. The score for each question is shown in brackets on the right.
- Read each question carefully before you answer. Answer in keeping with the score and the time.
- Show the steps of your working and give explanations wherever necessary. Calculators are not allowed.
- Draw neat figures wherever needed. For constructions use a ruler, a set square and compasses, and keep the construction lines.
Section AAnswer all questions · 10 × 1 = 10 marks
1.
A box has 80 beads, some black and some white. There are 12 more black beads than white beads. If the number of white beads is x, which equation gives x?
[1](a) x + 12 = 80(b) x + (x − 12) = 80(c) 2x + 12 = 80(d) 12x = 80
2.
√279 =
[1](a) 1⅓(b) 1⅔(c) 2⅓(d) 259
3.
Fill in the blanks: The side of a square of area 1.69 sq cm is cm. The side of a square of area 3 sq cm is written as cm.
[1]4.
The numbers 1 to 36 are written in rows of 6 (1–6 in the first row, 7–12 in the second, and so on). In any 2 × 2 square of these numbers, the products of the numbers at opposite corners always differ by
[1](a) 1(b) 5(c) 6(d) 7
5.
√29 =
[1](a) √23(b) 23(c) √29(d) 29
6.
A triangle has sides 2 cm, 3 cm and 4 cm. Which of these triangles has the same angles as it?
[1](a) 4 cm, 6 cm, 7 cm(b) 3 cm, 4.5 cm, 6 cm(c) 3 cm, 4 cm, 5 cm(d) 4 cm, 5 cm, 6 cm
7.
A point moves on the number line from −3 to −8. Its change of position is
[1](a) 5(b) −5(c) 11(d) −11
8.
Which of these statements about π is correct?
[1](a) π is exactly equal to 22/7.(b) π is the circumference of the circle of diameter 1, and it cannot be written as a fraction.(c) π is exactly equal to 3.14.(d) π is larger for larger circles.
9.
|−4| − |3 − 7| =
[1](a) 0(b) −8(c) 8(d) 14
10.
True or false? Give a reason: “For every real number x, |x| = x.”
[1]Section BAnswer all questions · 8 × 2 = 16 marks
11.
A pen and a notebook together cost ₹70. The notebook costs ₹4 more than twice the price of the pen. Taking the price of the pen as ₹x, form an equation and find the price of each.
[2]12.
In the figure, the lines l₁, l₂, l₃ are parallel. They cut one line at A, B, C and another line at P, Q, R. AB = 4 cm, BC = 6 cm and PQ = 5 cm. Find QR and PR.
[2]13.
Two natural numbers each leave remainder 2 on division by 3. Prove that their product leaves remainder 1 on division by 3. Check with one example.
[2]14.
(a) Write 6√3 with no square root in the denominator. (b) Find √45√5.
[2]15.
A triangle has sides 6 cm, 8 cm and 10 cm and area 24 sq cm. Another triangle has the same angles, and its longest side is 15 cm. Find (a) its other two sides (b) its area.
[2]16.
A point moves along the number line. Complete the table.
[2]| starting position | change of position | final position | |
|---|---|---|---|
| (i) | −6 | 9 | … |
| (ii) | 4 | −10 | … |
| (iii) | −2 | … | −9 |
| (iv) | … | −5 | 1 |
17.
The wheel of a bicycle has diameter 70 cm. How far does the bicycle go when the wheel turns once? How many turns does the wheel make to cover 1.1 km? (Take π = 22/7.)
[2]18.
For the polynomial p(x) = 7 − 3x² + 5x³ − x, write (a) its degree (b) the coefficient of x² (c) the coefficient of x (d) the constant term.
[2]Section CAnswer all questions · 6 × 3 = 18 marks
19.
Ammu’s mother is 26 years older than Ammu. After 6 years, the mother’s age will be 3 times Ammu’s age then. Taking Ammu’s present age as x years: (a) write the ages of both after 6 years in terms of x; (b) form an equation and solve it; (c) find their present ages and check.
[3]20.
In the calendar a 3 × 3 square of dates is marked. (a) Find the products of the dates at opposite corners of the marked square, 4 × 20 and 6 × 18, and their difference. (b) Prove that for every 3 × 3 square of dates in a calendar this difference is the same. (c) What is the difference for a 4 × 4 square? Give the reason.
[3]21.
(a) Show that (√7 + √5)(√7 − √5) = 2. (b) Using this, write 2√7 − √5 with no square root in the denominator. (c) Taking √7 ≈ 2.646 and √5 ≈ 2.236, find its value correct to two decimal places.
[3]22.
In the figure, ΔABC has sides 4 cm, 5 cm, 6 cm and angles 83°, 56°, 41° (to the nearest degree). ΔPQR has sides PR = 6 cm, QR = 7.5 cm and PQ = 9 cm. (a) Show that the sides of the two triangles are in the same ratio. (b) Find ∠P, ∠Q and ∠R, giving the reason. (c) How many times the area of ΔABC is the area of ΔPQR?
[3]23.
(a) Using the meaning of subtraction (“how much must be added?”), explain why 4 − (−6) = 10. (b) In a building the basement floors are numbered −1, −2, −3, …. A lift goes from floor −3 up to floor 7 and then down to floor −2. Write the change of floor for each trip as (final floor − starting floor). (c) Find the change from floor −3 to floor −2 directly and show that it is the sum of the two changes in (b).
[3]24.
A window has the shape shown: a rectangle 1.4 m wide and 1.5 m high with a semicircle on top. (a) Find the length of the semicircular arc. (b) Find the perimeter of the window. (c) Another window of the same shape is twice as wide and twice as high. What is its perimeter? (Take π = 22/7.)
[3]Section DAnswer all questions · 4 × 4 = 16 marks
25.
Squares in a house. (a) A square kolam has area 6¼ sq m. Find its side. (b) A square floor tile has area 0.0144 sq m. Find its side. (c) A square courtyard has area 5 sq m. Use the table to find between which two numbers with one decimal place, and between which two numbers with two decimal places, its side lies. (d) Write the side of the courtyard correct to a centimetre (two decimal places of a metre).
[4]| x | 2.2 | 2.3 | 2.23 | 2.24 | 2.236 | 2.237 |
|---|---|---|---|---|---|---|
| x² | 4.84 | 5.29 | 4.9729 | 5.0176 | 4.999696 | 5.004169 |
26.
On a map, a line AB of length 10 cm shows a straight stretch of a canal between two boat jetties A and B. A new jetty P is to be built on AB so that AP : PB = 3 : 4. (a) Calculate the lengths AP and PB on the map. (b) Draw AB = 10 cm and mark P using a ruler, compass and set squares, without measuring AP. Write the steps of construction. (c) Explain why your point P divides AB in the ratio 3 : 4.
[4]27.
A KSRTC bus runs on a straight east–west road. The road is drawn as a number line with the bus stand O at 0; distances are in km, east is positive. The stops are A (−6), J (−1), O (0), C (2) and B (9). (a) Find the distance between A and B using absolute value. (b) Raju’s house is on the road, 4 km from C. Write this as an equation with absolute value and find the possible positions of his house. (c) A fuel station is to be built less than 3 km from the junction J. Write this condition with absolute value, find the possible positions and show them on the number line. (d) Which of the stops are more than 5 km from C?
[4]28.
A rectangular paddy field is 10 m longer than it is wide. Its width is x m. A bund 1 m wide is made all round it, outside the field. (a) Write the area a(x) of the field as a polynomial. What is its degree? Write its coefficients. (b) Write the area b(x) of the bund as a polynomial and give its degree. (c) Is the length of the diagonal of the field a polynomial in x? Is the perimeter of the field a polynomial? Give reasons. (d) Find a(20) and b(20).
[4]✦ ✦ ✦