Chapter 7 · Model TestAttempt first – solutions on the next page

Model Test Paper മാതൃകാ ചോദ്യപേപ്പർ

Set a timer for 1½ hours, keep the textbook closed, and write your answers in a notebook. Show your working – write each step with its sign. Then check your work on the solved paper, which also shows how marks are given.

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Kerala State Syllabus · Standard IX · Mathematics Part 1

MATHEMATICS – Chapter 7: Negative Numbers (ന്യൂനസംഖ്യകൾ)

Time: 1½ hoursMaximum marks: 40
Instructions: Answer all questions. Write negative numbers with brackets when they follow a sign, for example 6 − (−4). Marks are given for correct steps even when the final answer is wrong. Section A: 8 × 1 = 8, Section B: 5 × 2 = 10, Section C: 4 × 3 = 12, Section D: 2 × 5 = 10.
SECTION A – Answer all questions8 × 1 = 8 marks
1.
−9 + 4 =
(1)
2.
3 − 10 =
(1)
3.
6 − (−4) =
(1)
4.
(−3) × (−7) =
(1)
5.
(−24) ÷ 6 =
(1)
6.
−(−8) =
(1)
7.
(−1)9 =
(a) 1(b) −1(c) 9(d) −9
(1)
8.
A point at −3 on the number line moves 5 to the right. Its new position is .
(1)
SECTION B – Answer all questions5 × 2 = 10 marks
9.
Complete the table:
xyx + y
7−10
−710
−7−10
−44
(2)
10.
Find the change of position from −6 to 5, and from 5 to −6, writing each as y − x.
(2)
11.
Using the reasoning of the textbook, explain why 4 − (−7) = 11.
(2)
12.
Compute (−2)(−3)(−4) and (−2)(−3)(−4)(−5).
(2)
13.
Find y in y = x² + 3x + 2 when x = −3 and when x = −4.
(2)
SECTION C – Answer all questions4 × 3 = 12 marks
14.
Show, with x = 12, y = −5, z = −3, that (x + y)z = xz + yz. Use it to explain why (−5) × (−3) must be 15.
(3)
15.
Find two pairs of integers (x, y) with x positive, y negative and x + y = 2; and two pairs with x negative, y positive and x + y = −2.
(3)
16.
Find z = xy − yx for
  1. x = 6, y = −3
  2. x = −6, y = −3
(3)
17.
A point moves along a line at 8 m/s. We start watching when it passes O. Find its position
  1. 3 seconds later, moving right
  2. 3 seconds earlier, moving right
  3. 3 seconds earlier, moving left.
Write one equation that gives the position in all cases.
(3)
SECTION D – Answer all questions2 × 5 = 10 marks
18.
  1. For four consecutive natural numbers a, b, c, d, show using algebra that a − b − c + d = 0.
  2. What is a + b − c − d?
  3. Check both with 10, 11, 12, 13 and with −1, −2, −3, −4.
  4. Find all pairs of integers (x, y) with x² + y² = 25.
(5)
19.
A ball is thrown straight up at 29.4 m/s; its speed decreases by 9.8 m/s every second.
  1. Find its speed after 1 second and after 2 seconds.
  2. When does it stop rising?
  3. Taking upward speed as positive, v = 29.4 − 9.8t. Find v when t = 5 and say what it means.
  4. Why is one equation enough when we use negative numbers?
  5. Find ½(1 + (−1)n) for n = 7 and n = 10.
(5)
✔ Finished?

Mark your answers using the solved paper. For each mistake, the solution tells you which page of this guide to revisit.