Using and Managing Data and Information Tasks: Math Homework Solutions

This document presents a comprehensive set of solutions for a math homework assignment centered around data and information management. The tasks include solving exponential equations, working with combinations, calculating perimeters, and interpreting linear equations. The solutions involve detailed step-by-step explanations for each problem, covering topics such as algebraic manipulations, solving for variables, and applying mathematical formulas. The assignment encompasses various mathematical concepts, including exponents, linear equations, and simultaneous equations, with practical applications. The solutions demonstrate how to apply these concepts to real-world scenarios, such as calculating the cost of tables and chairs or determining the amount of money in different bank accounts. The document provides a clear and concise approach to solving each problem, making it a valuable resource for students seeking to understand and master these mathematical concepts. The document includes tasks on solving for variables, simplifying expressions, and applying formulas to real-world problems, helping students improve their problem-solving abilities.

Using and Managing
Data and Information

TASKS
Task 1

Task 2
Task 3
i) 53 × 55 ÷ 52 = (5 × 5 × 5) × (5 × 5 × 5 × 5 × 5) ÷ (5 × 5) = 125 * 3125 ÷ 25 = 125 *
125 = 15625
ii) 10-4 × 10-6 × 103 = 10 (-4 – 6 + 3) = 10 -7
iii) (1/2)2 × (1/2)5 = (1/2)7 = 0.0078125

iv) 2-3 ÷ 2-5 = 2 [-3-(-5)] = 22 = 4
Task 4
Combinations of 5 students can we make from a class of 12 students= 12! /5! (12-5)!
= 12! /5!7!
= (12 * 11 * 10 * 8 * 7!)/ (5 * 4 * 3 * 2 * 1 * 7!)
= (12 * 11 *10 * 8) / (5 * 4 * 3 * 2 * 1)
= 792
Task 5
y= 2x + 1
In the above equation the meaning of 2 is m which is slop of the line and 1 is the b which is
intercept of Y.
A) Description of diagram
i) Gradient of line:
ii) Y= 3m+ 1
iii) Value of y if x is 5
3*5 +1 = 16
Task 6
Size of width = (2x + 3)
Let the length = 2 (2x + 3) = (4x + 6)
Perimeter: 2 (l + w)
= 2 (4x + 6) (2x + 3)
= 2 (4x (2x + 3) + 6 (2x + 3)
= 2 (8x2 + 12x + 12x + 18)
= 2 (8x2 + 24x + 18)
16x2+ 48x + 36

Task 7
a) 5x + 22 = 32
5x= 32-22
X = 10/5 = 2
b) X / 5 = -4/1
X = 5*-4
X= -20
c) 5(x + 1) = 40
5x + 5 = 40
5x = 40-5
5x = 35
X = 35/5 = 7
d) 5 (x+2) + 6 (x + 3) = 39
5x + 10 + 6x + 18 = 39
11x + 28 = 39
11x = 39-28
11x = 11
X = 11/11 = 1
e) x+7 / 2 =-5
(x+7) = -10
X = -10-7
X =-17

f) x + 5 = 13 –x
x + x = 13 – 5
2x = 8
X = 8 / 2 = 4
g) 2(x +3) = 4x - 4
2x +6 = 4x - 4
2x-4x = -4 -6
-2x = -14
X = -14 / 2 = -7
h) 3 (2x +3) + (2x -1) = 7 (x-4)
6x + 9 + 2x – 1 = 7x - 28
8x + 10 = 7x – 28
8x-7x = -28-10
X = -38
i) 1/5 x – 3 = x
x/5- 3 = 7.5
j) 5-2x/5 = 1 + 4/5 x
x = 20
k) 2x + 7 / 6 = 5 – 5x /5
5 (2x + 7) = 6 (5 -5x)
10x + 35 = 30 – 30x

10 x + 30 x = 30 – 35
40x = -5
X = -5 / 40
= -1 / 8
l) 5x + 2 / 3 (x +3) = 1 / 4 (x – 1)
5x +2x + 6 /3 = x – 1 / 4
60x + 8x + 24 = 3x – 3
65 x = -27
X = -27 /65
Task 8
Let no. of table = x
And, no. of chair = y
5x + 4y = £220 …………………………….….(i)
5x + 1y = £130 ………………………………..(ii)
Then, do (i)-(ii):
3y = £220 - £130
3y = £90
y = 90/3 = £30
Put y value in (ii) equation:
5x = £130
x = £130 / 5 = £ 26

Task 9
Let, Amounts are in saving bank account of:
Ali has = y
Banko = x
Cheng = z
Ali says he has £1,500 more than Banko
y = 1500 + x
Cheng says he has triple the amount that Banko
z = 3x
Total amount of money they have in account = 1500 + x + x + 3x
= 1500 + 4x
Task 10