100% TRUSTED workings, explanations
and solutions
Exam
(elaborations)
MIP1502
Assignment 3
(COMPLETE
ANSWERS)
, 2024 - DUE 9
July 2024
[Type the document subtitle]
[Pick the date]
[Type the abstract of the document here. The abstract is typically a short summary of the contents of
the document. Type the abstract of the document here. The abstract is typically a short summary of
the contents of the document.]
, Exam (elaborations)
MIP1502 Assignment 3 (COMPLETE ANSWERS) 2024
(369439) - DUE 9 July 202
Course
Mathematics for Intermediate II (MIP1502)
Institution
University Of South Africa (Unisa)
Book
Intermediate Mathematics 2
MIP1502 Assignment 3 (COMPLETE ANSWERS) 2024 (369439) - DUE 9
July 2024 ;100% TRUSTED workings, explanations and solutions.........
Question 1 1.1 Use examples to explain the difference between a number
sentence and an algebraic expression. (4)
A number sentence is a mathematical statement that includes numbers, operation symbols (such
as +, -, ×, ÷), and an equality or inequality symbol (such as =, <, >). It can be either true or false.
For example:
7+5=127 + 5 = 127+5=12 (true number sentence)
9−4>69 - 4 > 69−4>6 (false number sentence)
An algebraic expression, on the other hand, is a mathematical phrase that includes numbers,
variables (letters that represent unknown values), and operation symbols. It does not include an
equality or inequality symbol and cannot be true or false by itself. For example:
3x+23x + 23x+2
5y−75y - 75y−7
Here are specific examples to illustrate the difference:
1. Number Sentence Example 1: 8×3=248 \times 3 = 248×3=24
o This is a true number sentence because the product of 8 and 3 is indeed 24.
2. Number Sentence Example 2: 10+6<1510 + 6 < 1510+6<15
o This is a false number sentence because the sum of 10 and 6 is 16, which is not
less than 15.
, 3. Algebraic Expression Example 1: 4a+74a + 74a+7
o This expression involves a variable aaa and represents a value that depends on the
value of aaa.
4. Algebraic Expression Example 2: 2b−32b - 32b−3
o This expression involves a variable bbb and represents a value that depends on the
value of bbb.
In summary, a number sentence is a complete mathematical statement that can be evaluated as
true or false, while an algebraic expression is an incomplete mathematical phrase that involves
variables and cannot be evaluated without additional information.
1.2 Explain how you can use geometric patterns to help learners to
understand functions. (4)
Using geometric patterns can be an effective way to help learners understand functions by
providing a visual and tangible representation of mathematical concepts. Here’s how you can use
geometric patterns to aid in understanding functions:
1. Visual Representation of Relationships:
o Example: Consider a pattern of squares where the number of squares increases in
each step.
o Pattern: 1 square, 4 squares, 9 squares, 16 squares, and so on.
o Function: The number of squares can be represented by the function f(n)=n2f(n)
= n^2f(n)=n2, where nnn is the step number.
o Explanation: By counting the squares in each step and noticing the pattern,
learners can see that the relationship between the step number and the total
number of squares follows a specific rule, which is the function f(n)=n2f(n) =
n^2f(n)=n2.
2. Understanding Growth and Change:
o Example: Use a geometric pattern like a growing sequence of triangles.
o Pattern: A single triangle, a row of 3 triangles, a row of 6 triangles, etc.
o Function: The number of triangles in the nth row can be represented by the
function f(n)=n(n+1)2f(n) = \frac{n(n+1)}{2}f(n)=2n(n+1).
o Explanation: Learners can count the triangles and recognize how each new row
adds more triangles, which helps them understand how the function describes this
growth and change.
3. Connecting Patterns to Algebraic Expressions:
o Example: Use a pattern of dots forming shapes like L-shapes.
o Pattern: The first shape has 3 dots, the second has 6 dots, the third has 9 dots, and
so on.
and solutions
Exam
(elaborations)
MIP1502
Assignment 3
(COMPLETE
ANSWERS)
, 2024 - DUE 9
July 2024
[Type the document subtitle]
[Pick the date]
[Type the abstract of the document here. The abstract is typically a short summary of the contents of
the document. Type the abstract of the document here. The abstract is typically a short summary of
the contents of the document.]
, Exam (elaborations)
MIP1502 Assignment 3 (COMPLETE ANSWERS) 2024
(369439) - DUE 9 July 202
Course
Mathematics for Intermediate II (MIP1502)
Institution
University Of South Africa (Unisa)
Book
Intermediate Mathematics 2
MIP1502 Assignment 3 (COMPLETE ANSWERS) 2024 (369439) - DUE 9
July 2024 ;100% TRUSTED workings, explanations and solutions.........
Question 1 1.1 Use examples to explain the difference between a number
sentence and an algebraic expression. (4)
A number sentence is a mathematical statement that includes numbers, operation symbols (such
as +, -, ×, ÷), and an equality or inequality symbol (such as =, <, >). It can be either true or false.
For example:
7+5=127 + 5 = 127+5=12 (true number sentence)
9−4>69 - 4 > 69−4>6 (false number sentence)
An algebraic expression, on the other hand, is a mathematical phrase that includes numbers,
variables (letters that represent unknown values), and operation symbols. It does not include an
equality or inequality symbol and cannot be true or false by itself. For example:
3x+23x + 23x+2
5y−75y - 75y−7
Here are specific examples to illustrate the difference:
1. Number Sentence Example 1: 8×3=248 \times 3 = 248×3=24
o This is a true number sentence because the product of 8 and 3 is indeed 24.
2. Number Sentence Example 2: 10+6<1510 + 6 < 1510+6<15
o This is a false number sentence because the sum of 10 and 6 is 16, which is not
less than 15.
, 3. Algebraic Expression Example 1: 4a+74a + 74a+7
o This expression involves a variable aaa and represents a value that depends on the
value of aaa.
4. Algebraic Expression Example 2: 2b−32b - 32b−3
o This expression involves a variable bbb and represents a value that depends on the
value of bbb.
In summary, a number sentence is a complete mathematical statement that can be evaluated as
true or false, while an algebraic expression is an incomplete mathematical phrase that involves
variables and cannot be evaluated without additional information.
1.2 Explain how you can use geometric patterns to help learners to
understand functions. (4)
Using geometric patterns can be an effective way to help learners understand functions by
providing a visual and tangible representation of mathematical concepts. Here’s how you can use
geometric patterns to aid in understanding functions:
1. Visual Representation of Relationships:
o Example: Consider a pattern of squares where the number of squares increases in
each step.
o Pattern: 1 square, 4 squares, 9 squares, 16 squares, and so on.
o Function: The number of squares can be represented by the function f(n)=n2f(n)
= n^2f(n)=n2, where nnn is the step number.
o Explanation: By counting the squares in each step and noticing the pattern,
learners can see that the relationship between the step number and the total
number of squares follows a specific rule, which is the function f(n)=n2f(n) =
n^2f(n)=n2.
2. Understanding Growth and Change:
o Example: Use a geometric pattern like a growing sequence of triangles.
o Pattern: A single triangle, a row of 3 triangles, a row of 6 triangles, etc.
o Function: The number of triangles in the nth row can be represented by the
function f(n)=n(n+1)2f(n) = \frac{n(n+1)}{2}f(n)=2n(n+1).
o Explanation: Learners can count the triangles and recognize how each new row
adds more triangles, which helps them understand how the function describes this
growth and change.
3. Connecting Patterns to Algebraic Expressions:
o Example: Use a pattern of dots forming shapes like L-shapes.
o Pattern: The first shape has 3 dots, the second has 6 dots, the third has 9 dots, and
so on.
