Grade 9 Simple and Compound Interest

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Questions and Answers

What defines a proper fraction?

The numerator is zero.

The numerator equals the denominator.

The numerator is smaller than the denominator. (correct)

The numerator is greater than the denominator.

Which statement about the denominator is true?

It defines the value of the numerator.

It can be any integer, including zero.

It represents the total number of parts in a whole.

It must never be zero as this makes the fraction undefined. (correct)

What is the lowest common denominator (LCD)?

The smallest number into which all denominators can be divided. (correct)

The common factor of the numerators.

The average of all denominators in a set of fractions.

The highest number that can be divided by all numerators.

Which of the following correctly describes an improper fraction?

The numerator is greater than the denominator. (C) Signup and view all the answers

Why is understanding common fractions important in later mathematics?

They aid in understanding algebra and probability concepts. (A) Signup and view all the answers

What is the reciprocal of a fraction?

The multiplicative inverse of any number. (B) Signup and view all the answers

Which operation is primarily associated with solving problems involving fractions?

Addition, subtraction, multiplication, and division. (B) Signup and view all the answers

What is a common fraction?

It is expressed as two whole numbers separated by a horizontal line. (B) Signup and view all the answers

Which operation results in a product?

Multiplication of two numbers (D) Signup and view all the answers

What is the term for the result of a subtraction operation?

Difference (A) Signup and view all the answers

Which algebraic operation includes the use of a coefficient?

All of the above (D) Signup and view all the answers

In what grade do students learn to factorise trinomials?

Grade 10 (B) Signup and view all the answers

What is involved in simplifying algebraic fractions?

Using factorisation (B) Signup and view all the answers

Which expression represents the sum of two variable terms?

8a + 2b (C) Signup and view all the answers

What's the first step in multiplying a binomial by a trinomial?

Distributing each term in the binomial (D) Signup and view all the answers

What type of algebraic expression results in a quotient?

Division of two expressions (B) Signup and view all the answers

What is the total amount owed after applying simple interest on a principal of R1500 at an interest rate of 12% over 3 years?

R2040 (D) Signup and view all the answers

What is the formula used to calculate compound interest?

A = P(1 + i)n (A) Signup and view all the answers

How do you find the monthly instalment if the total owed after a deposit on a computer is R7666.72?

R212.96 (B) Signup and view all the answers

If a computer costs R5999 and a 10% deposit is paid, how much remains to be financed?

R5399.10 (A) Signup and view all the answers

What does 'per annum' mean in the context of an interest rate?

Every year (A) Signup and view all the answers

What principal amount is used to calculate the total owed after deposit if the computer price is R5999?

R5399.10 (B) Signup and view all the answers

In the context of hire purchase, what type of interest is used?

Simple Interest (D) Signup and view all the answers

What is the first step in calculating the monthly repayments for a hire purchase item?

Find the deposit amount (A) Signup and view all the answers

What is the first step to find the rule from input 'a' to output 'b' if only one operation is performed?

Multiply the input values by a constant factor (B) Signup and view all the answers

If input 'f' yields output 'g' with a common difference of 3, what operation would the rule most likely include?

Multiply by 3 and add 1 (C) Signup and view all the answers

What result do you get when applying the rule p + 5 = q if p = -1?

4 (C) Signup and view all the answers

When determining a rule with two operations, which of the following steps should NOT be performed?

Subtract the input from the output (D) Signup and view all the answers

In the equation 2a = b, what can we infer about the relationship between input 'a' and output 'b'?

Output 'b' is double input 'a' (C) Signup and view all the answers

If you start with -8 and have the rule 'add 4 then divide by -2', what is the final result?

2 (D) Signup and view all the answers

Which of the following represents a rule applied to input 'p' to achieve output 'q' that involves two operations?

p × 3 + 1 = q (A) Signup and view all the answers

What can be concluded about the outputs when the input increases linearly and the outputs change non-linearly?

The relationship cannot be expressed as a simple rule. (A) Signup and view all the answers

What does the 'F' in FOIL stand for?

First (B) Signup and view all the answers

When applying FOIL to (x + 4)(x - 5), what is the resulting term from the Outer product?

-5x (A) Signup and view all the answers

In the expression (a + 4)(a + 4), what is the coefficient of the linear term in the expanded form?

8 (A) Signup and view all the answers

What is the final result of squaring the binomial (y - 3)?

y^2 - 6y + 9 (C) Signup and view all the answers

When multiplying the binomials (x + 3)(x - 3), what happens to the middle terms?

They cancel each other out. (B) Signup and view all the answers

Which step is crucial when teaching learners about squaring a binomial?

Pointing out to write the binomial twice. (D) Signup and view all the answers

Which of the following correctly describes the application of FOIL when multiplying (a + 5)(a + 2)?

The result is a^2 + 7a + 10. (C) Signup and view all the answers

What common mistake do learners tend to make when squaring a binomial?

Only squaring the first term. (B) Signup and view all the answers

Study Notes

Simple Interest

Simple Interest is calculated using the formula: SI = p × i × n, where SI is the simple interest, p is the principal amount, i is the interest rate, and n is the number of years.
The total amount owed after simple interest is calculated by adding the simple interest to the original principal amount.

Compound Interest

Compound interest uses only one formula: A = P(1+i)^n, where A is the accumulated amount, P is the principal amount, i is the interest rate, and n is the number of times interest is allocated.
In Grade 9, n represents the number of years and interest is calculated per annum.

Hire Purchase

Hire purchase always uses simple interest.
A person can buy an item on credit by paying a deposit and the remaining balance over a period of months, which includes interest.

Finding Monthly Instalments

Calculate the deposit by finding a percentage of the total cost.
Subtract the deposit from the original price to find the new amount owed.
Use the compound interest formula to determine the total amount owing after the deposit is paid.
Divide the total amount owing by the number of months to find the monthly repayment.

Exchange Rates

Exchange rates are determined by the economy and constantly change.

Integers

This unit focuses on ordering integers, calculations with integers, and solving problems involving integers.
This knowledge is used in later topics including algebraic fractions.

Common Fractions

A common fraction is written with two whole numbers, a numerator on top and a denominator below, separated by a horizontal line.
The denominator cannot be 0, as it makes the fraction undefined.
Proper fractions have a numerator smaller than the denominator.
Improper fractions have a numerator larger than the denominator.
The Lowest Common Denominator (LCD) is the smallest number divisible by all the denominators of the fractions.
The reciprocal of a number is its multiplicative inverse.

Algebraic Expressions

An algebraic expression is a mathematical formula that can include variables, constants, and operations.
Terms in an algebraic expression are separated by + or - signs.
A coefficient is a number or symbol multiplied by a variable in a term.
Inverse operations can be used to solve for variables in equations.
Encourage learners to check their answers by working through the expression again.

Functions and Relationships

Functions are used to identify a rule that relates input values to output values.
Rules can involve one or two operations.
To find the rule, analyze both the input and output values.

Multiplying Binomials

FOIL (First, Outer, Inner, Last) is a mnemonic used to remember the four products that need to be found when multiplying binomials.
Each term in one bracket needs to be multiplied by each term in the other bracket.

Squaring Binomials

Squaring a binomial means multiplying it by itself.
FOIL can be used to find all the products.
Encourage learners to write the binomial out twice and use FOIL instead of taking shortcuts.

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Description

This quiz covers the concepts of simple interest, compound interest, and hire purchase as taught in Grade 9. You'll explore the formulas for calculating both types of interest, as well as how to determine monthly instalments for hire purchases. Test your understanding of these essential financial concepts.