Mathematics Chapter on Proportion and Interest

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Questions and Answers

What is the general form of a quadratic expression?

ax^2 + bx + c (a = 0)

ax^2 + bx + c (a ≠ 0) (correct)

ax^2 + b + c

a + bx^2 + c

Identify the coefficient of x in the expression 12x^2 - 13x - 20.

-13 (correct)

-20

Which of the following describes a trinomial?

An expression with four terms

An expression with three terms (correct)

An expression with one term

An expression with two terms

In the expansion of (3x - 5)(4x + 4), what is the constant term of the resulting expression?

-20 Signup and view all the answers

From the expression x^2 + x + 9, what is the coefficient of x^2?

1 Signup and view all the answers

What is the formula for calculating simple interest?

$I = \frac{P R T}{100}$ Signup and view all the answers

If Mr. Eze saves #50,000 at an interest rate of 5.5% for 2 years using simple interest, what would be the total interest earned?

#2,750 Signup and view all the answers

What is a key difference between simple interest and compound interest?

In compound interest, the interest earned is added to the principal. Signup and view all the answers

If you invest #70,000 at a compound interest rate of 5% per annum for 3 years, what will the total amount after 3 years be?

#81,500 Signup and view all the answers

How is the total amount calculated in compound interest at the end of the investment period?

By adding the compound interest to the principal. Signup and view all the answers

What is the total amount at the end of the 1st year given a principal of #70000 at a rate of 5%?

#73500 Signup and view all the answers

How much interest is earned in the 2nd year when the new principal is #73500 at a rate of 5%?

#3675 Signup and view all the answers

What formula is used to calculate the compound interest amount (A) after n years?

A = P[1 + (R/100)]^n Signup and view all the answers

What is the compound interest earned over 3 years on an initial principal of #70000 with an interest rate of 5%?

#11033.75 Signup and view all the answers

If a man borrows #600,000 at an 8.5% compound interest per annum and repays #85000 at the end of each year, what is the formula for the amount he owes after 2 years?

Amount = 600000(1 + 0.085)^2 - 85000 imes 2 Signup and view all the answers

What is direct proportion?

A type of relationship where both quantities increase or decrease at the same rate. Signup and view all the answers

In the context of direct proportion, what is the term used for the constant multiplier?

Constant of proportionality Signup and view all the answers

If d is directly proportional to t, which of the following equations represents this relationship?

d = vt Signup and view all the answers

What conclusion can be drawn if the ratio of quantity and cost for petrol remains constant?

The cost is directly proportional to the quantity. Signup and view all the answers

If a car travels 5 km in 15 minutes, how far will it travel in 60 minutes under constant speed?

20 km Signup and view all the answers

How would you express that quantity x is directly proportional to quantity y mathematically?

x = ky Signup and view all the answers

What is the proportional relationship between 8 litres of petrol costing 160 naira and 5 litres costing 100 naira?

Directly proportional Signup and view all the answers

If the cost of 10 litres of petrol is found to be 200 naira, what would be the cost of 2 litres of petrol?

40 naira Signup and view all the answers

What is the first step in solving the equation ( \frac{2x}{3} = -2 )?

Multiply both sides by 3 Signup and view all the answers

In the equation ( \frac{2(4x-1)}{2} = \frac{9(x+1)}{4} ), what is the correct method to isolate ( x )?

Use the Least Common Multiple to clear fractions Signup and view all the answers

After clearing the fractions in the equation ( 4(8x - 2) = 2(9x + 9) ), what is the resulting simplified equation?

32x - 8 = 18x + 18 Signup and view all the answers

Which of the following steps is correct when solving ( \frac{a-5}{2} = 5 + \frac{a}{3} )?

Find the Least Common Multiple before cross multiplying Signup and view all the answers

After performing cross multiplication on ( \frac{8}{4(x-2)} = \frac{1}{10} ), which of the following equations do you obtain?

8*10 = 4(x-2) Signup and view all the answers

What is the LCM of the denominators in the equation ( \frac{a-5}{2} = 5 + \frac{a}{3} )?

6 Signup and view all the answers

When solving ( \frac{8}{4(x-2)} = \frac{1}{10} ), what is the value of ( x ) after cross-multiplying and simplifying?

x = 4 Signup and view all the answers

In solving ( 3(a - 5) = 2(15a + a) ), what should be the first step after expanding?

Combine like terms Signup and view all the answers

Study Notes

Proportion

Proportion is an equation where two ratios are equal to each other.
It can be used to represent relationships between quantities.
There are three types of proportion:
- Direct Proportion: When one quantity increases, the other quantity increases at the same rate.
- Indirect/Inverse Proportion: When one quantity increases, the other quantity decreases at the same rate.
- Reciprocal Proportion: The product of two quantities is constant.
Direct Proportion Examples:
- Distance and time travelled by a vehicle moving at a constant speed.
- Price and number of articles (without discounts).
- Distance covered and fuel consumption.
- Exchange rates.

Simple Interest

Simple interest is calculated on the original principal amount.
The interest earned is calculated using the formula: I = (P * R * T) / 100, where:
- I = interest
- P = principal
- R = rate (per annum)
- T = time (in years)

Compound Interest

Compound interest is calculated on the principal amount and accumulated interest from previous periods.
It is applicable in banks, credit unions, and other financial institutions.
The compound interest can be calculated based on the accumulated amount:
- A = P + I
- I = A - P
Compound interest is also calculated using the formula: A = P [ 1 + (R / 100) ]^n, where:
- A = amount at maturity
- P = principal
- R = rate (per annum)
- n = number of periods

Fractional Equations

Fractional equations are equations containing fractions with variable in the numerator or denominator.
Solving fractional equations involves:
- Cross multiplication: Multiplying the numerator of one fraction with the denominator of the other.
- Clearing fractions: Finding the least common multiple (LCM) of denominators and multiplying both sides of the equation by the LCM.

Quadratic Expressions

A quadratic expression is a polynomial of the second degree.
It has the general form: ax^2 + bx + c, where:
- a, b, and c are constants.
- a ≠ 0.
Example: 12x^2 – 13x – 20 has coefficients of:
- x^2: 12
- x: -13
- Constant: -20

Trinomials

A trinomial is an algebraic expression with three terms.
Example: ax^2 + bx + c.

Factorization of Quadratic Expressions

Factoring a quadratic expression involves breaking it down into two binomials.
Example: Factorizing x^2 + 5x + 6 gives us (x + 2)(x + 3).

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Description

This quiz covers key concepts of proportion and simple interest, including definitions, formulas, and examples. Students will explore types of proportions such as direct, inverse, and reciprocal, as well as how simple interest is calculated using specific parameters. Test your understanding of these fundamental mathematical principles.