Mathematics Class 10 Quiz

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Questions and Answers

What is the amount of the investment after five years at a 9.5% annual interest rate compounded quarterly?

  • RM1,500,000
  • RM1,295.63
  • RM1,216.14 (correct)
  • RM1,500

How much is Farhan's down payment for his house priced at RM950,000?

  • RM95,000 (correct)
  • RM75,000
  • RM90,000
  • RM100,000

In an arithmetic sequence with terms x, −3, (x + 4), 1, what is the first term of the sequence?

  • x
  • -3
  • 1
  • -4 (correct)

What is the effective interest rate charged by the bank for Farhan's loan?

<p>4.07% (C)</p> Signup and view all the answers

What is the total amount paid by Farhan for his house after 25 years?

<p>RM1,448,900 (B)</p> Signup and view all the answers

What is the common difference of the arithmetic sequence x, −3, (x + 4), 1?

<p>-4 (D)</p> Signup and view all the answers

If Farhan missed the first five payments, how much does he owe on the sixth payment to settle all outstanding payments?

<p>RM27,304.66 (D)</p> Signup and view all the answers

What is the sum of the first seven terms of the arithmetic sequence defined as x, −3, (x + 4), 1?

<p>14 + 6x (B)</p> Signup and view all the answers

If a teacher borrows RM Q from a bank charging 3.5% simple interest per year, how much will she pay back after 5 years if it amounts to RM 28,200?

<p>RM 25,000 (B)</p> Signup and view all the answers

What is the monthly payment Farhan needs to make for his home loan?

<p>RM4,513 (D)</p> Signup and view all the answers

What is the formula to calculate the simple interest earned on an amount borrowed over a period?

<p>I = P * r * t (C)</p> Signup and view all the answers

What is the total interest paid by Farhan for his house over the loan term?

<p>RM498,900 (C)</p> Signup and view all the answers

After borrowing RM Q for 5 years at 3.5% simple interest, what would the total interest accrued over 2 years be?

<p>RM Q * 0.035 * 2 (C)</p> Signup and view all the answers

What is the loan amount Farhan needs after his down payment for the house?

<p>RM855,000 (B)</p> Signup and view all the answers

In the context of simple interest, what would RM Q represent?

<p>The principal amount borrowed (A)</p> Signup and view all the answers

What is the additional payment required to repay RM 28,200 after borrowing RM Q at 3.5% interest for 5 years?

<p>Principal + simple interest for 5 years (C)</p> Signup and view all the answers

What is the bank discount for Raju if he borrows RM 8,000 at a simple discount rate of 4% per year for 30 months?

<p>RM 600 (B)</p> Signup and view all the answers

What is the proceed amount Raju will receive after the bank discount is applied?

<p>RM 7,400 (A)</p> Signup and view all the answers

If a sum of RM 50,000 grows to RM 64,167.93 over five years, what is the monthly interest rate assuming compounding monthly?

<p>0.5% (C)</p> Signup and view all the answers

What is the effective annual interest rate if the nominal interest rate is 6% compounded monthly?

<p>6.28% (D)</p> Signup and view all the answers

In the equation 5^{2x+1} - 4x = 16, what is the value of x?

<p>1 (B)</p> Signup and view all the answers

What is the common ratio in the geometric sequence x, 1, y, 4, 8?

<p>2 (A)</p> Signup and view all the answers

How many years will it take for a smartphone depreciating at 10% per year to be valued at less than RM 1,000 if its initial cost is RM 2,000?

<p>12 years (C)</p> Signup and view all the answers

What is the interest earned if RM 50,000 grows to RM 64,167.93 over five years?

<p>RM 14,167.93 (C)</p> Signup and view all the answers

Flashcards

Common Difference

The value that is added to each term in an arithmetic sequence to get the next term.

Principal (P)

The total amount of money borrowed or invested.

Interest (I)

The extra amount of money paid back on a loan or investment.

Sum of the First n Terms (S_n)

The sum of all the terms in an arithmetic sequence up to a specific term.

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Arithmetic Sequence

A sequence where the difference between any two consecutive terms is constant.

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First Term (a)

The value of the first term in an arithmetic sequence.

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General Term (T_n)

A mathematical expression used to find the nth term of an arithmetic sequence.

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Amount (A)

The total amount of money that is paid back on a loan or investment.

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Bank discount

The amount of money deducted from the principal amount of a loan for the time it is borrowed. It is calculated as a percentage of the principal amount, known as the discount rate.

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Proceed

The amount of money that the borrower actually receives after the bank discount is deducted from the principal amount.

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Equivalent Simple Interest Rate

The equivalent simple interest rate that would result in the same amount of interest earned over the same period as the simple discount rate.

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Interest Rate (Compounded Monthly)

The annual interest rate that is applied to an investment or loan, compounded a specified number of times per year, usually monthly.

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Effective Interest Rate

The annual interest rate that is earned on an investment or loan, taking into account the effects of compounding.

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Interest Earned

The total amount of interest earned over a specified period on an investment or loan.

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Geometric Sequence

A sequence where each term is found by multiplying the previous term by a constant value, called the common ratio.

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Sum of First 'n' terms of a Geometric Sequence

The total sum of the first 'n' terms in a geometric sequence.

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Principal Amount

The amount of money originally invested in a financial product, which then earns interest over time. It is also known as the principal amount.

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Interest Rate

The rate of return on an investment, expressed as a percentage of the principal amount. It represents the cost of borrowing money or the reward for lending money.

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Compound Interest

The process of calculating interest on an investment, where the earned interest is added to the original principal amount, and then the next interest calculation is applied to the new, larger principal. This results in exponential growth.

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Amount of Investment

The total amount of money accumulated at the end of an investment period, including the original principal and any accumulated interest.

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Down Payment

The amount of money paid as a percentage of the total price of an asset, usually paid upfront, and the remaining balance is financed through a loan.

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Loan amount

The borrowed amount of money remaining after deducting the down payment from the total price of an asset.

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Monthly Installments

Regular periodic payments made towards the repayment of a loan, typically made monthly, over a set period of time.

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Study Notes

Section A (25 Marks)

  • The section contains three questions, all of which must be answered.
  • Question 1 involves an arithmetic sequence, asking for the first term, common difference, 17th term, and sum of the first seven terms.
  • Question 2(a) concerns a simple interest loan, calculating the borrowed amount and interest for the first two years.
  • Question 2(b) deals with calculating the simple discount, finding the proceeds, and the equivalent simple interest rate.
  • Question 3 considers compound interest. Calculate the interest rate, effective interest rate, and interest earned for a given sum of money.

Section B (75 Marks)

  • This section consists of seven questions, all requiring solutions.
  • Question 1(a) and (b) are algebraic equations requiring solutions.
  • Question 2(a) involves solving an equation with logarithms, 2(b) is log equation needing solution.
  • Question 3 is focused on solving a quadratic inequality.
  • Question 4 involves solving compound inequalities.
  • Question 5(a) relates to a geometric sequence, calculating the common ratio, determining values for x and y, and the total of the first five terms.
  • Question 5(b) is a word problem involving depreciation of a smartphone based on a given percentage, and requires calculating value after a given time and the time it takes for the smartphone to decrease to a specified value.
  • Question 6 examines compound interest, calculating the invested sum after five years, the accrued interest after eight years, and the effective interest rate.
  • Question 7 concerns a loan for a house, calculating the down payment, loan amount, monthly payment, effective interest rate, total interest paid, whole cost of the house, and calculating the amount due on a missed payment(s) based on monthly installment payment, compounded monthly.

Additional Information

  • Time Allocated: 2 hours
  • Time Per Question: Varied according to question complexity
  • Marking Scheme: Marks are given for each question or part of a question, to allow for a portion of the question to be solved even if some parts are not fully understood.

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