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Questions and Answers

In South Africa, which convention is typically used to separate whole numbers from decimal fractions?

  • Space
  • Apostrophe
  • Decimal point
  • Comma (correct)

Which key on a basic calculator is used to add a displayed number to the calculator's memory?

  • M-
  • MRC
  • M+ (correct)
  • +/-

What does the acronym 'BODMAS' stand for in the order of operations?

  • Brackets, Orders, Decimals, Multiplication, Addition, Subtraction
  • Bias, Orders, Division, Multiplication, Addition, Subtraction
  • Brackets, Of, Division, Multiplication, Addition, Subtraction
  • Brackets, Orders, Division, Multiplication, Addition, Subtraction (correct)

What is the result of multiplying a number by 1000?

<p>Shifting each digit three places to the left (B)</p> Signup and view all the answers

Which of the following describes a 'proper fraction'?

<p>The numerator is smaller than the denominator. (D)</p> Signup and view all the answers

What is the first step in adding or subtracting fractions with different denominators?

<p>Convert fractions to have a common denominator. (D)</p> Signup and view all the answers

What distinguishes 'rate' from 'ratio'?

<p>Rate compares two numbers with different units, while ratio compares numbers of the same type. (D)</p> Signup and view all the answers

How are common fractions converted into decimal fractions?

<p>By using division to divide the numerator by the denominator. (B)</p> Signup and view all the answers

What does the 'MRC' key on a calculator typically do?

<p>Displays the number stored in memory; press twice to clear memory. (D)</p> Signup and view all the answers

What is the result of adding a negative number to its positive counterpart?

<p>Always zero. (A)</p> Signup and view all the answers

What is the correct setup for dividing $\frac{3}{4}$ by $\frac{1}{2}$?

<p>$\frac{3}{4} \times \frac{2}{1}$ (D)</p> Signup and view all the answers

When rounding to the nearest 10, which numbers are rounded up?

<p>Numbers ending in 5 to 9 (C)</p> Signup and view all the answers

Which of the following is the correct method to calculate a percentage discount on an item?

<p>Multiply the original price by the percentage converted to a decimal, then subtract from the original price. (D)</p> Signup and view all the answers

A recipe requires a ratio of 2:3 of sugar to flour. If you want to make a larger batch using 6 cups of flour, how much sugar do you need?

<p>4 cups (B)</p> Signup and view all the answers

What is the primary reason for estimating answers before performing calculations?

<p>To think about the problem beforehand and check the accuracy of your calculations. (C)</p> Signup and view all the answers

A store offers a 20% discount on a dress originally priced at $50. What is the sale price of the dress?

<p>$40 (B)</p> Signup and view all the answers

If the unemployment rate in a country increases from 5% to 8%, what is the percentage increase in the unemployment rate?

<p>60% (C)</p> Signup and view all the answers

Which of the following scenarios requires understanding of both order of operations (BODMAS) and dealing with negative numbers?

<p>A bank statement showing an overdraft fee and interest calculation. (D)</p> Signup and view all the answers

You have two options for investing money: Option A offers a 10% interest rate compounded annually, and Option B offers a 9.5% interest rate compounded monthly. Assuming you invest the same principal amount for the same period (over 5 years), which option would yield a higher return?

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

Consider the equation $y = \frac{5x^2 + 3x - 2}{x - 1}$. What value does $y$ approach as $x$ approaches 1?

<p>8 (A)</p> Signup and view all the answers

If a car travels 240 kilometers in 3 hours, what is its average speed?

<p>80 km/h (D)</p> Signup and view all the answers

Convert the decimal fraction 0.75 to a common fraction in its simplest form.

<p>$\frac{3}{4}$ (D)</p> Signup and view all the answers

Which of the following represents 'Five million, two hundred thousand and fifty' in its numerical form?

<p>5 200 050 (C)</p> Signup and view all the answers

A store buys an item for $x$ and sells it for $y$. Express the profit as a percentage of the cost price.

<p>$\frac{y-x}{x} \times 100%$ (A)</p> Signup and view all the answers

In which direction are the digits shifted when multiplying a number by 100?

<p>Two places to the left (C)</p> Signup and view all the answers

What type of fraction is represented when the numerator is larger than the denominator?

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

What is the result of adding a positive number and its negative counterpart?

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

What is the purpose of estimating answers before performing complex calculations?

<p>To check the accuracy and reasonableness of the calculated result (A)</p> Signup and view all the answers

According to BODMAS, which operation should be performed first in the expression $9 + (6 - 2) imes 4 \div 2$?

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

How would you convert the common fraction $\frac{3}{8}$ into a decimal fraction?

<p>Divide 3 by 8 (C)</p> Signup and view all the answers

What information does a 'rate' provide that a 'ratio' does not?

<p>A comparison of two quantities with different units (D)</p> Signup and view all the answers

A shop buys an item for $x$ dollars and sells it for $y$ dollars. How is the profit expressed as a percentage of the cost price?

<p>$\frac{y-x}{x} imes 100$ (D)</p> Signup and view all the answers

Which of the following numbers would be rounded up to the nearest 10?

<p>85 (D)</p> Signup and view all the answers

A recipe requires a ratio of 3:5 for sugar to flour. If you want to make a larger batch using 10 cups of flour, how much sugar do you need?

<p>6 cups (A)</p> Signup and view all the answers

What key sequence would you use on a basic calculator to add 7 to the number already stored in the calculator's memory?

<p>7, M+ (C)</p> Signup and view all the answers

A store offers a 15% discount on an item priced at $80. What is the sale price of the item?

<p>$68 (A)</p> Signup and view all the answers

If the inflation rate in a country decreases from 7% to 3.5%, what is the percentage decrease in the inflation rate?

<p>50% (B)</p> Signup and view all the answers

Evaluate: $5 + 3 imes (8 - 2) \div 2 - 1$

<p>13 (C)</p> Signup and view all the answers

Consider a scenario where you need to calculate the final amount after applying a percentage discount and then adding sales tax. An item is priced at $P$, has a discount of $d%$ and a sales tax of $t%$. Which expression correctly gives the final price?

<p>$P(1 - \frac{d}{100})(1 + \frac{t}{100})$ (D)</p> Signup and view all the answers

A car travels 360 kilometers in 4 hours. What is its average speed?

<p>90 km/h (A)</p> Signup and view all the answers

Which of the following represents 'Three million, four hundred thousand and seventy' in its numerical form?

<p>3,400,070 (C)</p> Signup and view all the answers

What does the acronym 'MRC' stand for on a calculator, and what is its function?

<p>Memory Recall Clear: Recalls the number in memory with one press and clears it with a second press. (C)</p> Signup and view all the answers

Consider the infinite series: $1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + ...$. What value does this series converge to?

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

You are given two investment options: Option A offers simple interest at a rate of 8% per annum, while Option B offers compound interest at a rate of 7.5% per annum, compounded quarterly. Which option yields a higher return after 10 years, assuming the same principal amount is invested?

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

A store increases the price of an item by 20% and then decreases the new price by 20%. What is the overall percentage change in the price of the item?

<p>4% decrease (C)</p> Signup and view all the answers

Two painters can paint a house in 6 hours. How long would it take three painters, working at the same rate, to paint the same house?

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

In South Africa, which punctuation mark is conventionally used to separate the integer part from the fractional part of a number?

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

What is the function of the 'M+' key on a basic calculator?

<p>Adds the displayed number to the calculator's memory. (A)</p> Signup and view all the answers

According to the order of operations (BODMAS), which calculation should be performed first in the expression $10 - 2 imes (3 + 1)$?

<p>Addition within brackets (C)</p> Signup and view all the answers

What is the result of shifting the digits of a number two places to the left?

<p>Multiplying the number by 100 (C)</p> Signup and view all the answers

Before adding or subtracting fractions with different denominators, what initial step is required?

<p>Find a common denominator. (B)</p> Signup and view all the answers

What is the key difference between a 'rate' and a 'ratio'?

<p>A rate compares quantities of different units, while a ratio compares quantities of the same units. (D)</p> Signup and view all the answers

What mathematical operation is used to convert a common fraction into a decimal fraction?

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

What is the primary function of the 'MRC' key on a standard calculator?

<p>To recall the value stored in memory; pressing it twice clears the memory. (D)</p> Signup and view all the answers

What is the sum of a positive number and its corresponding negative number?

<p>Always zero (C)</p> Signup and view all the answers

When rounding to the nearest 10, numbers ending in which digit are typically rounded up?

<p>Digits 5 to 9 (B)</p> Signup and view all the answers

To calculate a percentage discount on an item, which step should be performed first?

<p>Convert the percentage discount to a decimal or fraction. (A)</p> Signup and view all the answers

A recipe calls for a sugar to flour ratio of 1:4. If you decide to use 12 cups of flour, how many cups of sugar are needed to maintain the ratio?

<p>3 cups (A)</p> Signup and view all the answers

What is the main purpose of estimating answers before performing exact calculations?

<p>To check if the final answer is reasonable. (B)</p> Signup and view all the answers

A shirt is priced at $40 and has a 25% discount. What is the sale price?

<p>$30 (B)</p> Signup and view all the answers

If a country's inflation rate decreased from 10% to 4%, what is the percentage decrease in the inflation rate?

<p>60% decrease (D)</p> Signup and view all the answers

Which of the following expressions requires the application of both BODMAS and rules for negative numbers?

<p>$-2 imes (5 - 8) + 6$ (A)</p> Signup and view all the answers

Consider two investment options for 3 years: Option A offers simple interest at 10% per year, and Option B offers compound interest at 9% per year, compounded annually. Which option yields a higher return?

<p>Option B will always yield a higher return. (C)</p> Signup and view all the answers

What value does the expression $ rac{x^2 - 4}{x - 2}$ approach as $x$ gets closer to 2?

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

If a train travels 450 kilometers in 5 hours, what is its average speed in kilometers per hour?

<p>90 km/h (C)</p> Signup and view all the answers

Which numerical representation corresponds to 'Two million, three hundred thousand and forty'?

<p>2,300,040 (D)</p> Signup and view all the answers

In which direction are the digits shifted when dividing a number by 100?

<p>Two places to the right (C)</p> Signup and view all the answers

Flashcards

Convention

A standard way of doing something.

Format

The way something appears or is set out.

South African Number Format

In South Africa, a comma separates whole numbers from decimals and spaces separate groups of three digits.

Measurements

Measurements are used for lengths and masses.

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Counting Numbers

Represent exact counts (e.g., number of people).

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Order Numbers

Indicate position (e.g., 1st, 2nd).

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Money Amounts

Represent financial values.

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Percentages

Represent rates.

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Codes

Used for identification.

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Writing Numbers in Words

Separating the number into groups of three digits from right to left, read each group individually and name it.

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Place Value

Using a place value table to identify the value of each digit.

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Estimating

A quick way to find an approximate answer.

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Calculator Memory Key M+

Adds a number to the memory.

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Calculator Memory Key M-

Subtracts a number from the memory.

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Calculator Memory Key MRC

Displays the number stored in memory (press twice to clear memory).

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Change Sign Key (+/-)

Changes the sign of a number (e.g., from positive to negative).

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BODMAS

Brackets, Orders, Division and Multiplication, Addition and Subtraction.

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Multiplying by 10/100/1000

Shift each digit one/two/three places to the left.

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Proper Fraction

Numerator is smaller than the denominator.

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Improper Fraction

Numerator is larger than the denominator.

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Mixed Number

A combination of a whole number and a fraction.

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Decimal Fraction

A fraction whose denominator is a power of ten.

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Positive Numbers

Greater than zero.

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Negative Numbers

Less than zero.

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Rounding to the Nearest 10

Numbers with units digits 1-4 round down, 5-9 round up.

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Estimating Answers

Used to check answers and think about a problem before calculating.

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Breaking Down and Multiplying

Break down large numbers into smaller, manageable parts, multiply each part, and then add the results.

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Grouping Numbers

Rearrange numbers in addition or multiplication to simplify the calculation.

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Definition of Proper Fractions

Fractions in which the numerator is smaller than the denominator; represents a value less than one.

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Definition of Improper Fractions

Fractions in which the numerator is greater than or equal to the denominator; represents a value equal to or greater than one.

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Definition of Mixed Numbers

A number consisting of a whole number and a proper fraction.

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Using Negative Numbers

Represent values below zero; denoted with a minus sign (-).

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Contextual Rounding

Consider the situation and its practical implications to make appropriate rounding decisions.

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Ratio

A comparison of two or more quantities with the same units. Written as a:b.

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Rate

A comparison of two quantities with different units. Expressed as one quantity 'per' another.

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Proportion

An equation stating that two ratios are equal, allowing you to find unknown values.

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Calculating a Percentage

Convert the percentage to a fraction or decimal and multiplying it by the total amount. For example: 10% of 50 = 0.10 * 50 = 5

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Percentage Discount

A reduction from the original price, calculated as a percentage. Subtract the discount amount from the original price.

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Percentage Increase

An increase in the original price, calculated as a percentage. Add the increased amount to the original price.

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Dividing Fractions

Multiply by the reciprocal of the divisor (the fraction you are dividing by).

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Decimal to Common Fraction

Convert the decimal to a fraction with a denominator of 10, 100, 1000, etc.

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What is Rate in Mathematics?

A comparison of two quantities with different units, showing how much of one thing there is for every unit of another.

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Adding/Subtracting Fractions

When adding or subtracting fractions, find an equivalent fraction so the denominators are the same.

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Calculate Value After Percentage Increase

To find the value after an increase, calculate the increase amount and add it to the original price.

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Common Fraction to Decimal

To convert, divide the numerator by the denominator.

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Study Notes

Number Formats and Conventions

  • A convention signifies a standard way of doing something.
  • A format is the way something appears or is set out.
  • South Africa uses a decimal comma to separate whole numbers from decimal fractions, and spaces to separate groups of three digits (e.g., R 1 000 000,00).
  • Measurements, counting numbers, order numbers, money amounts, percentages, and codes are different types of numbers used in various contexts.
  • To write numbers in words, separate the number into groups of three digits from right to left, then read each group individually and name it.
  • Large numbers are easier to read in symbol form due to place value; use a place value table to identify the value of each digit.
  • To order numbers, create a place value table, write the numbers in the table, compare the numbers column by column from left to right, and then arrange the numbers accordingly.
  • Decimal Fraction Representation in South Africa uses a decimal comma (e.g., 1 000 000,00), while other regions may use a decimal point (e.g., 1,000,000.00).

Operations Using Numbers and Calculator Skills

  • Estimating answers helps in thinking about a problem before working it out and checking answers for accuracy.
  • Calculators typically have keys for On/Off, memory functions (M+, M-, MRC), basic operations (+, -, *, /), and other functions like square root, percentage, and change sign.
  • M+ adds a number to the memory, M- subtracts a number from the memory, and MRC displays the number stored in memory (press twice to clear memory).
  • The change sign key changes the sign of a number from positive to negative or vice versa.
  • Calculations must follow the order of operations, often remembered by the acronym BODMAS:
    • Brackets
    • Orders (powers, roots)
    • DMivision and Multiplication (from left to right)
    • ASddition and Subtraction (from left to right)
  • Multiplication can be simplified by breaking down large numbers into smaller parts, multiplying each part, and then adding the results.
  • Grouping involves rearranging numbers to make multiplication and addition easier.
    • Multiplying by 10 shifts each digit one place to the left.
    • Multiplying by 100 shifts each digit two places to the left.
    • Multiplying by 1000 shifts each digit three places to the left.

Common Fractions

  • Proper fractions have a numerator smaller than the denominator.
  • Improper fractions have a numerator larger than the denominator.
  • Mixed numbers combine a whole number and a fraction.
  • When adding and subtracting fractions, convert them to have a common denominator before performing the operation.
  • Multiplying fractions involves multiplying the numerators together and the denominators together.
  • Dividing fractions involves multiplying by the reciprocal of the divisor.

Decimal Fractions

  • A decimal fraction is another way to write fractions whose denominators are powers of ten.
  • Common fractions can be converted to decimal fractions using division.
  • Decimal fractions can be converted to common fractions with a denominator of 10, 100, 1000, etc.

Positive and Negative Numbers

  • Positive numbers are greater than zero, while negative numbers are less than zero.
  • Each positive number has an opposite negative number; adding a number and its opposite results in zero.

Rounding, Ratio, Rates and Percentages

  • Rounding to the nearest 10 involves rounding numbers with units digits 1-4 down and 5-9 up.
  • Contextual rounding means considering the practical implications of rounding in real-life situations.
  • A ratio compares two or more numbers of the same type.
  • A rate compares two numbers with different units.
  • A proportion is a relationship indicating that two ratios are equal.
  • Simplify ratios by dividing both terms by their greatest common divisor.
  • Calculating unit rates involves dividing the given quantities.
  • Missing values can be found by setting up equivalent ratios or using cross-multiplication.
  • To find the value of a percentage, convert the percentage to a fraction and multiply the fraction by the given amount.
  • Discount is a decrease from the original price, and increase is an additional amount added to the original price.

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