Mental Maths (Without Calculators) - Chapter 1
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Questions and Answers

What is the simplest form of the fraction for the decimal 0.04?

  • 4/10
  • 1/25 (correct)
  • 2/5
  • 2/50

What is the solution for the equation x + 7 = - 7 + 3x?

  • – 5 (correct)
  • 9
  • 7
  • 2

Which of the following is a characteristic of terminating decimals?

  • They cannot be multiplied by whole numbers.
  • They cannot be expressed as fractions.
  • They always have infinite decimal places.
  • They can be converted into fractions easily. (correct)

What result do you get when multiplying a decimal by 100?

<p>It increases by two places. (C)</p> Signup and view all the answers

Which of the following operations can check if a number is a solution to an equation?

<p>Plugging the number into the equation (A)</p> Signup and view all the answers

Which of the following conversions results in the simplest fraction form?

<p>0.66 to 2/3 (A), 0.125 to 1/8 (B), 0.75 to 3/4 (D)</p> Signup and view all the answers

When dividing a decimal by a whole number, what is the expected outcome?

<p>The result may be a smaller decimal. (D)</p> Signup and view all the answers

What is the best estimate for the value of f(24.75) given the points (24,81) and (25,93)?

<p>87 (A)</p> Signup and view all the answers

Which set of sides can form a right triangle?

<p>5, 12, 13 (A)</p> Signup and view all the answers

Given triangle ABC, where angle A is 30 degrees and side a = 10, what is the length of side b using the sine ratio?

<p>8.66 (C)</p> Signup and view all the answers

What is the cosine of a 45-degree angle?

<p>$\frac{\sqrt{2}}{2}$ (B)</p> Signup and view all the answers

Which trigonometric ratio corresponds to the opposite side over the hypotenuse?

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

What is the result of the expression $25/5 + 3 \times 7$?

<p>21 (C)</p> Signup and view all the answers

What is the cube of the number 4?

<p>64 (C)</p> Signup and view all the answers

If the volume of a cube is 1,000 cm³, what is the length of each side?

<p>10 cm (B)</p> Signup and view all the answers

What is the square of 9?

<p>81 (A)</p> Signup and view all the answers

What is the square root of 144?

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

What is the result of $8^2 - 5^2$?

<p>48 (B)</p> Signup and view all the answers

What is the cube root of 729?

<p>9 (A)</p> Signup and view all the answers

If $x$ is a whole number such that $x^2 = 100$, what is the value of x?

<p>10 (B)</p> Signup and view all the answers

If the ratio of red fish to blue fish in a tank is 3:5 and there are 20 blue fish, how many red fish are there?

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

What is the new price of a shirt that originally costs 85 AED after a 20% discount?

<p>68 AED (B)</p> Signup and view all the answers

In terms of units of time, which of the following would correctly describe a decade?

<p>10 years (A)</p> Signup and view all the answers

Which of the following statements best describes a ratio?

<p>It compares quantities in the same unit. (A)</p> Signup and view all the answers

How do you convert the decimal 0.75 into a percentage?

<p>75% (A)</p> Signup and view all the answers

When comparing two rates, which of the following is true?

<p>Rates can compare quantities in different units. (A)</p> Signup and view all the answers

If a graph shows 12 people picked blue and 16 picked orange, how many picked either blue or orange?

<p>28 (A)</p> Signup and view all the answers

What does a percentage of 45% represent?

<p>45 out of 100 (C)</p> Signup and view all the answers

What is the area of a square with a side length of 5 cm?

<p>25 cm² (D)</p> Signup and view all the answers

How do you find the area of a rectangle with a width of 4 cm and a length of 10 cm?

<p>Multiply 4 by 10 (C)</p> Signup and view all the answers

What is the volume of a prism that has a base area of 20 cm² and a height of 5 cm?

<p>100 cm³ (A)</p> Signup and view all the answers

Given the points (2, 3) and (4, 7), what is the slope of the line connecting these points?

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

If a quadratic function has a vertex at (3, 5), what is the maximum value of this function?

<p>5 (D)</p> Signup and view all the answers

Which of the following statements correctly describes an exponential growth function?

<p>It increases indefinitely over time. (B)</p> Signup and view all the answers

What would be the area of a trapezoid with bases measuring 8 cm and 6 cm, and a height of 4 cm?

<p>28 cm² (B)</p> Signup and view all the answers

For the quadratic function represented by the equation $y = x^2 - 4x + 6$, what is the value of the function at its vertex?

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

What is the correct definition of a leap year?

<p>A year that is divisible by 4, except for years divisible by 100 unless they are also divisible by 400 (C)</p> Signup and view all the answers

How many seconds are there in one hour?

<p>3600 seconds (D)</p> Signup and view all the answers

Convert 150 minutes into hours and minutes.

<p>2 hrs 30 min (A)</p> Signup and view all the answers

What is the sum of the interior angles of a hexagon?

<p>720° (C)</p> Signup and view all the answers

Find the measure of one exterior angle in a regular pentagon.

<p>72° (B)</p> Signup and view all the answers

What is the area of a circle with a radius of 7 units?

<p>$154 ext{ units}^2$ (C)</p> Signup and view all the answers

What is the measure of each interior angle of a regular octagon?

<p>135° (A)</p> Signup and view all the answers

What is the missing side ratio of two similar triangles if one side is 10 cm and the corresponding side of the other triangle is 30 cm?

<p>1:3 (B)</p> Signup and view all the answers

Flashcards

BODMAS

The order of operations in mathematics, acronym stands for Brackets, Orders (powers and square roots), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).

Square of a number

The result of multiplying a number by itself. For example, the square of 5 is 5 x 5 = 25.

Square root of a number

The inverse operation of squaring. The square root of a number is the value that when multiplied by itself equals the original number. For example, the square root of 25 is 5, because 5 x 5 = 25.

Square number

Numbers that can be expressed as the product of two equal integers. For example, 9 is a square number because 3 x 3 = 9.

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Cube of a number

The process of multiplying a number by itself three times. For example, the cube of 2 is 2 x 2 x 2 = 8.

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Cube root of a number

The inverse operation of cubing. The cube root of a number is the value that when multiplied by itself three times equals the original number. For example, the cube root of 8 is 2, because 2 x 2 x 2 = 8.

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Cube number

Numbers that can be expressed as the product of three equal integers. For example, 27 is a cube number because 3 x 3 x 3 = 27.

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Divisible

A number that can be divided evenly by another number, leaving no remainder. For example, 12 is divisible by 3, because 12 ÷ 3 = 4.

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What is a ratio?

A ratio is a comparison of two quantities, often expressed as a fraction.

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What is a proportion?

Proportion is a statement that two ratios are equal. It means that the two quantities are in the same relationship.

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What is a rate?

A rate is a ratio that compares two quantities with different units.

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How to calculate total quantity from a ratio?

When given a ratio and the value of one of the terms, you can calculate the total quantity by setting up a proportion and solving for the unknown value.

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How to find value of each quantity from a ratio?

If you know the ratio between two quantities, you can find the value of each quantity if you know the total amount. Set up a proportion and solve for the unknown values.

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How to convert a fraction to a decimal?

A fraction can be converted into a decimal by dividing the numerator by the denominator.

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How to convert a terminating decimal to a fraction?

A terminating decimal can be converted into a fraction by writing it as a fraction with a denominator of 10, 100, 1000, etc., depending on the number of decimal places and then simplifying it.

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How to multiply a decimal by a power of 10?

To multiply a decimal number by a power of 10, move the decimal point to the right by the number of zeros in the power of 10.

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Interpolation

A method to estimate an unknown value within a range of known data points. It uses the relationship between existing data points to predict the value of an unknown point.

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Pythagorean Theorem

A theorem stating that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

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Trigonometry in right triangles

The study of relationships between angles and sides of triangles, particularly right-angled triangles. Key ratios are sine (SOH), cosine (CAH), and tangent (TOA).

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Cosine (Cos)

The trigonometric ratio that represents the ratio of the adjacent side to the hypotenuse in a right-angled triangle.

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Sine (Sin)

The trigonometric ratio that represents the ratio of the opposite side to the hypotenuse in a right-angled triangle.

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What is a Percentage?

A percentage is a fraction out of 100. It is represented by the symbol '%'.

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What is Interpreting Graphs?

Interpreting graphs involves understanding the relationship between the different data points and their respective coordinates. This includes recognizing trends and patterns.

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What is Handling Data?

Data handling involves organizing, analyzing, and interpreting data. It includes understanding different units of measurement for various quantities.

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Leap Year

A year that has 366 days instead of 365 days. It occurs every four years, except for years divisible by 100 but not by 400.

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Time Units Relationship

The number of seconds in a minute is 60. The number of minutes in an hour is 60. The number of hours in a day is 24. The number of days in a week is 7. The number of weeks in a month is roughly 4. The number of months in a year is 12. The number of days in a year is 365 (or 366 in a leap year).

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Time Unit Conversion

Converting between different units of time, like seconds to minutes, minutes to hours, etc.

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Time Addition and Subtraction

Adding or subtracting values representing time, expressed in terms of seconds, minutes, hours, days, months, and years.

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Radius of a Circle

The line segment that joins the center of the circle to any point on the circle.

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Circumference of a Circle

The distance around a circle.

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Area of a Circle

The amount of space enclosed within a circle.

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Polygon

A closed plane figure formed by three or more straight line segments.

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Area (2D shapes)

The amount of space a two-dimensional shape occupies. It's measured in square units like square centimeters or square inches.

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Volume (3D shapes)

The space enclosed within a three-dimensional shape. It's measured in cubic units like cubic meters or cubic feet.

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Slope of a line

The steepness of a line. It tells us how much the line rises or falls for every unit it moves horizontally.

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Quadratic function

A function that has a graph shaped like a parabola. It has a highest or lowest point called the vertex.

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Exponential function

A function that grows or decays at an exponential rate. It has a consistent multiplier.

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Parallelogram

A four-sided figure with two parallel sides. You find its area by multiplying the base by the height.

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Rectangle

A special type of parallelogram with four right angles. You find its area by multiplying the length and width.

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Trapezoid

A four-sided figure with one pair of parallel sides. You find its area by averaging the lengths of the parallel sides and multiplying by the height.

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Study Notes

Mental Maths (Without Calculators) - Chapter 1: Heart of Algebra

  • Learning Objectives: Perform four operations with signed numbers. Simplify numerical expressions with whole numbers (up to 3 digits) and basic arithmetic operations, resulting in positive whole numbers. Include brackets in expressions.

  • Four Operations (BODMAS): Focuses on applying the order of operations (Brackets, Orders, Division, Multiplication, Addition, Subtraction).

  • Powers and Roots: Finding squares and square roots of whole numbers between 1 and 20. Finding square roots of perfect squares between 1 and 400 via inspection or prime factorisation. Finding cubes of whole numbers between 1 and 10. Finding cube roots of whole cubes between 1 and 1000.

  • Sample Question (Powers and Roots): Example problem provided for finding squares and square roots or cubes and cube roots.

Decimals and Fractions

  • Learning Objectives: Perform addition, subtraction, multiplication, and division of fractions. Convert fractions to decimals and vice-versa (terminating decimals). Write decimals as fractions in simplest form. Multiply and divide decimal numbers by powers of 10. Multiply/divide decimal numbers by whole numbers. Solve problems related to decimals.

  • Sample Question (Decimals and Fractions): Convert 0.04 into a fraction in simplest form. More sample problems on basic decimal calculations and fraction conversion.

Chapter 2: Statistics and Data Analysis - Ratio, Proportions, and Rates

  • Learning Objectives: Calculate the total quantity when the ratio and the value of one term are known. Calculate the values of remaining terms in a ratio. Understanding Proportions and converting it into ratios and vice-versa. Understanding Rates (compare numbers or quantities with different units).

  • Sample Question (Ratios and Proportions): Find the number of red fish if the ratio of red fish to blue fish is 3:5, and there are 20 blue fish in a tank.

Percentages

  • Learning Objectives: Understanding the concept of percentages. Use the symbol (%) to represent percentages. Convert fractions/decimals with denominators/decimal places that are factors of 100 into percentages. Convert between decimal numbers and percentages. Calculate reverse percentage problems.

  • Sample Question (Percentages): A shirt with a price of 85 AED has a 20% discount. Find the new price.

Interpreting Graphs

  • Learning Objectives: Interpret graphs, find relations between coordinates, solve problems based on graphs.

  • Sample Question (Graphs): Interpret/describe a graph and calculate values from the graph.

Handling Data

  • Learning Objectives: Identifying time units (seconds, minutes, hours, days, months, years, etc.) and calculating related measures in days. Distinguishing leap years. Constructing relationships between time units and solving real-life problems.

  • Sample Question (Handling Data): Convert 90 minutes into hours.

Chapter 3: Geometry

  • Basic Geometrical Terms (Circles): Understand basic geometric terms, parts of a circle (radius, diameter, circumference), area of a circle. Understand properties of triangles inside circles.
  • Polygons: Find the sum of interior, exterior, and central angles in polygons. Calculate interior/exterior/central angles of regular polygons (e.g., hexagon).
  • Triangles: Identify characteristics of triangles, find missing sides of similar triangles, calculate the area of different triangle types.
  • Area of 2D Shapes (Area, Perimeter): Calculate the area of squares, rectangles, parallelograms.
  • Sample Question (Geometry): Calculate the value of x in a circle problem, find interior angles of a regular hexagon, find area of triangles or other shapes.

Chapter 4: Advanced Mathematics

  • Slopes and Equations of Lines: Find the slope of a straight line given two points. Understanding slope based on the graph.
  • Characteristics of Quadratic and Exponential Functions: Solve problems involving quadratic functions' minimum/maximum values. Determining if an exponential function represents growth or decay.
  • Sample Question (Slopes and Equations): What is the slope of the line passing through (8, -10) and (6, -4)?

Volume of 3D Shapes

  • Sample Question (Volume of 3D Shapes): Find the volume of prisms, solve problems involving 3D shapes.

Trigonometry in Right Triangles

  • Sample Question (Trigonometry): Use trigonometric ratios (SOH CAH TOA) to solve problems with missing sides and angles. Indentify if three sides form a right-angled triangle.

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Description

This quiz focuses on essential mental math skills, including operations with signed numbers and simplification of numerical expressions. You'll apply the order of operations through BODMAS and explore powers, roots, decimals, and fractions. Strengthen your arithmetic abilities without relying on calculators!

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