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Questions and Answers
Using interpolation, what is the estimated value of f(24.75) given the points (24, 81) and (25, 93)?
Using interpolation, what is the estimated value of f(24.75) given the points (24, 81) and (25, 93)?
Which set of sides can form a right triangle?
Which set of sides can form a right triangle?
Which trigonometric ratio corresponds to the cosine of an angle in a right triangle?
Which trigonometric ratio corresponds to the cosine of an angle in a right triangle?
What is the length of the missing side 'c' in a right triangle if the other sides are 8 and 15?
What is the length of the missing side 'c' in a right triangle if the other sides are 8 and 15?
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If angle X has a cosine value of 0.6, what is one possible length relationship in a right triangle?
If angle X has a cosine value of 0.6, what is one possible length relationship in a right triangle?
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What is the simplest form of the fraction that represents the decimal 0.04?
What is the simplest form of the fraction that represents the decimal 0.04?
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What is the result of solving the equation x + 7 = -7 + 3x?
What is the result of solving the equation x + 7 = -7 + 3x?
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If the ratio of apples to oranges is 2:3 and there are 10 apples, how many oranges are there?
If the ratio of apples to oranges is 2:3 and there are 10 apples, how many oranges are there?
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Which operation is used to convert a decimal number by a power of 10?
Which operation is used to convert a decimal number by a power of 10?
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Which of the following fractions cannot be converted into a terminating decimal?
Which of the following fractions cannot be converted into a terminating decimal?
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What is the result of dividing a decimal number by powers of 10?
What is the result of dividing a decimal number by powers of 10?
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What is the term for a fraction whose decimal representation ends after a finite number of digits?
What is the term for a fraction whose decimal representation ends after a finite number of digits?
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If the ratio of two quantities is 4:5 and one quantity is 40, what is the total quantity?
If the ratio of two quantities is 4:5 and one quantity is 40, what is the total quantity?
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What is the result of simplifying the expression $25/5 + 3 \times 7$?
What is the result of simplifying the expression $25/5 + 3 \times 7$?
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What is the square of the number 9?
What is the square of the number 9?
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Which expression represents $3^3$?
Which expression represents $3^3$?
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What is the cube root of 1000?
What is the cube root of 1000?
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If a square has an area of 144 cm², what is the length of each side?
If a square has an area of 144 cm², what is the length of each side?
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Which of the following numbers is the cube of 4?
Which of the following numbers is the cube of 4?
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What is the result of $8 + 3 \times 4 - 2$?
What is the result of $8 + 3 \times 4 - 2$?
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What is the square root of 144?
What is the square root of 144?
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What is the area of a square with a side length of 5 cm?
What is the area of a square with a side length of 5 cm?
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If a rectangle has a length of 8 cm and a width of 3 cm, what is its area?
If a rectangle has a length of 8 cm and a width of 3 cm, what is its area?
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How do you calculate the volume of a prism with a base area of 10 cm² and a height of 4 cm?
How do you calculate the volume of a prism with a base area of 10 cm² and a height of 4 cm?
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What is the slope of a line that passes through the points (2, 4) and (5, 10)?
What is the slope of a line that passes through the points (2, 4) and (5, 10)?
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For a quadratic function, what represents the minimum value if the parabola opens upwards?
For a quadratic function, what represents the minimum value if the parabola opens upwards?
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If a quadratic function has the vertex at (3, -2), what type of value does the function reach at this point?
If a quadratic function has the vertex at (3, -2), what type of value does the function reach at this point?
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What is the primary characteristic of an exponential function that represents growth?
What is the primary characteristic of an exponential function that represents growth?
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What is the slope of a line that represents a decrease as it moves from left to right?
What is the slope of a line that represents a decrease as it moves from left to right?
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Which of the following is a leap year?
Which of the following is a leap year?
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Convert 150 seconds into minutes.
Convert 150 seconds into minutes.
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How many days are there in 3 months assuming each month has 30 days?
How many days are there in 3 months assuming each month has 30 days?
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What is the measure of each interior angle of a regular pentagon?
What is the measure of each interior angle of a regular pentagon?
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If a triangle has angles measuring 50° and 60°, what is the measure of the third angle?
If a triangle has angles measuring 50° and 60°, what is the measure of the third angle?
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Find the area of a circle with a radius of 7 cm.
Find the area of a circle with a radius of 7 cm.
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What is the relationship between hours and days in terms of time measurement?
What is the relationship between hours and days in terms of time measurement?
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How many degrees are in the sum of the interior angles of a hexagon?
How many degrees are in the sum of the interior angles of a hexagon?
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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?
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?
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A shirt priced at 85 AED is marked down by 20%. What is the new price of the shirt?
A shirt priced at 85 AED is marked down by 20%. What is the new price of the shirt?
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Which of these must be true about rates and ratios?
Which of these must be true about rates and ratios?
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If you have a graph showing the number of pets owned, which statement is true?
If you have a graph showing the number of pets owned, which statement is true?
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How many hours are in a decade?
How many hours are in a decade?
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Which of the following represents a percentage correctly?
Which of the following represents a percentage correctly?
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If the cost of a single item is 50 AED and the total cost for 3 items is 150 AED, what concept does this demonstrate?
If the cost of a single item is 50 AED and the total cost for 3 items is 150 AED, what concept does this demonstrate?
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What is the primary difference between a rate and a ratio?
What is the primary difference between a rate and a ratio?
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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 of whole numbers (no more than three digits), and simplify such expressions including brackets.
- Four Operations (BODMAS): Key concept for order of operations involving whole numbers.
- Sample Question (25/5 + 3 x 7): Applying BODMAS, the order of calculations is division, multiplication, and lastly addition. Answer is 21.
Powers and Roots
- Find the square of whole numbers between 1 and 20: This involves squaring whole numbers from 1 to 20.
- Represent square root of a number by √: Introduce the square root symbol.
- Find square roots of whole square numbers: Identifying perfect squares between 1 and 400. This can be by inspection (directly recognizing) or by finding prime factors.
- Find the cube of whole numbers: Cubing numbers from 1 to 10.
- Find the cubic root: Determining the cube roots of whole numbers between 1 and 1000.
Decimals and Fractions
- Operations with fractions and decimals: Adding, subtracting, multiplying, and dividing fractions and decimals.
- Convert fractions to decimals: Converting fractions that can be converted to terminating decimals to their decimal equivalent form.
- Convert decimals to fractions: Converting terminating decimals to fractions in simplest form.
- Multiplying/Dividing decimals by powers of 10: Multiplying and dividing decimal numbers by powers of ten.
- Multiplying/Dividing decimals by whole numbers: Methods for performing these operations.
- Solving problems related to decimals: Applying decimal concepts in word problems.
- Example Question (Converting 0.04 to a fraction): Converting decimal numbers to fractions. The answer is 1/25.
- Basic Equation Calculation: Solving simple linear equations of the form ax + b = c.
Chapter 2: Statistics and Data Analysis - Ratio, Proportions, and Rates
- Calculating total quantity given ratio and value of one term: Calculations involving ratios.
- Calculate values of remaining terms: Calculating unknowns associated with ratios.
- Proportions and Rates: Key differences and relationships between proportions and rates. Proportions involve numbers of same units, rates involve different units.
- Sample Question (Ratio of red fish to blue fish): Solving problems involving ratios and a given value of a term.
Percentages
- Understanding Percentage: Definition, symbol (%), conversion to percentage from fractions and decimal numbers.
- Reverse Percentages: Solving problems involving reverse percentages.
- Sample Question (Discounted shirt): Calculating the new price of a shirt given a discount percentage.
Interpreting Graphs
- Interpreting Relationships from Graphs: Using graphs to find relationships and solve problems based on the coordinates.
Handling Data
- Units of Time: Identifying units of time (seconds, minutes, hours, days, months).
- Leap Years: Introduction to leap years.
- Conversion of Time Units: Converting between different units of time.
- Operations with Time: Adding and subtracting time in various units.
- Sample Question (Converting minutes into hours): Converting given time in minutes to hours.
Chapter 3: Geometry
- Basic Geometric Terms: Understanding fundamentals like the parts of a circle and triangles inside.
- Circles: Calculating the area of circles.
- Polygons: Understanding interior, exterior, and central angles in polygons.
- Regular polygons: Calculating internal angles of regular polygons.
- Triangles: Working with triangles including characteristics, similarities and areas.
- Area of 2D shapes: Calculating areas of squares, rectangles, parallelograms, and more.
- Sample Questions (Finding the value of X based on an angle): Finding unknown measurements in geometrical figures.
- Sample Question (Calculating the area of a triangle): Calculating areas of geometric figures.
Chapter 4: Advanced Mathematics
- Slopes and Equations of Lines: Finding slopes of lines, understanding the shape of the line based on the graph.
- Characteristics of Quadratic and Exponential Functions: Understanding properties of quadratic and exponential functions, and determining growth/decay.
- Sample Questions (Involving Slopes of Lines): Calculating slopes of lines and applying this to problems.
- Sample Questions (Finding the area of a trapezoid): Demonstrating how to calculate areas of commonly encountered 2D shapes.
- Sample Questions (Finding the volume of a prism): Calculations involving the volume of 3D shapes.
- Interpolation Formula: Using interpolation to estimate values based on known data points.
- Pythagorean Theorem: Identifying and calculating sides of right-angled triangles.
- Trigonometry in right triangles: Calculating trigonometric ratios and using them to solve problems involving sides and angles.
- Sample Questions (Cos X): Calculations involving cosine and finding angles.
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Description
Test your knowledge on performing operations with signed numbers, simplifying numerical expressions, and understanding the order of operations in this quiz focused on mental maths. You will also explore powers and roots, squaring numbers, and identifying perfect squares.
