Knowt

0.0(0)

Generate Practice test

Chat with Kai

undefined Flashcards

0 Cards0.0(0)

math f edxcel

Here's a set of flashcards based on the detailed breakdown of topics in each area of the syllabus you've provided:

Number 1: Number, Structure, and Calculation

Flashcard 1: Ordering Numbers

Question:
How do you order positive and negative integers, decimals, and fractions?

Answer:
Use symbols like =, ≠, <, >, ≤, ≥ to compare and order numbers.
Example:

3.5 > -2
-5 < -3

Flashcard 2: Place Value

Question:
How do you use place value when working with decimals and large numbers?

Answer:
Recognize each digit's position in a number.
Example:

3.547 → 3 is in the ones place, 5 is in the tenths place, 4 is in the hundredths place.

Flashcard 3: Operations with Integers

Question:
How do you apply addition and subtraction to integers?

Answer:
Add and subtract integers by considering their signs.
Example:

5 + (-3) = 2
-4 - 6 = -10

Flashcard 4: Operations with Decimals

Question:
How do you multiply and divide decimals?

Answer:
Adjust decimal places for multiplication and division.
Example:

0.6 × 0.2 = 0.12
0.75 ÷ 0.25 = 3

Flashcard 5: Working with Fractions

Question:
How do you add and subtract fractions?

Answer:
Find a common denominator.
Example:

1/2 + 1/3 = 5/6
3/4 - 1/2 = 1/4

Flashcard 6: Negative Fractions

Question:
How do you calculate with negative fractions?

Answer:
Apply the same rules for fractions, keeping track of the signs.
Example:

-1/2 + 3/4 = 1/4
-3/4 × -1/2 = 3/8

Flashcard 7: Fractions and Mixed Numbers

Question:
How do you add and subtract mixed numbers?

Answer:
Convert mixed numbers into improper fractions.
Example:

2 1/3 + 1 2/3 = 4
3 1/2 - 1 1/4 = 2 1/4

Flashcard 8: Using Prime Factorization

Question:
What is prime factorization, and how do you find it?

Answer:
Prime factorization involves breaking a number down into its prime factors.
Example:

18 = 2 × 3 × 3

Flashcard 9: Highest Common Factor (HCF)

Question:
How do you find the highest common factor (HCF)?

Answer:
Find the largest factor common to both numbers.
Example:

HCF of 12 and 18 = 6

Flashcard 10: Lowest Common Multiple (LCM)

Question:
How do you find the lowest common multiple (LCM)?

Answer:
Find the smallest multiple common to both numbers.
Example:

LCM of 4 and 5 = 20

Flashcard 11: Inverse Operations

Question:
How do you use inverse operations?

Answer:
Inverse operations reverse the effect of the original operation.
Example:

The inverse of addition is subtraction (5 + 3 = 8, 8 - 3 = 5).

Flashcard 12: Powers and Roots

Question:
How do you use powers and roots?

Answer:
Powers involve multiplying a number by itself, and roots reverse this process.
Example:

2² = 4
√16 = 4

Flashcard 13: Standard Form

Question:
How do you use standard form for very large or small numbers?

Answer:
Express numbers as a × 10ⁿ, where 1 ≤ a < 10.
Example:

5,000 = 5 × 10³
0.00025 = 2.5 × 10⁻⁴

Flashcard 14: Calculations with π

Question:
How do you calculate with multiples of π?

Answer:
Use the approximation π ≈ 3.14 or the exact value when needed.
Example:

Area of a circle with radius 3: A = πr² = 3.14 × 3² ≈ 28.26

Flashcard 15: Roots and Integer Indices

Question:
How do you calculate using roots and integer indices?

Answer:
Apply the index rules for powers and roots.
Example:

3³ = 27
√9 = 3

Flashcard 16: Relationships Between Operations

Question:
How do you recognize and use relationships between operations?

Answer:
Use inverse operations and order of operations to simplify expressions.
Example:

2 × (3 + 5) = 16
(3 + 5) × 2 = 16

Number 2: Algebra

Flashcard 1: Algebraic Notation

Question:
How do you interpret algebraic notation?

Answer:
Understand how multiplication, powers, and division are represented algebraically.
Example:

ab means a × b
3y means y + y + y
a² means a × a

Flashcard 2: Substitution

Question:
How do you substitute values into an expression?

Answer:
Replace variables with given values and simplify.
Example:

If x = 2, substitute into 3x + 4: 3(2) + 4 = 10.

Flashcard 3: Simplifying Expressions

Question:
How do you simplify algebraic expressions?

Answer:
Combine like terms and apply the distributive property.
Example:

3x + 4x = 7x
5(2x + 3) = 10x + 15

Flashcard 4: Solving Equations

Question:
How do you solve simple linear equations?

Answer:
Isolate the variable on one side.
Example:

Solve 2x + 3 = 7:
2x = 4 → x = 2

Flashcard 5: Expanding Brackets

Question:
How do you expand brackets in algebra?

Answer:
Multiply the term outside the bracket by each term inside.
Example:

3(x + 2) = 3x + 6

Flashcard 6: Factorising Quadratics

Question:
How do you factorise a quadratic expression?

Answer:
Find two numbers that multiply to give the constant and add to give the middle term.
Example:

x² + 5x + 6 = (x + 2)(x + 3)

Flashcard 7: Solving Simultaneous Equations

Question:
How do you solve simultaneous equations?

Answer:
Use substitution or elimination to find the solution.
Example:

Solve x + y = 10 and x - y = 4:
x = 7, y = 3

Flashcard 8: Rearranging Formulae

Question:
How do you rearrange a formula to make a different variable the subject?

Answer:
Move terms around using inverse operations.
Example:

Rearrange A = πr² to make r the subject:
r = √(A/π)

Flashcard 9: Working with Functions

Question:
How do you interpret expressions as functions?

Answer:
Treat the expression as a rule for input and output.
Example:

f(x) = 2x + 3, if x = 4, then f(4) = 2(4) + 3 = 11.

Flashcard 10: Quadratic Graphs

Question:
What are the features of quadratic graphs?

Answer:
Quadratic graphs are parabolas with a vertex and axis of symmetry.
Example:

y = x²: Vertex at (0,0), axis of symmetry x = 0.

Flashcard 11: Graphing Linear Functions

Question:
How do you graph linear equations?

Answer:
Plot points using the equation y = mx + c, where m is the gradient and c is the y-intercept.
Example:

y = 2x + 1: Plot points (0,1), (1,3), etc.

Flashcard 12: Gradient of a Line

Question:
What is the gradient of a line, and how is it found?

Answer:
The gradient is the slope of the line, calculated by the formula (change in y) / (change in x).
Example:

Line through (0, 1) and (2, 5): Gradient = (5 - 1) / (2 - 0) = 2

Flashcard 13: Roots of Quadratics

Question:
How do you find the roots of a quadratic equation?

Answer:
Use factorisation, completing the square, or the quadratic formula.
Example:

x² - 5x + 6 = 0: Roots are x = 2 and x = 3.

Flashcard 14: Interpreting Inequalities

Question:
How do you solve and represent inequalities?

Answer:
Isolate the variable and represent the solution on a number line.
Example:

Solve 2x + 1 < 5: x < 2

Flashcard 15: Working with Expressions

Question:
How do you simplify algebraic expressions?

Answer:
Combine like terms and apply distributive properties.
Example:

3x +

4x - 2 = 5x - 2

Flashcard 16: Using Indices

Question:
How do you simplify expressions with indices?

Answer:
Apply index rules (multiplying, dividing, and raising powers).
Example:

x² × x³ = x⁵
(x⁴)² = x⁸

Flashcard 17: Algebraic Fractions

Question:
How do you simplify algebraic fractions?

Answer:
Factorize and cancel common terms.
Example:

(x² + 2x) / x = x + 2

Flashcard 18: Factorising Algebraic Expressions

Question:
How do you factorise algebraic expressions?

Answer:
Look for common factors and apply factorisation methods.
Example:

3x² + 6x = 3x(x + 2)

Flashcard 19: Quadratic Inequalities

Question:
How do you solve quadratic inequalities?

Answer:
Factorize and solve the inequality.
Example:

Solve x² - 5x + 6 > 0.

Flashcard 20: Algebraic Fractions with Different Denominators

Question:
How do you add or subtract algebraic fractions with different denominators?

Answer:
Find the common denominator and then simplify.
Example:

(x/2) + (y/3) = (3x + 2y)/6

Flashcard 21: Cubic Equations

Question:
How do you solve cubic equations?

Answer:
Factor or use numerical methods to find the roots.
Example:

Solve x³ - 3x² = 0: Roots are x = 0 and x = 3.

Flashcard 22: Simultaneous Non-Linear Equations

Question:
How do you solve simultaneous non-linear equations?

Answer:
Use substitution or graphical methods.
Example:

Solve y = x² and y = 4x.

Flashcard 23: Solving Equations with Fractions

Question:
How do you solve equations with fractions?

Answer:
Multiply both sides by the denominator to eliminate fractions.
Example:

Solve 2/x = 4. Multiply both sides by x.

Flashcard 24: Formulae and Substitution

Question:
How do you work with formulae and substitute values?

Answer:
Replace variables with their values and simplify.
Example:

Given A = πr², if r = 4, find A.

Flashcard 25: Completing the Square

Question:
How do you complete the square for a quadratic expression?

Answer:
Rewrite the quadratic expression as a perfect square.
Example:

x² + 6x + 9 = (x + 3)²

Number 3: Ratio, Proportion, and Rates of Change

Flashcard 1: Understanding Ratio

Question:
How do you express and simplify ratios?

Answer:
Write ratios in the form of a:b and simplify by dividing by the greatest common factor.
Example:

6:9 = 2:3.

Flashcard 2: Ratio as a Fraction

Question:
How do you convert a ratio to a fraction?

Answer:
Express the ratio as a fraction of two numbers.
Example:

3:4 = 3/4.

Flashcard 3: Dividing in a Given Ratio

Question:
How do you divide a quantity in a given ratio?

Answer:
Find the total parts of the ratio and divide the quantity accordingly.
Example:

Divide 40 in the ratio 2:3. Total parts = 2 + 3 = 5, so each part = 40 ÷ 5 = 8.
2 parts = 16, 3 parts = 24.

Flashcard 4: Proportion and Scaling

Question:
How do you solve problems involving direct and inverse proportion?

Answer:
Use the formula y = kx for direct proportion, and y = k/x for inverse proportion.
Example:

If y is directly proportional to x, and when x = 2, y = 6, find y when x = 4:
y = 6 * 4 / 2 = 12.

Flashcard 5: Solving Proportions

Question:
How do you solve proportions?

Answer:
Set up a proportion as a fraction and solve for the unknown.
Example:

If 2/x = 4/5, then x = (2 * 5) / 4 = 2.5.

Flashcard 6: Rates of Change

Question:
How do you calculate rates of change?

Answer:
Rate of change is calculated as the difference in values divided by the change in time or distance.
Example:

If a car travels 100 miles in 2 hours, the rate of change (speed) is 100 ÷ 2 = 50 miles per hour.

Flashcard 7: Scaling Factors

Question:
What is the scaling factor in enlargement?

Answer:
The scaling factor is the ratio of the new size to the original size.
Example:

If a shape is enlarged by a factor of 2, every dimension is doubled.

Flashcard 8: Percentage Increase and Decrease

Question:
How do you calculate percentage increase and decrease?

Answer:
Use the formula:
Percentage Change = (Change ÷ Original Value) × 100.
Example:

Percentage increase from 50 to 60: ((60 - 50) ÷ 50) × 100 = 20%.

Flashcard 9: Percentage of an Amount

Question:
How do you find a percentage of an amount?

Answer:
Multiply the amount by the percentage expressed as a decimal.
Example:

20% of 150 = 150 × 0.20 = 30.

Flashcard 10: Compound Interest

Question:
How do you calculate compound interest?

Answer:
Use the formula A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the interest rate, n is the number of times interest is compounded, and t is the time.
Example:

If $100 is invested at an interest rate of 5% compounded annually for 3 years:
A = 100(1 + 0.05/1)^(1*3) = 100(1.05)³ = 115.76.

Flashcard 11: Simple Interest

Question:
How do you calculate simple interest?

Answer:
Use the formula:
Interest = Principal × Rate × Time.
Example:

If you invest $200 at 4% for 2 years, the interest is 200 × 0.04 × 2 = $16.

Flashcard 12: Working with Compound Proportions

Question:
How do you solve compound proportion problems?

Answer:
Set up the proportional relationship between different variables.
Example:

If 5 oranges cost $2, how much do 12 oranges cost?
(5/2) = (12/x), so x = 2.4 dollars.

Flashcard 13: Understanding Direct Proportion

Question:
What is direct proportion?

Answer:
Direct proportion means that as one quantity increases, the other increases at the same rate.
Example:

If 1 apple costs $1, 3 apples cost $3.

Flashcard 14: Understanding Inverse Proportion

Question:
What is inverse proportion?

Answer:
Inverse proportion means that as one quantity increases, the other decreases at the same rate.
Example:

If a worker completes a task in 5 hours, then 2 workers would complete the same task in 2.5 hours.

Flashcard 15: Ratio and Proportion in Recipes

Question:
How do you adjust recipes using ratios?

Answer:
Multiply or divide the ingredients by the same factor to maintain the ratio.
Example:

If a recipe calls for 2 cups of flour for 4 servings, for 8 servings, use 4 cups of flour.

Flashcard 16: Percentage Change Over Time

Question:
How do you calculate percentage change over time?

Answer:
Use the formula:
Percentage Change = ((New Value - Old Value) ÷ Old Value) × 100.
Example:

The price of a product increases from $50 to $60:
((60 - 50) ÷ 50) × 100 = 20%.

Flashcard 17: Scaling in Similar Shapes

Question:
How do you find the scaling factor of similar shapes?

Answer:
The scaling factor is the ratio of corresponding sides of two similar shapes.
Example:

If the side of a small square is 2 cm and the side of a larger square is 4 cm, the scaling factor is 4 ÷ 2 = 2.

Flashcard 18: Speed, Distance, and Time

Question:
How do you calculate speed, distance, and time?

Answer:
Use the formula:
Speed = Distance ÷ Time.
Example:

If a car travels 120 miles in 3 hours, speed = 120 ÷ 3 = 40 mph.

Flashcard 19: Converting Units of Measurement

Question:
How do you convert between different units of measurement?

Answer:
Use conversion factors.
Example:

To convert 5 kilometers to meters, multiply by 1,000 (5 × 1,000 = 5,000 meters).

Flashcard 20: Rate of Work

Question:
How do you calculate the rate of work?

Answer:
Rate of work = Work done ÷ Time taken.
Example:

If a worker completes 40 units of work in 8 hours, rate of work = 40 ÷ 8 = 5 units per hour.

Flashcard 21: Profit and Loss in Business

Question:
How do you calculate profit and loss?

Answer:
Profit = Selling Price - Cost Price, and Loss = Cost Price - Selling Price.
Example:

If you bought a book for $10 and sold it for $15, profit = $15 - $10 = $5.

Flashcard 22: Interest Rate Comparison

Question:
How do you compare different interest rates?

Answer:
Convert different interest rates to a common format, such as annual percentage rate (APR).
Example:

Compare 6% simple interest and 6% compound interest for 3 years to see which gives more return.

Flashcard 23: Currency Exchange Rate

Question:
How do you calculate currency exchange?

Answer:
Multiply the amount by the exchange rate.
Example:

If the exchange rate is 1 USD = 0.85 GBP, then $100 = 100 × 0.85 = 85 GBP.

Flashcard 24: Markup and Discount

Question:
How do you calculate markup and discount?

Answer:
Markup = Selling Price - Cost Price; Discount = Original Price - Sale Price.
Example:

A $50 item with a 20% markup: Markup = 50 × 0.20 = $10, selling price = $50 + $10 = $60.

Flashcard 25: Percentage Off

Question:
How do you calculate a percentage off?

Answer:
Find the amount of the discount by multiplying the original price by the percentage, then subtract it from the original price.
Example:

For a 25% discount on a $200 item: Discount = 200 × 0.25 = $50, sale price = $200 - $50 = $150.

Number 4: Proportions, Percentages, and Probability

Flashcard 1: Probability Basics

Question:
What is probability?

Answer:
Probability is the likelihood of an event occurring, expressed as a ratio or fraction between 0 and 1.
Example:

The probability of rolling a 4 on a fair 6-sided die is 1/6.

Flashcard 2: Probability of Independent Events

Question:
How do you find the probability of independent events?

Answer:
Multiply the probabilities of the individual events.
Example:

The probability of rolling a 3 on a die (1/6) and flipping a coin and getting heads (1/2) is:
(1/6) × (1/2) = 1/12.

Flashcard 3: Probability of Dependent Events

Question:
How do you calculate the probability of dependent events?

Answer:
Multiply the probability of the first event by the conditional probability of the second event.
Example:

If you draw a red card from a deck and do not replace it, the probability of drawing a second red card changes.

Flashcard 4: Calculating Expected Frequency

Question:
How do you calculate expected frequency in probability?

Answer:
Multiply the probability of an event by the total number of trials.
Example:

If the probability of an event is 0.25 and there are 100 trials, the expected frequency is 0.25 × 100 = 25.

Flashcard 5: Compound Probability

Question:
How do you calculate compound probability?

Answer:
Combine the probabilities of multiple events, depending on whether they are independent or dependent.
Example:

The probability of drawing a red card from a deck and then a black card:
(26/52) × (26/51).

Flashcard 6: Probability of Mutually Exclusive Events

Question:
What is the probability of mutually exclusive events?

Answer:
For mutually exclusive events, add the probabilities.
Example:

The probability of drawing a red or a black card from a deck:
(26/52) + (26/52) = 1.

Flashcard 7: Tree Diagrams

Question:
How do you use tree diagrams for probability?

Answer:
Tree diagrams help represent all possible outcomes of multiple events and their associated probabilities.
Example:

For flipping a coin twice, the outcomes are: HH, HT, TH, TT.

Flashcard 8: Conditional Probability

Question:
What is conditional probability?

Answer:
Conditional probability is the probability of an event occurring given that another event has already occurred.
Example:

Given that it is raining, the probability that the temperature is below freezing.

Flashcard 9: Working with Odds

Question:
How do you calculate odds?

Answer:
Odds are calculated as the ratio of the number of successful outcomes to the number of unsuccessful outcomes.
Example:

Odds of drawing a red card from a deck are 26:26.

Flashcard 10: Using Venn Diagrams

Question:
How do you use Venn diagrams for probability?

Answer:
Venn diagrams visually represent sets and their intersections for probability.
Example:

The probability of drawing a card that is either a heart or a red card.

Flashcard 11: Probability and Ratios

Question:
How do you express probability as a ratio?

Answer:
Probability is the ratio of favorable outcomes to possible outcomes.
Example:

The probability of drawing an Ace from a deck is 4/52 or 1/13.

Flashcard 12: Percentages in Probability

Question:
How do you express probability as a percentage?

Answer:
Multiply the probability by 100.
Example:

If the probability of an event is 0.25, then the percentage is 0.25 × 100 = 25%.

Flashcard 13: Expected Value in Probability

Question:
How do you calculate expected value?

Answer:
Multiply each outcome by its probability and sum the results.
Example:

Expected value for rolling a fair die:
(1/6) × 1 + (1/6) × 2 + ... + (1/6) × 6 = 3.5.

Flashcard 14: Probability of Non-Exclusive Events

Question:
What is the probability of non-exclusive events?

Answer:
For non-exclusive events, subtract the probability of the intersection from the sum of the probabilities.
Example:

P(A or B) = P(A) + P(B) - P(A ∩ B).

Flashcard 15: Probability in Games

Question:
How do you calculate probability in games of chance?

Answer:
Count the favorable outcomes and divide by the total possible outcomes.
Example:

The probability of drawing a red card from a deck of 52 cards is 26/52 = 1/2.

Flashcard 16: Probability with Replacement

Question:
How do you calculate probability with replacement?

Answer:
If an item is replaced after each draw, the probabilities stay the same.
Example:

The probability of drawing a red ball twice from a bag with 5 red balls and 5 blue balls:
(5/10) × (5/10) = 25/100 = 1/4.

Flashcard 17: Probability without Replacement

Question:
How do you calculate probability without replacement?

Answer:
Adjust the total number of items after each draw.
Example:

The probability of drawing two red cards without replacement:
(26/52) × (25/51).

Flashcard 18: Calculating Simple Probabilities

Question:
How do you calculate simple probabilities?

Answer:
Divide the number of favorable outcomes by the total number of possible outcomes.
Example:

The probability of rolling a 3 on a six-sided die is 1/6.

Flashcard 19: Using Probabilities to Make Predictions

Question:
How do you use probability to make predictions?

Answer:
Use the probability of an event to estimate the likelihood of future events.
Example:

The probability of drawing a red card from a deck is 26/52 = 0.5, so you would expect to draw a red card half the time.

Flashcard 20: Compound Probability with AND/OR

Question:
How do you calculate compound probabilities using AND/OR?

Answer:
Use the addition rule for OR and multiplication rule for AND.
Example:

AND: The probability of drawing a red card and then a black card:
(26/52) × (26/51).
OR: The probability of drawing a red or a black card:
(26/52) + (26/52).

Flashcard 21: Expected Outcomes in Games

Question:
How do you use probability to calculate expected outcomes in games?

Answer:
Multiply each outcome by its probability and sum the results.
Example:

In a game where

you win $5 with a probability of 1/10, and lose $2 with a probability of 9/10, the expected value is:
(5 × 1/10) + (-2 × 9/10) = -0.5.

Flashcard 22: Calculating Cumulative Probability

Question:
How do you calculate cumulative probability?

Answer:
Add the probabilities of all favorable outcomes up to a point.
Example:

The probability of rolling a 1, 2, or 3 on a die is:
P(1) + P(2) + P(3) = 1/6 + 1/6 + 1/6 = 1/2.

Flashcard 23: Combining Probabilities

Question:
How do you combine probabilities for multiple events?

Answer:
Add the probabilities for OR and multiply for AND.
Example:

The probability of rolling a 2 or a 3 on a die is:
P(2) + P(3) = 1/6 + 1/6 = 2/6 = 1/3.

Flashcard 24: Probability of Non-Event

Question:
What is the probability of a non-event?

Answer:
The probability of an event not occurring is 1 minus the probability of the event occurring.
Example:

The probability of not rolling a 1 on a die is 1 - 1/6 = 5/6.

Flashcard 25: Probability of Multiple Events

Question:
How do you calculate the probability of multiple events?

Answer:
Use the multiplication rule for independent events or adjust for dependent events.
Example:

The probability of rolling a 3, then a 4 on a fair die is:
(1/6) × (1/6) = 1/36.

Number 5: Algebraic Expressions, Equations, and Inequalities

Flashcard 1: Algebraic Expressions

Question:
What is an algebraic expression?

Answer:
An algebraic expression is a mathematical phrase that includes numbers, variables, and operations (such as addition, subtraction, multiplication, and division).
Example:

2x + 5 is an algebraic expression.

Flashcard 2: Simplifying Algebraic Expressions

Question:
How do you simplify an algebraic expression?

Answer:
Combine like terms by adding or subtracting the coefficients of terms with the same variable.
Example:

Simplify 3x + 4x:
3x + 4x = 7x.

Flashcard 3: Evaluating Algebraic Expressions

Question:
How do you evaluate an algebraic expression?

Answer:
Substitute the given values of variables into the expression and perform the operations.
Example:

If x = 3 in the expression 2x + 5, then:
2(3) + 5 = 6 + 5 = 11.

Flashcard 4: Solving Linear Equations

Question:
How do you solve a linear equation?

Answer:
To solve a linear equation, isolate the variable by performing inverse operations.
Example:

Solve 2x + 3 = 7:
2x = 7 - 3 → 2x = 4 → x = 4/2 → x = 2.

Flashcard 5: Solving Multi-Step Equations

Question:
How do you solve multi-step equations?

Answer:
Perform operations in reverse order: start with parentheses, then exponents, multiplication/division, and lastly, addition/subtraction.
Example:

Solve 3x + 4 = 10:
3x = 10 - 4 → 3x = 6 → x = 6/3 → x = 2.

Flashcard 6: Solving Equations with Fractions

Question:
How do you solve equations with fractions?

Answer:
Multiply both sides of the equation by the denominator to eliminate the fraction.
Example:

Solve 1/2x + 3 = 7:
Multiply both sides by 2:
x + 6 = 14 → x = 14 - 6 → x = 8.

Flashcard 7: Solving Equations with Variables on Both Sides

Question:
How do you solve equations with variables on both sides?

Answer:
Move all the variable terms to one side and constants to the other side.
Example:

Solve 3x + 5 = 2x + 8:
3x - 2x = 8 - 5 → x = 3.

Flashcard 8: Solving Inequalities

Question:
How do you solve inequalities?

Answer:
Treat inequalities like equations but reverse the inequality symbol when multiplying or dividing by a negative number.
Example:

Solve x - 5 < 7:
x < 7 + 5 → x < 12.

Flashcard 9: Graphing Linear Inequalities

Question:
How do you graph linear inequalities?

Answer:
Graph the boundary line as if it were an equation, then shade above or below the line depending on the inequality sign.
Example:

For x + y < 5, graph the line x + y = 5, then shade below the line.

Flashcard 10: Solving Systems of Equations

Question:
How do you solve a system of equations?

Answer:
Use substitution or elimination methods to find the values of the variables that satisfy both equations.
Example:

Solve the system:
2x + y = 10
x - y = 4
Add both equations to eliminate y:
3x = 14 → x = 14/3.
Substitute x = 14/3 into the first equation to find y.

Flashcard 11: Word Problems Involving Equations

Question:
How do you solve word problems using equations?

Answer:
Translate the problem into an equation using variables for unknowns and solve.
Example:

A number is 3 less than twice another number. If the sum of the two numbers is 16, find the numbers.
Let x be the first number and y be the second number.
2x - 3 = y and x + y = 16.
Solve the system of equations.

Flashcard 12: Inequalities Word Problems

Question:
How do you solve word problems with inequalities?

Answer:
Translate the problem into an inequality and solve.
Example:

A store sells T-shirts for $15 each. You want to spend no more than $60. How many T-shirts can you buy?
15x ≤ 60 → x ≤ 4.

Flashcard 13: Absolute Value Equations

Question:
How do you solve absolute value equations?

Answer:
Set up two cases: one for the positive value and one for the negative value of the expression inside the absolute value.
Example:

Solve |x + 3| = 7:
x + 3 = 7 or x + 3 = -7,
x = 4 or x = -10.

Flashcard 14: Algebraic Expressions with Exponents

Question:
How do you simplify expressions with exponents?

Answer:
Use exponent rules: multiply powers with the same base, divide powers with the same base, and raise a power to a power.
Example:

Simplify x² × x³ = x⁵.

Flashcard 15: Solving Quadratic Equations

Question:
How do you solve quadratic equations?

Answer:
Use factoring, completing the square, or the quadratic formula.
Example:

Solve x² + 6x + 9 = 0:
(x + 3)² = 0 → x = -3.

Flashcard 16: Solving Equations with Exponents

Question:
How do you solve equations involving exponents?

Answer:
Use logarithms or apply exponent rules.
Example:

Solve 2^x = 8:
x = log₂8 = 3.

Number 6: Sequences and Series

Flashcard 1: Arithmetic Sequences

Question:
What is an arithmetic sequence?

Answer:
An arithmetic sequence is a sequence where the difference between consecutive terms is constant.
Example:

2, 5, 8, 11, ... is an arithmetic sequence with a common difference of 3.

Flashcard 2: Finding the nth Term of an Arithmetic Sequence

Question:
How do you find the nth term of an arithmetic sequence?

Answer:
Use the formula:
nth term = a + (n - 1) × d,
where a is the first term, n is the term number, and d is the common difference.
Example:

Find the 5th term of the sequence 3, 7, 11, 15, ...
nth term = 3 + (5 - 1) × 4 = 3 + 16 = 19.

Flashcard 3: Geometric Sequences

Question:
What is a geometric sequence?

Answer:
A geometric sequence is a sequence where each term is found by multiplying the previous term by a constant ratio.
Example:

3, 6, 12, 24, ... is a geometric sequence with a common ratio of 2.

Flashcard 4: Finding the nth Term of a Geometric Sequence

Question:
How do you find the nth term of a geometric sequence?

Answer:
Use the formula:
nth term = a × r^(n - 1),
where a is the first term, r is the common ratio, and n is the term number.
Example:

Find the 4th term of the sequence 5, 10, 20, 40, ...
nth term = 5 × 2^(4 - 1) = 5 × 8 = 40.

Flashcard 5: Sum of an Arithmetic Series

Question:
How do you find the sum of an arithmetic series?

Answer:
Use the formula:
Sum = (n/2) × (a + l),
where n is the number of terms, a is the first term, and l is the last term.
Example:

Find the sum of the first 5 terms of the sequence 2, 5, 8, 11, 14.
Sum = (5/2) × (2 + 14) = 5 × 8 = 40.

Flashcard 6: Sum of a Geometric Series

Question:
How do you find the sum of a geometric series?