A- Level Maths : Pure (Paper 1)

Name: A- Level Maths : Pure (Paper 1)
Rating: 4.4 (3 reviews)

Master A-level maths (first year)

Created bySandeep Kumar Mathur

Last updated 7/2026

English

English [Auto],

What you'll learn

Solving inequations
Knowledge of Functions
Coordinate Geometry
Problems related to above topics

Course content

8 sections • 64 lectures • 5h 40m total length

Introduction27:55
Review the standard form and roots of a quadratic equation. Outline solving methods, including factorization, completing the square, and the quadratic formula, noting a quadratic has at most two roots.
Example-11:40
Solve two quadratic equations with imaginary roots. Derive x = ± i√2 from x^2+2=0 and x = ± i√(5/2) from x^2 = -5/4.
Example-26:03
Apply the quadratic formula to solve ax^2+bx+c=0, finding roots 4 and -3 for x^2−x−12=0 and (-3±√2)/5 for 25x^2+30x+7=0.
Example-35:58
Learn to solve quadratic equations with the quadratic formula, using examples that yield roots sqrt(3) and 1/√3, and 5/3 and 3/5.
Example-41:40
example-4 demonstrates solving two quadratic equations with the quadratic formula, teaching discriminants and the emergence of complex roots, namely (-1 ± i√3)/2 and (1 ± i√7)/2.
Example-51:39
Apply the quadratic formula to solve two equations: first with a=1, b=3, c=5, yielding roots (-3 ± i√11)/2; second with a=2, b=1, c=1, yielding roots (-1 ± i√7)/4.
Example-62:08
Demonstrate solving equations with the quadratic formula by identifying a, b, c and computing the discriminant, yielding complex roots with iota in two examples.
Example-74:55
Identify a, b, c from the standard form and use the quadratic formula to find real or complex roots; the example demonstrates with 21x^2-28x+10=0 and 2x^2-4x+3=0.
Example-81:57
Compute the roots of x^2 - 7x + 12 = 0 using the quadratic formula. Determine p = -7 and q = 12, yielding roots 4 and 3.
Example-95:04
Solve a quadratic by setting one part as x and the other as 39 minus x to produce 338, using the quadratic formula to obtain x = 13 or 26.
Example-103:48
Let one number be x and the other be 9 − x, then use the sum of squares to form a quadratic whose roots are 5 and 4.
Example-115:39
This example uses algebra to find two consecutive positive even integers whose squares sum to 340, by setting them as 2x and 2x+2 and solving for x and verifying.
Example-124:32
Determine the two-digit number that equals four times the sum and three times the product of its digits, and find that the number is 24.
Example-136:36
Apply pythagoras theorem to a right triangle with hypotenuse 17 cm and a side difference of 7 cm to determine the legs as 8 cm and 15 cm.
Example-146:08
Solve a rectangle problem where the original length is twice the width; after adding four to the length and subtracting three from the width, the area is 600 square meters.
Example-157:30
A rectangular garden of 10 by 16 meters is bordered by a uniform-width concrete walk whose area is 120 square meters; solving (16+2x)(10+2x)-160=120 yields x=2 meters.
Example-167:05
Set up present ages x and y, form equations from two years ago and in three years, solve the quadratic, and find father's age 29 and son's age 5.
Equations reducible to Quadratic Form3:11
Explore equations reducible to quadratic form by simplifying through addition, squaring, and solving fractional parts. Beware extraneous roots from squaring, and verify each candidate against the original equation.
Example-15:06
derive a quadratic from the rational equation and solve x^2 - 4x - 8 = 0 to obtain roots x = 2 ± 2√3.
Example-25:30
Solve a rational equation by rewriting fractions as simpler forms, cross-multiplying, and solving for x, yielding x equals 9/2.
Example-35:20
Solve the equation a/(x+1) + b/(bx+1) = a + b for x, with a ≠ 0, b ≠ 0, and a + b ≠ 0, yielding roots x = 0 and x = (b^2 - a^2)/(ab(a + b)).
Example-43:48
Rewrite the equation as 256y^2 - 32y + 1 = 0 with y = 2^x, then solve the quadratic to get y = 1/16. Conclude 2^x = 1/16, so x = -4.
Example-54:31
Let y = x^2 - 5x to get y^2 - 30y - 216 = 0, solve by factorization or quadratic formula, and find x = 9, -4, 3, 2.
Example-67:33
Set y = x^2+5x and solve y^2+10y-96=0 to get y=6 or y=-16. Then x^2+5x-6=0 gives x=-6 or 1; x^2+5x+16=0 yields complex roots.
Example-72:18
Let y be x^(1/3). Then x^(2/3) + x^(1/3) = 2 becomes y^2 + y - 2 = 0, factor to (y+2)(y-1) = 0, giving x = -8 or 1.
Example-84:11
Solve a quadratic from the equation involving square roots and reciprocal expressions, derive y from sqrt(x/(x+3)), solve 8y^2-2y-1=0, obtain y=1/2, back-substitute to x=1, discarding extraneous roots.
Example-94:09
solve an equation with nested square roots by rationalizing the denominator and simplifying to obtain x equals plus or minus a.
Example-103:22
Square both sides to remove the square root and solve the resulting quadratic. Check each candidate in the original equation to identify extraneous roots; here only x=4 satisfies.

Basic Concepts1:40
Explore solution sets for quadratic inequations of f(x)=ax^2+bx+c with real a, b, c, and analyze inequalities f(x)≥0, f(x)≤0, f(x)>0, f(x)<0 with illustrations.
Example-16:37
solve the inequality 2x^2 + x - 15 >= 0 by factoring into (2x - 5)(x + 3) >= 0. derive solution sets: x <= -3 or x >= 5/2.
Example-23:46
Factor the inequality after flipping the sign to get (x-1)(x-2) < 0, and determine the solution is x in the interval (1,2).
Example-34:17
Solve x^2 - 9 >= 0 by factoring as (2x+3)(2x-3) and applying sign analysis, yielding x <= -3/2 or x >= 3/2.

Arithmetic Progressions10:07
learn about arithmetic progressions, where consecutive terms differ by a constant d. apply the general term a_n = a + (n-1)d and the end-term form a + (m-n)d.
Example-12:40
Demonstrates that the sequence a_n defined as 4n+5 forms an arithmetic progression with a common difference of 4, and lists the first four terms as 9, 13, 17, 21.
Example-25:25
Demonstrate that the sequence defined by terms like log(a) and log(a^2/b), log(a^3/b^2), … forms an arithmetic progression with common difference log(a/b).
Example-34:10
This example proves the given sequence is an arithmetic progression with common difference three, computes the 16th term as 54, and derives the general term a_n = 3n + 6.
Example-42:55
Solve for n in the arithmetic progression 4, 9, 14, 19 to show 124 is the nth term using a_n = a + (n-1)d, yielding 124 as the 25th term.
Example-52:42
Identify the sequence as an arithmetic progression with first term 3 and difference 3, then find 37 terms using the last term 111.
Example-64:09
Examine whether 184 belongs to the arithmetic sequence 3, 7, 11 with difference 4 by solving a_n equals 184; n is not an integer, so 184 is not a term.
Example-75:33
Identify this arithmetic progression with first term eight minus six iota and common difference minus one plus two iota, yielding fourth term purely real and ninth term purely imaginary.
Example-88:34
Demonstrates proving two AP identities by using first term A, common difference D, and nth term formulas for pth, qth, and rth terms, simplifying and canceling terms to yield zero.
Example-96:14
Let m a_m = n a_n in an arithmetic progression with first term a and difference d, m ≠ n. Then a + (m+n−1)d = 0.
Example-104:00
Analyze an arithmetic progression where the nth term is 1/n and the nth term is 1/m, derive the first term and common difference, and show the mth term equals 1.
Basic concepts of A.G.P.18:30
Explore arithmetico-geometric progression (agp): combine AP and GP, derive t_n = (a+(n−1)d) r^(n−1), and find sums to n terms and to infinity when |r|<1.

Some Special Sequences6:50
Learn formulas for the sum of the first n natural numbers, their squares and cubes, using sigma notation and the method of difference.
Example-11:34
Compute the sum of the even-square series by setting t_n = (2n)^2 = 4n^2, applying the sum of squares formula, and deriving S_n = (2/3) n(n+1)(2n+1).
Example-25:59
Find the sum to n terms of the series with general term t_n = n(n+1)(n+2), i.e., one into two into three, using sigma notation to obtain s_n = n(n+1)(n+2)/4.
Example-36:33
Derive the sum of the series 1×2^2 + 2×3^2 + ... using t_n = n(n+1)^2 and standard sums to obtain S_n = n(n+1)(n+2)(3n+5)/12.
Example-45:37
Sum the series where each term is the product of two arithmetic progressions, yielding the nth term 3n times (3n+5) and the sum S_n = 3 n(n+1)(n+3).
Example-53:01
Compute s_n for the series with nth term n^2 + 2^n by splitting into sums: n(n+1)(2n+1)/6 for squares and 2(2^n-1) for powers; hence s_n = n(n+1)(2n+1)/6 + 2(2^n-1).

Inverse Function4:18
Explore inverse functions and define them with f(g(x))=x and g(f(x))=x, using examples like f(x)=x^2 and g(x)=sqrt(x), plus log x and exp as inverses.
Example-12:31
Learn how to find the inverse of f(x)=1/(1-x) by setting y=f(x), solving for x in terms of y, and substituting back to get f inverse x equals (x-1)/x.
Example-21:12
Learn how to find the inverse of a linear function f(x)=2x-3 by solving for x, applying cross multiplication, and replacing y with x to obtain f inverse x.
Example-31:16
apply the inverse function definition to solve f x = 9, which yields x^2 + 5x = 0 and gives f inverse nine as {0, -5}.
Example-42:25
Compute the inverse function by reversing the mapping of f(x)=3x from a to b, yielding f inverse: 0→0, -3→-1, -9→-3, 6→2.

Basic Concepts10:23
Explore the meaning of an angle, the sense of rotation, and how angles are measured across sexagesimal, centesimal, and circular systems, including right angles and radian definitions.
Theorems Related with Circular System10:20
Explains how a radian is a constant angle defined by arc length equal to the radius, and that central angles in radians equal arc length divided by the radius.
Relation between the Three Systems of Measurement3:25
Relate degrees, grades, and radians with 90 equal to 100 and pi/2, via d/90 = g/100 = 2r/pi, and note 30 per hour and 6 per minute.

Example-14:37
Example-24:22
Example3:50
Demonstrate that three lines are concurrent by solving two lines and checking the third, obtaining the common point of intersection (2, -4).
Example2:47
Find a line parallel to the given line 3x - 2y + 5 = 0 through (5, -6) using ax + by + λ = 0, yielding 3x - 2y - 27 = 0.
Example2:36
Find the equation of a line perpendicular to 3x+2y+5=0 that passes through (3,4) using the ax+by+c=0 form; substitute the point to solve for lambda and obtain 2x-3y+6=0.

Requirements

Elementary knowledge of Math

Description

A-Level Pure Mathematics Paper 1: Core Topics

This course provides a focused and comprehensive review of essential topics for A-Level Pure Mathematics Paper 1. We'll dive deep into Quadratic Inequations, equipping you with the skills to solve and interpret inequalities involving quadratic expressions.

Next, you'll master Coordinate Geometry, exploring lines, circles, and other fundamental geometric concepts within the coordinate plane. Finally, we'll thoroughly cover Functions, including their properties, transformations, and applications.

To ensure a solid understanding, numerous worked examples are integrated throughout the course, illustrating key concepts and problem-solving techniques. This structured approach aims to build your confidence and proficiency, preparing you thoroughly for your Pure Mathematics Paper 1 examination.

More topics will be added after feedback from the students.

We're confident that by actively engaging with the course material, participating in discussions, and taking advantage of the resources available, you'll gain a solid foundation in A level pure maths Paper.. We wish you all the best in your academic journey!

We understand that learning can be challenging at times. That's why we encourage you to actively participate and ask questions! We have a dedicated Q&A forum where you can seek clarification and share your doubts with your instructor. Don't hesitate to ask for help – we're here to support your learning journey every step of the way.

Who this course is for:

Students taking (or planning to take) A-level maths.

A- Level Maths : Pure (Paper 1)

What you'll learn

Explore related topics

Course content

Quadratic Equations28 lectures • 2hr 29min

Quadratic Inequations4 lectures • 16min

Sequence and Series12 lectures • 1hr 15min

Some Special Sequences6 lectures • 30min

Functions5 lectures • 12min

Measurement of Angles3 lectures • 24min

Coordinate Geometry5 lectures • 18min

Differential Calculus1 lecture • 16min

Requirements

Description

Who this course is for: