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AS LEVEL MATHS EDEXCEL CORE REVISIOIN TEST OF THE YEAR 2024, Exams of Mathematics

AS LEVEL MATHS EDEXCEL CORE REVISIOIN TEST OF THE YEAR 2024

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Available from 06/07/2024

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AS LEVEL MATHS EDEXCEL CORE
REVISIOIN TEST OF THE YEAR
2024
1. Index laws - Correct Answers - if multiplying add the powers
- if dividing subtract the powers
- If powering multiply the powers.
- (ab)^c = a^cb^c
2. am x aⁿ = - Correct Answers a^(men)
3. am ÷ aⁿ = - Correct Answers a^(m-n)
4. (am)ⁿ = - Correct Answers am
5. (ab)ⁿ = - Correct Answers aⁿbⁿ
6. base - Correct Answers number subject to the index
7. index/power/exponent - Correct Answers a small number that tells
how many times something is multiplied (×) by itself
8. To find the product of two expressions - Correct Answers multiply
each term in one expression by each term in the other expression.
9. You can write expression as - Correct Answers a product of their
factors
10. Factorizing - Correct Answers The opposite of expanding
brackets
pf3
pf4
pf5
pf8
pf9
pfa
pfd
pfe
pff
pf12
pf13

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AS LEVEL MATHS EDEXCEL CORE

REVISIOIN TEST OF THE YEAR

  1. Index laws - Correct Answers - if multiplying add the powers
    • if dividing subtract the powers
    • If powering multiply the powers.
    • (ab)^c = a^cb^c
  2. am x aⁿ = - Correct Answers a^(men)
  3. am ÷ aⁿ = - Correct Answers a^(m-n)
  4. (am)ⁿ = - Correct Answers am
  5. (ab)ⁿ = - Correct Answers aⁿbⁿ
  6. base - Correct Answers number subject to the index
  7. index/power/exponent - Correct Answers a small number that tells how many times something is multiplied (×) by itself
  8. To find the product of two expressions - Correct Answers multiply each term in one expression by each term in the other expression.
  9. You can write expression as - Correct Answers a product of their factors
  10. Factorizing - Correct Answers The opposite of expanding brackets
  1. Quadratic expression form - Correct Answers ax² + box + c where a, b and c are real numbers and a ≠ 0.
  2. Difference of two squares. - Correct Answers x² - y² = (x + y)(x
    • y)
  3. Rational numbers - Correct Answers Those that can be written as a/b where a and b are integers
  4. a^1/m = - Correct Answers ^mea
  5. an/m = - Correct Answers ^meaⁿ
  6. a^-m = - Correct Answers 1/am
  7. a ⁰ = - Correct Answers 1
  8. If n is an integer that is not a square, then √n is a - Correct Answers surd
  9. Irrational numbers example - Correct Answers Surds
  10. Irrational numbers - Correct Answers cannot be written in the form a/b where a and b are both integers.
  11. √ab = - Correct Answers √a x √b
  12. √a/b = - Correct Answers √a / √b
  13. If a fraction has a surd in the denominator - Correct Answers rearrange it so the denominator is a rational number.
  14. Rules to rationalize denominators: 1/√a - Correct Answers multiple the numerator and denominator by √a
  15. Rules to rationalize denominators: 1/(a+√b) - Correct Answers multiple the numerator and denominator by a-√b
  16. Rules to rationalize denominators: 1/(a-√b) - Correct Answers multiply the numerator and denominator by a+√b
  1. roots of a function - Correct Answers values of x for which f(x) = 0
  2. Find the coordinates of the turning point of a quadratic graph. - Correct Answers complete the square. If f(x) = a(pop)² + q, the graph of y = f(x) has a turning point at (-iPAQ)
  3. The discriminant - Correct Answers b²-4ac
  4. The value of the discriminant shows how many - Correct Answers roots f(x) has
  5. If b²-4ac > 0 then - Correct Answers f(x) has two distinct real roots.
  6. If b² - 4ac = 0 then - Correct Answers f(x) has one repeated root
  7. If b² - 4ac < 0 then - Correct Answers f(x) has no real roots.
  8. Mathematical model - Correct Answers mathematical description of a real-life situation.
  9. Linear simultaneous equations - Correct Answers have one set of values that will make a pair of equations true at the same time.
  10. Quadratic simultaneous equations - Correct Answers Simultaneous equations with one linear and one quadratic equation can have up to two pairs of solutions. You need to make sure the solutions are paired correctly.
  11. To solve linear simultaneous equations - Correct Answers Use elimination or substitution.
  12. The solutions to a pair of simultaneous equations represent - Correct Answers the points of intersection of their graphs
  13. On a graph, the discriminant - Correct Answers determines the number of points of intersection.
  1. Find the midpoint - Correct Answers (x1+x2/2, y1+y2/2)
  2. Perpendicular line rules - Correct Answers - The perpendicular bisector of a line segment AB is the straight line that is perpendicular to AB and passes through the midpoint of AB.
    • If the gradient of AB is m, the the gradient of its perpendicular bisector will be -1/m
  3. Equation of a circle with center (0,0) - Correct Answers x² + y² = r²
  4. Equation of a circle with center (am) - Correct Answers (x-a)²
    • (y-b)² = r²
  5. Equation of a circle with f and g - Correct Answers x² + y² + 2fx + 2gy + c = 0
    • The circle has center (-f,-g) and radius √(f² + g² - c)
    • If you need to find the center and radius of a circle with an equation given in an expanded form it is usually safest to complete the square for x and y terms
  6. Intersections of straight lines and circles - Correct Answers - A straight line can intersect a circle once, by just touching the circle, or twice.
    • Not all straight lines will intersect a given circle
  7. Tangent - Correct Answers a tangent to a circle is perpendicular to the radius of the circle at the point of intersection.
  8. Perpendicular bisector of a chord will... - Correct Answers go through the center of a circle
  9. Derivative notations - Correct Answers y = f(x) is written as f'(x) or die/dx
  10. f'(x) = - Correct Answers lime h->0 (f(x + h) - f(x)/h)
  11. The gradient of a curve is - Correct Answers constantly changing
    1. By substituting points either side of the SP into the gradient function (f'(x))
    1. Deduce the shape of the curve from a sketch of the values produced.
  1. This method is useful if the second derivative, f''(x) is equal to 0 at the stationary point.
  2. Integration - Correct Answers The reverse process of differentiating
  3. To integrate you - Correct Answers increase the power by one and divide by the new power
  4. In all integrations you need to add a - Correct Answers constant of integration (c).
  5. You can calculate an integral between two - Correct Answers limits
  6. An integral between two limits is called a - Correct Answers definite integral
  7. A definite integral usually produces a - Correct Answers value
  8. an indefinite integral always produces a - Correct Answers function
  9. If an area is bound ... the x axis the value you get from a definite integral will be negative - Correct Answers below
  10. Set of solution of an inequality - Correct Answers the set of all real number x that make the inequality true.
  11. To solve a quadratic inequality - Correct Answers - Rearrange so that the right hand side of the inequality is 0.
    • Solve the corresponding quadratic equation to find the critical values.
    • Sketch the graph of the quadratic function.
    • Use your sketch to find the required set of values.
  1. Graph f(x) < g(x) - Correct Answers The values of x for which the curve y=f(x) is below the curve y=g(x)
  2. Graph f(x) > g(x) - Correct Answers The curve y=f(x) is above the curve y=g(x)
  3. Graph y<f(x) region - Correct Answers the points on the coordinate grid below the curve y=f(x)
  4. Graph y>f(x) region - Correct Answers points on the coordinate grid above the curve y=f(x)
  5. Line for < - Correct Answers dotted line
  6. line for ≦ - Correct Answers solid line
  7. Cubic function - Correct Answers f(x) = ax³ + bx² + cx + d where a, b, c and d are real numbers and a is not zero
  8. Graph crosses the x-axis at the - Correct Answers root of the function
  9. Quartic function - Correct Answers f(x) = ax^4 + bx³ + cx² + dx
+ e 
  1. Reciprocal function - Correct Answers a fraction over x
  2. The graphs of y = k/x and y = k/x², where k is a real constant has asymptotes - Correct Answers at x = 0 and y = 0
  3. Asymptote - Correct Answers line which the graph approaches by never reaches
  4. X-coordinates of the points of intersection of y = f(x) and y = g(x) are - Correct Answers the solutions to the equations f(x) = g(x)
  5. y = f(x) + a - Correct Answers translate graph a up
  6. y = f(a) - Correct Answers translate graph a left
  1. In a circle, the angle in a semicircle is always a - Correct Answers right angle
  2. To find the center of a circle given three points on the circumference. - Correct Answers - Find the equations of the perpendicular bisectors of two different chords.
    • Find the coordinates of the point of intersection of the perpendicular bisectors.
  3. Circumcircle - Correct Answers a circle that goes through all the vertices of a triangle.
  4. Circumcenter - Correct Answers the point of intersection of the three right bisectors of the sides of a triangle
  5. Simplify algebraic fractions using division. - Correct Answers When simplifying an algebraic fraction, where possible factories the numerator and denominator and then cancel common factors.
  6. Polynomial - Correct Answers Finite expression with positive whole number indices.
  7. Divide a polynomial - Correct Answers Use long division to divide a polynomial by (x ± p), where p is a constant.
  8. The factor theorem - Correct Answers If f(x) is a polynomial then:
    • If f(p) = 0, then (x-p) is a factor of f(x)
    • If (x-p) is a factor of f(x), then f(p) = 0
  9. Conjecture - Correct Answers Mathematical statement.
  10. Theorems - Correct Answers Previously established mathematical facts
  11. Statement - Correct Answers Final step in a proof
  12. Proof by deduction - Correct Answers Starting from known facts or definitions, then using logical steps to reach the desired conclusion.
  1. Mathematical proof rules - Correct Answers - State any information or assumptions you are using
    • Show every step of your proof clearly
    • Make sure that every step follows logically from the previous step
    • Make sure you have covered all possible cases
    • Write a statement of proof at the end of your working
  2. Prove an identity - Correct Answers - Start with the expression on one side of an identity
    • Manipulate that expression algebraically until it matches the other side
    • Show every step of your algebraic working
  3. Identical - Correct Answers is always equal to (≡)
  4. Proof by exhaustion - Correct Answers Breaking the statement into smaller cases and proving each case separately.
  5. Disproof by counter-example - Correct Answers A counter- example is one example that does not work for the statement. You do not need to give more than one example.
  6. Pascal's triangle - Correct Answers To build the triangle, start with "1" at the top, and then continue placing numbers below it in a triangular pattern. Each number is just the two numbers above it added together (except for the edges, which are all "1").
  7. (n+1)the row of Pascal's triangle gives the - Correct Answers coefficients in the expansion of (abs)^c
  8. Factorial notation - Correct Answers 3! = 3 x 2 x 1
  9. Find entries in Pascal's triangle quickly - Correct Answers - The number of ways of choosing r items from a group of n items is written as nacre = n!/(r!(n-r)!)
    • The rah entry in the nth row of Pascal's triangle is given by n- 1Cr-
  1. If the vector number is negative - Correct Answers The new vector has a different length and the opposite direction.
  2. Scalar example - Correct Answers Real numbers. They have magnitude but no direction.
  3. If the vector number is positive - Correct Answers The new vector has a different length but the same direction
  4. Any vector parallel to the vector may be written as - Correct Answers laminar (a), where laminar is a non-zero scalar.
  5. Parallelogram law - Correct Answers System of determining the resultant force of 2 concurrent forces obtained from the diagonal at a parallelogram having adjacent sides which represent the 2 force vectors being added
  6. Displacement - Correct Answers How to describe a vector
  7. Column vector - Correct Answers a matrix with only one column. Top is change in x axis, bottom is change in y axis
  8. To multiply a column vector by a scalar - Correct Answers multiple each component by the scalar. n(p q) = (np nq)
  9. To add two column vectors - Correct Answers Add the x- components and y-components:
  10. (p q) + (r s) = (par qasr)
  11. Unit vector - Correct Answers A vector of length 1. The unit vectors along the x and y axes are usually denoted by me and j respectively.
  12. I = (1 0) j = (0 1)
  13. You can write any two-dimensional vector in the from - Correct Answers pi + qi
  14. For any two-dimensional vector:(p q) = - Correct Answers pi + qi
  1. To calculate the magnitude of a vector - Correct Answers Use Pythagoras' theorem
  2. For the vector a = xi + in = (x y), the magnitude of the vector is given by - Correct Answers /a/ = root(x^2 + y^2)
  3. A unit vector in the direction of a is - Correct Answers a/(/a/)
  4. Magnitude-direction form - Correct Answers You can define a vector by giving its magnitude and the angle between the vector and one of the coordinate axes.
  5. Position vectors - Correct Answers Vectors giving the position of a point, relative to a fixed origin.
  6. A point P with coordinates (p, q) has a position vector - Correct Answers - OP = pi + qi + (p q)
    • AB = OB - OA, where OA and OB are the position vectors of A and B respectively.
  7. If the point P divides the line segment AB in the ratio λ:u, then - Correct Answers - OP = OA + (λ/(up))AB
    • = OA + (λ/(up))(OB-OA)
  8. If a and b are two non-parallel vectors and pa + qi = ran + sub then - Correct Answers p = r and q = s
  9. Mechanics vector quantities - Correct Answers - Velocity
- Displacement - Force 
  1. Mechanics scalars - Correct Answers - Speed is the magnitude of the velocity vector
    • Distance is the magnitude of the displacement vector
  2. Cosine rule to find missing side - Correct Answers a² = b² + c²
- 2bcCosA 
  1. For all values of θ such that cost ≠ 0, tan ≡ - Correct Answers sin/cost
  2. Use trigonometric identities to - Correct Answers simplify trigonometric expressions.
  3. Solutions to sin = k and cost = k only exist when - Correct Answers -1 < k < 1
  4. When you use the inverse trigonometric functions on your calculator, the angle you get is called the - Correct Answers principal value
  5. Solutions to tan = p exist for - Correct Answers all values of p
  6. principal value is also calls - Correct Answers arcos, arcsine and arc tan
  7. For a point P(x, y) on a unit circle such that OP makes an angle theta with the positive x axis: - Correct Answers cosTheta = x = x- coordinate of P
  8. sin Theta = y = y-coordinate of P
  9. tan Theta = y/x = gradient of OP
  10. Unit Circle - Correct Answers a circle with a radius of 1
  11. You always measure positive angles Theta... - Correct Answers anticlockwise from the x axis
  12. When Theta is obtuse, cosTheta is - Correct Answers negative because the x coordinate of P is negative
  13. The x-y plane is divided into - Correct Answers quadrants
  14. You can use the quadrants to determine whether each of the trigonometric ratios is - Correct Answers positive or negative
  15. Use quadrant rules to find - Correct Answers sin, cos or tan of any of the corresponding acute angles made with the x axis, Theta.
  1. sin30 - Correct Answers 1/
  2. cos30 - Correct Answers √3/
  3. tan30 - Correct Answers √3/
  4. sin60 - Correct Answers √3/
  5. cos60 - Correct Answers 1/
  6. tan60 - Correct Answers
  7. Fins sin cos and tan of 30 ⁰ and 60 ⁰ exactly using - Correct Answers equilateral triangles
  8. find sin cos and tan of 45 ⁰ exactly using - Correct Answers isosceles right angled triangles
  9. sin45 - Correct Answers √2/
  10. cos45 - Correct Answers √2/
  11. tan45 - Correct Answers 1
  12. For a values of Theta, sin²Theta + cos²Theta = - Correct Answers 1
  13. For all values of Theta such that cos /=/ 0, tan Theta = - Correct Answers sin Theta / cosTheta
  14. In the expression 2^x , x can be called - Correct Answers an index, a power, or an exponent
  15. Exponential functions - Correct Answers Functions of the form f(x) = ax, where a is a constant
  16. If f(x) = ax then - Correct Answers f'(x) = ax
  17. If y = ax then - Correct Answers die/dx = ax
  1. The graph or y = ln(x) is a - Correct Answers reflection of the graph y = ax in the line y = x
  2. e^(ln(x)) = - Correct Answers ln(ax) = x
  3. If y = axⁿ then the graph of log(y) against log(x) will be - Correct Answers a straight line with gradient n and vertical intercept log(a)
  4. If y = ax then the graph of log(y) against x will be - Correct Answers a straight line with gradient log(b) and vertical intercept log(a).
  5. For y = ax you need to plot - Correct Answers log(y) against x to obtain a linear graph.