Maths A level Questions and Answers Rated A

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Maths A level Questions and Answers Rated A What is 2^x multiplied by 3^x? ✔✔Let x=2 2^2 X 3^2 = 4 X 9 = 36 36=6^2 So answer is 6^x How would you solve (x^3 - 2x)/3x^2 ✔✔Break down fract ... ion to (x^3/ 3x^2) - (2x/3x^2) then continue to simplify fractions and cancel out like terms How would you factorise 4x^4 - 13x^2 + 9 ✔✔Change 4x^4 and 13x^2 into 4(x^2)^2 and 13(x^2) Then let (x^2) be y and substitute y to get 4y^2-13y+9=0 which factorises into (4y-9)(y-1)=0 Which is equal to (4x^2 -9)(x^2 -1) This is difference between two squares so they simplify into 4 linear factors which are: (2x-3)(2x+3)(x-1)(x+1) X^5 What is the base and what is the exponent ✔✔X is base and must be same when applying indices law 5 is the exponent What must you watch out for when expanding brackets ✔✔THE NEGATIVE OUTSIDE BRACKETS In the quadratic expression, what are a, b and c ✔✔Real numbers (all positive, negative, zero, fractions and surds) And a is not equal to 0 What is x^4 as a term written as a function of a function ✔✔(X^2)^2 What is a rational number? ✔✔Written as a/b where a and b are integers What are irrational numbers? ✔✔They can't be written in form a/b where a and b are integers Eg surds are irrational numbers Change quadratic expression into completing the square form ✔✔a(x + (b/2a))^2 - (c - (b^2/4a) If given 3x^2 + 6x + 1 What do you do to change it into completing the square form ✔✔You can't divide by 3 for all so move the 1 outside 3((x-1)^2 - 1^2 ) + 1 .... What is a domain ✔✔Set of possible inputs for a function What is a range ✔✔Set of possible outputs for function Give example of a function, domain and range ✔✔Function = f(x) = x^2 Domain= eg 3. So f(3) = ..... Range = 3^2 = 9 In f(3) = 9 3 is the domain 9 is the range How do you calc roots of a function ✔✔Solve for x in equation to find roots and equate it to 0 What is a function ✔✔A relationship where each input has a single output. These sets of inputs are called domain, and they provide a set of outputs of the function called range. What may some function questions include ✔✔These function questions may have x E R. This occurs when input is a real number. This is a value that represents a quantity on a number line (opposite of imaginary number. x E R. This means x is a member of a real number What should you consider f(x) as? ✔✔A function of a function What is the curved shape of a quadratic graph called? ✔✔Parabola What is the graph of y= a(x+ p)^2 + q A translation of? ✔✔Of graph y= ax^2 by vector ( -p q) What is the other method to finding the turning point other than completing the square ✔✔You can use symmetry to find x coordinates of min point and then substitute this into equation to find y coordinate When you sketch a graph, what must you include? ✔✔Smooth curve and intercepts and turning point and label axis ( not plotted or drawn to scale) What is discriminant used for ✔✔b^2 - 4ac is used to find out about the type of roots if b^2 - 4ac = 0 ✔✔2 equal real roots if b^2 - 4ac >0 ✔✔2 different real roots if b^2 - 4ac < 0 ✔✔No real roots. Can't square root a non real negative number so you use imaginary number instead What is a mathematical model ✔✔Mathematical description of a real-life situation (quadratics can be used) If 'k' is a constant what does this mean ✔✔It has the same value in both equations simultaneous equations with one linear and one quadratic equation can have how many solutions ✔✔Up to 2 pairs of solutions Solutions to a pair of simultaneous equations represent what ✔✔The points of intersection of their graphs What must you always use when dealing with inequalities ✔✔Set notation When you must find the set of values of x that satisfy two separate inequalities what must you do ✔✔Solve for x for each inequality and then draw number line and see where they overlap What does N represent ✔✔natural number - positive integers what does Z mean ✔✔all intergers - neg and pos what does R mean ✔✔real numbers what does x E A mean ✔✔x belongs in A What does O with a slash across it represent ✔✔empty set values of x for which the cruve y=f[x] is below the curve y=g[x] satisfy the inequality ........ ✔✔f[x] <g[x] values of x for which the curve y=f[x] is above the curve y=g[x] satisfy the inequality ........ ✔✔f[x] > g[x] if the region inequaltity is greater than or smaller than, the line is ✔✔dotted if the region inequaltity is greater than or equal to and smaller than or equal to , the line is ✔✔solid cubic function; when a is positive ✔✔ cubic function when a is negative ✔✔ when roots = [x-4]³, there is ...... ✔✔no bounce but a POINT OF INFLECTION, where graph e.g. goes from pos gradient to stationary to pos gradient when roots = [x-4]², theres a..... ✔✔bounce at x=4 point of inflection ✔✔ when x→∞ ✔✔x tends towards positive infinity when x → -∞ ✔✔x tends towards negative infinity quartic graph when a is greater than 0 ✔✔graph looks like a W quartic graph when a is less than 0 ✔✔the graph looks like an M y=k/x, where k is greater than 0 ✔✔ y=k/x where k is less than 0 ✔✔curves in 2nd and 4th quadrant y=k / x², where k is greater than 0 ✔✔curves in 1st and 2nd quadrant y=k/x², where k is less than 0 ✔✔curves in 3rd and 4th quadrant to find a root to an equation, you can actually ✔✔sub in a number into x and try to find the correct value of x that when the equation is simplified will equate to 0 for y=k/x, as k increases, ✔✔the graph increasingly reaches out away from axis y=f[x] +a ✔✔translates graph by a units in vertical direction y=f[x+a] ✔✔translatesgraph by -a units in horizontal direction y=af[x] ✔✔stetches graph by scale factor of a in y direction y=f[ax] ✔✔stretches graph by scale factor of 1/a in x direction y=-f[x] ✔✔reflect in x-axis y=f[-x] ✔✔reflect in y axis what does x≠0 mean ✔✔to solve for x, you should multiply by x² instead of x as it would either be pos or neg , but x² is never neg m [gradient] of line joining point [x₁,y₁] to point [x₂,y₂] has equation ✔✔m= y₂-y₁ / x₂-x₁ you can define a staight line by giving ✔✔1. 1 point on line with m 2. two diff points on line equation of a line with gradient m that passes through point [x₁,y₁] is ✔✔y-y₁=m[x-x₁] you can write the equation in the form ax+by+c=0 distance between points A[x₁,y₁] and B[x₂,y₂] is found by equation ✔✔d=√[[x₂-x₁]²+[y₂-y₁]²] two quantities are in direct proportion when ✔✔they increase at the same rate. This produces a graph of these quantities as a straight line through the origin y=kx is a straight line. As x increases by 1 unit... ✔✔y increases by k units the further the points are from the line, the less appropriate a linear model for the data, but even if all points dont fall under line, ✔✔linear model could still be used [Show More]

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