Algebra and functions: OCR A‑Level Maths questions

Every OCR A-Level Maths exam question on P.2 Algebra and functions, 2018–2025, with its mark scheme and examiner’s report.

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494 questions

Q1
June 2025 · Paper 1
8 marksP.2 Algebra and functions
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Q2
June 2025 · Paper 1
4 marksP.7 Differentiation P.2 Algebra and functions
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Q5
June 2025 · Paper 1
8 marksP.2 Algebra and functions
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Q10
June 2025 · Paper 1
12 marksP.2 Algebra and functions P.7 Differentiation
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Q12
June 2025 · Paper 1
11 marksP.8 Integration P.2 Algebra and functions
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$June 2025 Paper 1, question 12: 4 x + 12 (a) Express ( in partial fractions. [4] x 1 x )( 1 x ) + - d = y 2 4 x + The gradient of a curve is given by and the curve passes through the d x x ( 1$
Q1
June 2025 · Paper 2
3 marksP.2 Algebra and functions
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Q2
June 2025 · Paper 2
9 marksP.2 Algebra and functions P.6 Exponentials and logarithms
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Q1
June 2025 · Paper 3
5 marksP.2 Algebra and functions
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Q2
June 2025 · Paper 3
4 marksP.2 Algebra and functions
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Q3
June 2025 · Paper 3
7 marksP.2 Algebra and functions P.6 Exponentials and logarithms
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Q4
June 2025 · Paper 3
8 marksP.2 Algebra and functions
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Q1
June 2025 · AS Paper 1
8 marksP.2 Algebra and functions
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Q3
June 2025 · AS Paper 1
5 marksP.3 Coordinate geometry P.2 Algebra and functions
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Q2
June 2025 · AS Paper 2
4 marksP.2 Algebra and functions
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Q4
June 2025 · AS Paper 2
10 marksP.2 Algebra and functions P.7 Differentiation
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Q5
June 2025 · AS Paper 2
5 marksP.2 Algebra and functions
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Q6
June 2025 · AS Paper 2
6 marksP.2 Algebra and functions
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Q7
June 2025 · AS Paper 2
9 marksP.8 Integration P.2 Algebra and functions
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Q2
June 2024 · Paper 1
6 marksP.2 Algebra and functions
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Q6
June 2024 · Paper 1
8 marksP.2 Algebra and functions P.6 Exponentials and logarithms
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All 110 questions on Algebra and functions, as a list

June 2025, Paper 1, Q1 (8 marks): Express each of the following in the form pxq, where p and q are constants. 1 2 (a) [1] 4 x ^ h 3 (b) x x [2] 5 3 5 (c) x x [2] 2 8 # ^ h 1 5 6 3 (d) x x [3] 27
June 2025, Paper 1, Q2 (4 marks): y x O The diagram shows the curve y ax x ( b ) , where a and b are constants and b 0 . = - 2 (a) Given that the curve has a stationary point at x = , state the
June 2025, Paper 1, Q5 (8 marks): Scientists are comparing h, the average height of a child in cm, with t, the age of the child in years. They suggest the model h at + for t b 2 , where a and b
June 2025, Paper 1, Q10 (12 marks): ex e x 2 1 10 The graph of y can be transformed to the graph of y - by a stretch parallel to the = = x-axis followed by a translation. (a) (i) State the scale f
June 2025, Paper 1, Q12 (11 marks): 4 x + 12 (a) Express ( in partial fractions. [4] x 1 x )( 1 x ) + - d = y 2 4 x + The gradient of a curve is given by and the curve passes through the d x x ( 1
June 2025, Paper 2, Q1 (3 marks): In this question you must show detailed reasoning. 2 Solve the inequality x 3 x 10 . [3] + G
June 2025, Paper 2, Q2 (9 marks): In this question you must show detailed reasoning. Solve the following equations. 2 3 (a) ( x 5 ) 8 [3] - = 2 3 = y (b) e 2 [2] 4 2 (c) x 3 x 4 0 [4] - - =
June 2025, Paper 3, Q1 (5 marks): ^ h 2 - 2 1 (a) Express x 3 12 x 17 in the form a x b c where a, b and c are constants. [3] + - + 2 (b) State the coordinates of the minimum point of the curve
June 2025, Paper 3, Q2 (4 marks): 2 (a) The curve y is translated by 4 units in the positive x-direction. = 3 x Write down the equation of the curve after it has been translated. [2] 5 2 (b) The
June 2025, Paper 3, Q3 (7 marks): (a) Sketch the graph of y x [2] 2 5 on the grid provided in the Printed Answer Booklet. = - (b) Solve the inequality x [2] 2 5 1 . - 1 (c) In this question you
June 2025, Paper 3, Q4 (8 marks): Functions f and g are defined for all real values of x by x k - and ( )x 2 ( )x x kx , where k is a constant. f g 5 = = + + 2 1 ( )x kx You are given that the e
June 2025, AS Paper 1, Q1 (8 marks): In this question you must show detailed reasoning. Solve the following equations. 2 - (a) x 11 = 5 [2] 6 3 (b) y 7 y 8 0 [4] + - = 10 = 3 z (c) 2 - 16 [2]
June 2025, AS Paper 1, Q3 (5 marks): - 2 3 (a) Express x 6 x in the form ( x p ) + , where p and q are constants. q [2] + (b) Hence or otherwise determine the centre and radius of the circle with e
June 2025, AS Paper 2, Q2 (4 marks): In this question you must show detailed reasoning. D C 2 12 cm A B ( 3 3 cm ) - The diagram shows the rectangle ABCD where AB ( 3 3 ) cm. = - cm2 The area of AB
June 2025, AS Paper 2, Q4 (10 marks): 2 4 The cubic polynomial x 2 kx 4 x + , where k is a constant, is denoted by ( )x k f . - + It is given that f ( ) 2 16 . l = (a) Show that k = 3. [4] For the r
June 2025, AS Paper 2, Q5 (5 marks): In this question you must show detailed reasoning. G H F E ( 2 x 1 ) cm + B C ( x 2 ) cm - A D 3 cm The diagram shows the cuboid ABCDEFGH where AD = 3 cm, AF (
June 2025, AS Paper 2, Q6 (6 marks): (a) The curve y ln x is stretched by a scale factor 3 in the x-direction. = State the equation of the curve after it has been stretched. [2] 2 (b) Describe full
June 2025, AS Paper 2, Q7 (9 marks): y (1, 0) a x O (3, –16) The diagram shows the curve with equation y f ( ) x where ( ) f x is a quadratic function. The = curve intersects the x-axis at the poin
June 2024, Paper 1, Q2 (6 marks): You are given that y is inversely proportional to x6 and z is directly proportional to the cube root 2 of y. (a) (i) Find an equation for z in terms of x and k,
June 2024, Paper 1, Q6 (8 marks): In this question you must show detailed reasoning. 3 2 The cubic polynomial ( )x f is defined by ( )x f 4 x 25 x 58 x 16 . = - - + 1 (a) Show that x is a root o
June 2024, Paper 1, Q7 (10 marks): The point A has coordinates (1, 7), and the point B has coordinates (h, 10). (a) You are given that the gradient of the line AB is 2. Find the value of h. [2] (
June 2024, Paper 1, Q8 (7 marks): (a) State the set of values for which x 2 . x [1] (b) You are given that n is an integer such that n 9 . G (i) Find the maximum value of n 2 1 . [1] - (ii) Find
June 2024, Paper 2, Q3 (6 marks): 2 3 The function f is defined by ( ) f x x x 5 x - . 3 = - - (a) Show that ( x 3 ) is a factor of ( ) f x . [1] - (b) Factorise ( ) f x completely. [2] Three st
June 2024, Paper 2, Q6 (10 marks): In this question you must show detailed reasoning. (a) (i) Use the formula for cos A ( B ) , and the double angle formulae, to show that + 3i cos 3 4 cos 3 cos
June 2024, Paper 3, Q1 (4 marks): Simplify each of the following. ^ h 3 2 3 1 (a) 2 a a - [2] # 4 2 4 x 9 - (b) ^ h [2] 2 2 x 5 x 12 2 ( x 3 ) + - +
June 2024, Paper 3, Q2 (5 marks): In this question you must show detailed reasoning. A O 2rad (3x + 1) cm B The diagram shows a sector AOB of a circle with centre O and radius ( x . The angle AO
June 2024, AS Paper 1, Q6 (7 marks): A curve has the following properties: d y • The gradient of the curve is given by d 2 x . =- x • The curve passes through the point ( , 4 13 ) . - Determine the
June 2024, AS Paper 1, Q7 (5 marks): In this question you must show detailed reasoning. 4 2 4 3 2 (a) Show that ( x 2 ) 6 ( x 2 ) 16 x 8 x 18 x 8 x 24 . [1] + - + - / + + + - 4 3 2 (b) Hence solve
June 2024, AS Paper 1, Q9 (5 marks): a 7 a 5 - m n 9 Express 2 2 in the form a a , where m and n are integers and a 0 or 1 . [5] + ! a 3 a - 2
June 2024, AS Paper 2, Q1 (5 marks): + 2 1 (a) Write x 3 24 x + in the form ( 5 a x b ) + , where a, b and c are constants to be determined. c + [3] 2 The finite region R is enclosed by the curve y
June 2024, AS Paper 2, Q3 (6 marks): + 3 The quadratic equation kx 2 kx 2 k 3 x - , where k is a constant, has no real roots. 1 + = (a) Show that k satisfies the inequality 2 4 k 16 k 9 2 0 . [4] +
June 2024, AS Paper 2, Q4 (4 marks): - is stretched by a scale factor 1 4 (a) The curve y 2 x 1 4 parallel to the x-axis. = [2] Find the equation of the curve after it has been stretched. c m, and
June 2023, Paper 1, Q2 (8 marks): 1 a 2 (a) (i) Show that can be written in the form b , where a, b and c are + cx 3 2 x 3 2 x + - + constants to be determined. [2] 1 1 (ii) Hence solve the equa
June 2023, Paper 1, Q5 (8 marks): (a) The function ( )x f is defined for all values of x as ( ) f x ax b , where a and b are positive = - constants. (i) The graph of y f ( ) x + , where c is a c
June 2023, Paper 2, Q1 (5 marks): - 2 1 (a) (i) Express x 8 x 11 in the form ( x a ) + where a and b are constants. b [2] + - 2 - (ii) Hence write down the minimum value of x 8 x 11 . [1] + 2 -
June 2023, Paper 3, Q3 (8 marks): 3 The cubic polynomial ( ) f x is defined by ( )x f x px + , where p and q are constants. q = + (a) (i) Given that f 2 ( ) 13 , find the value of p. [2] l = (ii
June 2023, AS Paper 1, Q6 (11 marks): 3 6 (a) Determine the two real roots of the equation x x [3] 8 7 1 0 . + - = 7 49 4 (b) Determine the coordinates of the stationary points on the curve y x x x
June 2023, AS Paper 2, Q1 (3 marks): + 1 The quadratic equation kx 3 x k 0 has no real roots. + = Determine the set of possible values of k. [3]
June 2023, AS Paper 2, Q2 (4 marks): In this question you must show detailed reasoning. Solve the equation x 5 32 x 45 2 x . Give your answer in the form a 5 + , where a and b b + = + are integers
June 2023, AS Paper 2, Q5 (5 marks): y 2 x 3 2 y + = 2 x 3 y = x O + . The graph of y 2 x 3 2 x 3 2 2 x 3 The diagram shows the graphs of y and y can be = = = 2 x 3 2 transformed to the graph of y
June 2023, AS Paper 2, Q7 (7 marks): y l2 C l1 1a k , 3 2 x O 2 The diagram shows the curve C with equation y 4 x 10 x + and two straight lines, l1 and l2. 7 = - 1a k. The line l2 is the normal to
June 2022, Paper 1, Q3 (7 marks): (a) In this question you must show detailed reasoning. 2 Find the coordinates of the points of intersection of the curves with equations y x 2 x + 1 = - 2 and y
June 2022, Paper 1, Q4 (8 marks): + 2 4 (a) Write x x p x q + , where p, q and r are constants. r [3] 2 6 + in the form 7 ( ) + 2 (b) State the coordinates of the minimum point on the graph of y
June 2022, Paper 1, Q5 (8 marks): 2x 2x 4 5 (a) The graph of y can be transformed to the graph of y + either by a translation or = = by a stretch. (i) Give full details of the translation. [2] (
June 2022, Paper 2, Q1 (8 marks): In this question you must show detailed reasoning. Solve the following equations. x x 1 - (a) x 0 [3] - = x 1 2 + + 8 7 (b) 1 0 [3] 6 - - = 3 x x 1 x 7 (c) 3 2
June 2022, Paper 2, Q6 (6 marks): (a) The diagrams show five different graphs. In each case the whole of the graph is shown. y y y x x x Fig. 1.1 Fig. 1.2 Fig. 1.3 y y x x Fig. 1.4 Fig. 1.5 Plac
June 2022, Paper 3, Q1 (3 marks): Solve the equation x 2 3 9 . [3] - =
June 2022, Paper 3, Q2 (5 marks): x3 2 (a) Give full details of the single transformation that transforms the graph of y to the graph = 3 of y x - . 8 [2] = 3 The function f is defined by ( ) f
June 2022, AS Paper 1, Q2 (5 marks): In this question you must show detailed reasoning. ^ h 3 2 The cubic polynomial f(x) is defined by f x 5 x 4 x ax 2 , where a is a constant. = - + - You are giv
June 2022, AS Paper 1, Q3 (7 marks): 3 The diagram in the Printed Answer Booklet shows part of the graph of y x 4 x + . 3 = - 2 - (a) It is required to solve the equation x 3 x 1 0 graphically by d
June 2022, AS Paper 1, Q7 (8 marks): (a) In this question you must show detailed reasoning. Find the range of values of the constant m for which the simultaneous equations y mx and = 2 2 x y 6 x 2
June 2022, AS Paper 2, Q1 (2 marks): Write the solution of the inequality ( x 2 )( x 3 ) 2 0 using set notation. [2] - +
June 2022, AS Paper 2, Q2 (4 marks): In this question you must show detailed reasoning. Solve the equation x 3 1 4 x . [4] + =
June 2022, AS Paper 2, Q5 (7 marks): y x O 1 ( , 1 ) - 2 The diagram shows a curve C for which y is inversely proportional to x. The curve passes through a k. 1 the point ,1 - 2 (a) (i) Determine t
November 2021, Paper 1, Q1 (4 marks): + 1 Determine the set of values of k such that the equation x 4 x ( k 3 ) 0 has two distinct real + + = roots. [4]
November 2021, Paper 1, Q2 (4 marks): Alex is comparing the cost of mobile phone contracts. Contract A has a set-up cost of £40 and then costs 4p per minute. Contract B has no set-up cost, does not
November 2021, Paper 1, Q3 (4 marks): It is given that x is proportional to the product of the square of y and the positive square root of z. When y 2 and z 9 , x 30 . = = = (a) Write an equation fo
November 2021, Paper 1, Q4 (7 marks): In this question you must show detailed reasoning. 3 2 The cubic polynomial ( ) f x is defined by ( ) f x 2 x 3 x 11 x + . 6 = - - (a) Use the factor theorem to
November 2021, Paper 1, Q5 (7 marks): (a) The graph of the function y f ( ) x passes through the point P with coordinates (2, 6), and = is a one-one function. State the coordinates of the point corr
November 2021, Paper 1, Q8 (10 marks): Functions f and g are defined for 0 x 2 by ( ) f x 2 tan x and ( ) g x sec x . G G = = r (a) (i) State the range of f. [1] (ii) State the range of g. [1] (b) (i
November 2021, Paper 2, Q8 (6 marks): 8 The number K is defined by K n + , where n is an integer greater than 2. 1 = ^h h, find the constants b and c. ^ 3 2 (a) Given that n 1 n 1 n bn c [1] + / + +
November 2021, Paper 3, Q1 (3 marks): Show in a sketch the region of the x-y plane within which all three of the following inequalities hold. x2 y , x y 2 , x 0 . H + G H You should indicate the reg
November 2021, Paper 3, Q4 (5 marks): (a) Sketch, on a single diagram, the following graphs. • y x 1 = - k • y , where k is a negative constant [2] = x (b) Hence explain why the equation x x 1 k has
November 2021, Paper 3, Q7 (8 marks): A curve C in the x-y plane has the property that the gradient of the tangent at the point P x y is ( , ) three times the gradient of the line joining the point
November 2021, AS Paper 1, Q3 (6 marks): The diagram shows the curve y f ( ) x , where ( )x f is a cubic polynomial in x. = This diagram is repeated in the Printed Answer Booklet. y 2 1 x 0 –3 –2 –1 1
November 2021, AS Paper 1, Q6 (3 marks): The power output, P watts, of a certain wind turbine is proportional to the cube of the wind speed - . 1 v ms When v = 3.6, P = 50. Determine the wind speed tha
November 2021, AS Paper 1, Q9 (6 marks): In this question you must show detailed reasoning. Find the equation of the straight line with positive gradient that passes through (0, 2) and is a 2 tangent t
November 2021, AS Paper 2, Q1 (2 marks): + 1 Given that ( x 2 ) is a factor of x 2 kx - , find the value of the constant k. 4 [2] -
November 2021, AS Paper 2, Q2 (3 marks): y 4 x R O 2 –4 2 The diagram shows the line y x + and the curve y x - . The region R is the unshaded 2 4 4 = - = region together with its boundaries. Write down
November 2020, Paper 1, Q2 (8 marks): Simplify fully. 5 (a) 12 a 3 a [2] # 1 1 3 4 (b) ( 64 b ) ( 4 b ) - [2] # 3 2 3 c 2 c (c) 7 9 4 27 [4] - # #
November 2020, Paper 1, Q9 (9 marks): y x O The diagram shows the graph of y 2 x 3 . = - (a) State the coordinates of the points of intersection with the axes. [2] (b) Given that the graphs of y 2 x
November 2020, Paper 1, Q12 (9 marks): Find the general solution of the differential equation d y 3 2 ( 2 x 3 x 11 x 6 ) y ( 20 x 35 ) . - - + = - d x Give your answer in the form y = f(x). [9]
November 2020, Paper 2, Q2 (4 marks): 2 2 x x 7 x - . 6 + - 2 Simplify fully [4] 2 x x 2 - -
November 2020, Paper 2, Q5 (5 marks): - and n 2 + are positive integers. (a) Determine the set of values of n for which n 1 1 5 [3] 2 2 2 2 2 A ‘Pythagorean triple’ is a set of three positive intege
November 2020, Paper 3, Q2 (3 marks): + . ex e x 2 3 2 A sequence of transformations maps the curve y to the curve y = = Give details of these transformations. [3]
November 2020, Paper 3, Q3 (11 marks): The functions f and g are defined for all real values of x by 2 f x ( ) 2 x 6 x and ( ) g x 3 x + . 2 = + = (a) Find the range of f. [3] (b) Give a reason why f
November 2020, AS Paper 1, Q5 (8 marks): The function f is defined by ( ) f x ( x a x )( 3 a x )( b ) where a and b are positive integers. = + + - (a) On the axes in the Printed Answer Booklet, sketch
November 2020, AS Paper 1, Q6 (13 marks): In this question you must show detailed reasoning. 2 (a) Solve the inequality x x 6 0 , giving your answer in set notation. [4] 2 + - 3 3 (b) Solve the equation
November 2020, AS Paper 1, Q7 (5 marks): 7 Determine the points of intersection of the curve xy 3 x 14 0 and the line x 2 y 4 . [5] + + = + =
November 2020, AS Paper 2, Q2 (5 marks): k 2 Two curves have equations y ln x and y , where k is a positive constant. = = x (a) Sketch the curves on a single diagram. [3] (b) Explain how your diagram s
November 2020, AS Paper 2, Q4 (9 marks): In this question you must show detailed reasoning. 3 2 The cubic polynomial x 6 kx 57 x 20 is denoted by f (x). It is given that ( 2 x 1 ) is a factor of + + -
November 2020, AS Paper 2, Q5 (5 marks): 5 A curve has equation y a x ( b ) + , where a, b and c are constants. The curve has a stationary c = + point at ( 3 2 , ) . - (a) State the values of b and c.
June 2019, Paper 1, Q1 (4 marks): In this question you must show detailed reasoning. 2 Solve the inequality 10 x x 2 2 0 . [4] + -
June 2019, Paper 1, Q3 (7 marks): 3 The function f is defined by ( ) f x ( x 3 ) 17 for x k , where k is a constant. = - - H 1 (a) Given that f - ( )x exists, state the least possible value of k
June 2019, Paper 1, Q9 (11 marks): 9 (a) Express cos 3 3 x 7 sin 3 x in the form R cos ( 3 x ) , where R 2 0 and 0 1 1 r. [3] + - a a 2 (b) Give full details of a sequence of three transformation
June 2019, Paper 2, Q7 (5 marks): In this question you must show detailed reasoning. 6 2 4 3 2 Use the substitution u x + to solve the equation x 36 x 12 x 7 x x 2 0 . [5] = + + + - =
June 2019, Paper 3, Q2 (8 marks): 2 2 A circle with centre C has equation x y 6 x 4 y 4 0 . + - + + = (a) Find (i) the coordinates of C, [2] (ii) the radius of the circle. [1] (b) Determine the
June 2019, Paper 3, Q3 (7 marks): (a) In this question you must show detailed reasoning. Solve the inequality x 2 2 x 6 . [4] - G - (b) Give full details of a sequence of two transformations nee
June 2019, Paper 3, Q6 (10 marks): y x O 2 x 1 - The diagram shows part of the curve y . = 2 x x ( 2 3 )( 1 ) + + Find the exact area of the shaded region, giving your answer in the form p q ln r
June 2019, AS Paper 1, Q3 (10 marks): In this question you must show detailed reasoning. 3 2 (a) The polynomial ( )x f is defined by ( )x f 2 x 3 x 8 x + . 3 = + - (i) Show that ( ) f 1 0 . [1] = (i
June 2019, AS Paper 1, Q4 (6 marks): 2 4 (a) Find the coordinates of the stationary points on the curve y x 6 x 9 x . [4] = - + 3 2 (b) The equation x 6 x 9 x k 0 has exactly one real root. - + + =
June 2019, AS Paper 1, Q6 (6 marks): B xcm 60° A ycm C The diagram shows triangle ABC, with AB = x cm, AC = y cm and angle BAC = 60°. It is given that ^ h 3cm2 the area of the triangle is x y . + (
June 2019, AS Paper 2, Q1 (3 marks): In this question you must show detailed reasoning. Solve the equation ( x 3 5 ) 24 , giving your answer in the form a b 5 , where a and b are - = + positive int
June 2019, AS Paper 2, Q2 (6 marks): ^ h 2 - 2 2 (a) Express x 5 20 x + in the form 3 p x q r , where p, q and r are integers. [3] + + 2 (b) State the coordinates of the minimum point of the curve
June 2019, AS Paper 2, Q3 (5 marks): 3 (a) Sketch the curve y . [1] =- 2 x 1 (b) The curve y is translated by 2 units in the positive x-direction. =- 2 x State the equation of the curve after it ha
June 2019, AS Paper 2, Q8 (8 marks): (a) Show that the equation x kx where k is a constant, can be expressed in 2 log log ( 1 ) 3 , = - + 2 2 2 - x kx [4] the form 8 8 0 . + = (b) Given that the eq
June 2018, Paper 1, Q3 (4 marks): In this question you must show detailed reasoning. 4 2 Find the two real roots of the equation x x [4] 5 4 . Give the roots in an exact form. - =
June 2018, Paper 1, Q6 (9 marks): 2 6 The cubic polynomial ( )x is defined by ( )x x x x f f 2 7 2 + . 3 = - + (i) Given that ( x is a factor of ( )x , express ( )x [3] 3 ) f f in a fully factor
June 2018, Paper 1, Q9 (7 marks): 9 The function f is defined for all real values of x as ( )x c x x , where c is a constant. f 8 = + - (i) Given that the range of f is ( )x , find the value of
June 2018, Paper 2, Q1 (7 marks): (i) Express 2x2 - 12x + 23 in the form a(x + b)2 + c. 1 [4] (ii) Use your result to show that the equation 2x2 - 12x + 23 = 0 has no real roots. [1] (iii) Given
June 2018, Paper 2, Q3 (4 marks): Ayesha, Bob, Chloe and Dave are discussing the relationship between the time, t hours, they might spend revising for an examination, and the mark, m, they would
June 2018, Paper 3, Q2 (3 marks): Solve the equation x 2 1 x 3 . [3] - = +
June 2018, Paper 3, Q3 (6 marks): In this question you must show detailed reasoning. A gardener is planning the design for a rectangular flower bed. The requirements are: • the length of the flo
June 2018, Paper 3, Q4 (8 marks): In this question you must show detailed reasoning. The functions f and g are defined for all real values of x by ^ h ^ h x3 2 f x and g x x 2 . = = + (i) Write
June 2018, AS Paper 1, Q1 (5 marks): In this question you must show detailed reasoning. 7 in the form a b, where a is an integer and b is a prime number. (i) Express 32 [2] 2 (ii) Express 1 in the
June 2018, AS Paper 1, Q2 (4 marks): + 2 (i) The equation x 3 x k 0 has repeated roots. Find the value of the constant k. [2] + = 2 2 (ii) Solve the inequality 6 x x 0 . [2] + -
June 2018, AS Paper 1, Q6 (7 marks): Sketch the following curves. 2 (i) y [2] = x 3 2 (ii) y x 6 x 9 x [5] = - +
June 2018, AS Paper 2, Q2 (4 marks): 2 (i) The curve y + is translated by four units in the positive x-direction. State the equation of the = 3 x curve after it has been translated. [2] 2 5 (ii) De
June 2018, AS Paper 2, Q4 (6 marks): ^ h 2 - 2 4 (i) Express x 4 12 x 11 in the form a x b c . [3] + + + 2 - (ii) State the number of real roots of the equation x 4 12 x 11 0 . [1] + = ^ h 2 (iii)
June 2018, AS Paper 2, Q5 (5 marks): In this question you must show detailed reasoning. 2 - The line x 5 y k is a tangent to the curve x 4 y 10 . Find the value of the constant k. [5] + = =

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