Algebra and functions: OCR MEI A‑Level Maths questions

Every OCR MEI 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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560 questions

Q1
June 2025 · Paper 1
5 marksP.2 Algebra and functions
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Q2
June 2025 · Paper 1
4 marksP.2 Algebra and functions
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$June 2025 Paper 1, question 2: x 25 - 2 Express ( in partial fractions. [4] 2 x x 1 )( 4 ) - -$
Q8
June 2025 · Paper 1
7 marksP.2 Algebra and functions
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Q4
June 2025 · Paper 2
5 marksP.2 Algebra and functions
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Q2
June 2025 · Paper 3
2 marksP.2 Algebra and functions
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Q9
June 2025 · Paper 3
5 marksP.7 Differentiation P.2 Algebra and functions
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Q10
June 2025 · Paper 3
6 marksP.10 Vectors P.2 Algebra and functions
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Q11
June 2025 · Paper 3
5 marksP.2 Algebra and functions P.4 Sequences and series
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Q12
June 2025 · Paper 3
7 marksP.2 Algebra and functions
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Q4
June 2025 · AS Paper 1
4 marksP.2 Algebra and functions
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Q9
June 2025 · AS Paper 1
5 marksP.8 Integration P.2 Algebra and functions
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Q11
June 2025 · AS Paper 1
9 marksP.7 Differentiation P.2 Algebra and functions
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Q1
June 2025 · AS Paper 2
2 marksP.2 Algebra and functions P.6 Exponentials and logarithms
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Q6
June 2025 · AS Paper 2
6 marksP.7 Differentiation P.2 Algebra and functions
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Q15
June 2025 · AS Paper 2
7 marksP.6 Exponentials and logarithms P.2 Algebra and functions
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Q11
June 2024 · Paper 1
8 marksP.4 Sequences and series P.2 Algebra and functions
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Q2
June 2024 · Paper 2
2 marksP.2 Algebra and functions
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Q8
June 2024 · Paper 2
6 marksP.7 Differentiation P.2 Algebra and functions
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Q16
June 2024 · Paper 2
12 marksP.8 Integration P.2 Algebra and functions
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Q1
June 2024 · Paper 3
2 marksP.2 Algebra and functions
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All 113 questions on Algebra and functions, as a list

June 2025, Paper 1, Q1 (5 marks): (a) Sketch the function y 2 x 3 . [2] = - (b) In this question you must show detailed reasoning. Solve the equation x 2 3 4 - . x [3] - =
June 2025, Paper 1, Q2 (4 marks): x 25 - 2 Express ( in partial fractions. [4] 2 x x 1 )( 4 ) - -
June 2025, Paper 1, Q8 (7 marks): (a) Determine the two values of k for which the line y x 3 + is a tangent to the curve 5 = x2 y k kx [4] . = - - x2 (b) These values of k are used to define two
June 2025, Paper 2, Q4 (5 marks): 2 4 (a) Use the factor theorem to show that ( x 3 ) is a factor of x 4 8 x 11 x - . 3 [1] - - - 3 2 2 (b) Hence show that 4 x 8 x 11 x 3 ( x 3 )( ax b ) , where
June 2025, Paper 3, Q2 (2 marks): You are given that 3 f x ( ) on the domain { : x x , x 0 } = d R ! x g x ( ) x - on the domain { : 1 x x } . = d R Find gf x . You must state the domain. ( ) [2
June 2025, Paper 3, Q9 (5 marks): 3 x 9 The function ( ) f x is defined on all real numbers by ( ) f x x e . = + 3 3 x (a) Differentiate x e . [2] + (b) Write down the coordinates of the point w
June 2025, Paper 3, Q10 (6 marks): KKKKKKK OOOOOOO 10 The magnitude of the vector 1 is an integer. - x L P Determine all possible integer values of x. [6]
June 2025, Paper 3, Q11 (5 marks): 1 11 The nth term of a sequence is defined by a + , for n H . 1 n = - n 1 1 n 1 1 + - + (a) Prove that every term in the sequence, an, is a rational number. [3]
June 2025, Paper 3, Q12 (7 marks): 3 a x - 12 (a) Show that for the point on the curve where x , 0 as given in line 10. [1] H = a x + (b) Use the equation of the curve given in line 8 to show tha
June 2025, AS Paper 1, Q4 (4 marks): 2 4 (a) Show that the equation x kx k 0 has real roots for all real values of k. [2] + - = c m . – ! 1 5 2 2 (b) Show that the roots of the equation x kx k 0 ar
June 2025, AS Paper 1, Q9 (5 marks): a k in the form x 1 3 5 p q 9 (a) Write the expression x x x [1] 3 . + + 2 2 a k. The curve passes through the point (1, –2). d y 1 3 5 (b) A curve has gradient
June 2025, AS Paper 1, Q11 (9 marks): In this question you must show detailed reasoning. 2 f x x x x You are given that ( ) ( 2 )( 7 6 ) . = + - + (a) Solve the equation ( ) f x [3] 0 . = (b) Show t
June 2025, AS Paper 2, Q1 (2 marks): You are given that b, c and d are integers greater than 1. a k . c 0 (a) State the value of d [1] (b) State the value of log b b . [1]
June 2025, AS Paper 2, Q6 (6 marks): The equation of a curve is 4 3 y x 8 x 20 . = - + d , is y (a) Show that the gradient function, x d d y 2 4 x ( x 6 ) . [2] = - d x (b) (i) On the axes in the P
June 2025, AS Paper 2, Q15 (7 marks): 3x 15 (a) On the axes in the Printed Answer Booklet, sketch the graph of y [2] . = 3x (b) Determine the exact coordinates of the points of intersection of the c
June 2024, Paper 1, Q11 (8 marks): The first three terms of a geometric sequence are k 5 - , k 2 3 - , k 6 + , where k is a constant. 2 2 - (a) Show that k satisfies the equation k 11 k 10 0 . [3
June 2024, Paper 2, Q2 (2 marks): e o and a stretch scale 3 ex 2 The equation of a curve is y . The curve is subject to a translation 0 = factor 2 parallel to the y-axis. Write down the equation
June 2024, Paper 2, Q8 (6 marks): The equation of a curve is 3 2 y 2 x 3 mx 9 mx + . 4 = + - Determine the range of values of m for which the curve has no stationary values. [6]
June 2024, Paper 2, Q16 (12 marks): In this question you must show detailed reasoning. Find the particular solution of the differential equation d = y 9 y , d x ( x 1 )( x 2 ) - + given that x 2 w
June 2024, Paper 3, Q1 (2 marks): Solve the inequality x 1 2 6 - . x [2] 5
June 2024, Paper 3, Q2 (4 marks): (a) The function ( )x f is defined by 1 f ( )x 1 2 x for x H - . = + 2 1 Find an expression for f - ( )x and state the domain of this inverse function. [3] 2 (b
June 2024, Paper 3, Q4 (2 marks): In this question you must show detailed reasoning. 1 1 1 Determine the exact value of 2 . [2] + + 1 3 2 2 3 + + +
June 2024, Paper 3, Q16 (2 marks): x x x x x x c m c m c m is equivalent to + + - P Q P Q P Q 16 Show that the expression a b c a + + - 2 2 2 x x c m + P Q ax x b c , as given in lines 15 and 16.
June 2024, AS Paper 1, Q6 (6 marks): 2 6 The polynomial x 4 x 10 x 21 is denoted by ( )x f . - + - (a) Use the factor theorem to show that ( x 3 ) is a factor of ( )x f . [2] - 2 (b) The polynomial
June 2024, AS Paper 2, Q1 (3 marks): + 2 1 Express 2 x x ( 3 ) 5 x 2 ( x 3 ) in the form ax bx + , where a, b and c are integers to be c + + - - determined. [3]
June 2024, AS Paper 2, Q2 (3 marks): - 2 (a) Find the discriminant of the equation x 3 2 x 5 0 . [2] + = 2 - (b) Use your answer to part (a) to find the number of real roots of the equation x 3 2 x
June 2024, AS Paper 2, Q4 (3 marks): In this question you must show detailed reasoning. 1 4 3 + Express 2 in the form a b 3 , where a and b are integers to be determined. [3] + 3 +
June 2024, AS Paper 2, Q8 (4 marks): In this question you must show detailed reasoning. Determine the coordinates of the point of intersection of the line with equation y 2 x + and the 3 = 2 2 curv
June 2024, AS Paper 2, Q13 (5 marks): 2 13 Determine the range of values of x for which y 4 x 7 x 6 x + is a decreasing function. 8 [5] = + -
June 2023, Paper 1, Q2 (4 marks): x 1 + 2 Express x in partial fractions. [4] 2 - - x 12
June 2023, Paper 1, Q7 (7 marks): Determine the exact distance between the two points at which the line through (4, 5) and (6, -1) 2 meets the curve y 2 x 7 x + . 1 [7] = -
June 2023, Paper 2, Q3 (3 marks): In this question you must show detailed reasoning. 3 d n - 64 m 2 Find the smallest possible positive integers m and n such that . [3] = n 49
June 2023, Paper 2, Q12 (4 marks): It is given that 1 • x x x f ( ) , 0 = 2 ! x • g ( ) x , x 3 = 2 x 3 - • 2 h ( ) x x 2 , x . = + ! R (a) Explain why f (x) is not a function. [1] (b) Find gh (x
June 2023, Paper 3, Q2 (4 marks): The straight line y 5 2 x is shown in the diagram. = - y x O (a) On the copy of the diagram in the Printed Answer Booklet, sketch the graph of y 5 2 x . = - [1]
June 2023, Paper 3, Q3 (3 marks): In this question you must show detailed reasoning. 1 1 k Find the value of k such that . [3] + = 5 6 6 7 5 7 + + +
June 2023, Paper 3, Q4 (4 marks): In this question you must show detailed reasoning. 3 2 Find the coordinates of the points where the curve y x 2 x 5 x + crosses the x‑axis. 6 [4] = - -
June 2023, AS Paper 1, Q6 (5 marks): 2 2 6 Show that the expression x 3 x 6 x - can be written in the form ( 5 x 2 )( ax bx c ) + d + - + + + where a, b, c and d are constants to be determined. [5]
June 2023, AS Paper 1, Q9 (9 marks): x 9 The graph shows the function y e . = y x O x 2 x (a) Describe the transformation of the graph of y e that gives the graph of y e . [2] = = x A second functi
June 2023, AS Paper 2, Q2 (3 marks): - 2 2 (a) Express x 6 x + in the form ( 1 x a ) - , where a and b are integers to be determined. [2] b - 2 (b) Hence state the coordinates of the turning point
June 2023, AS Paper 2, Q4 (3 marks): k 4 The equation of a curve is y , where k is a constant. = 2 x The curve passes through the point (2, 1). (a) Find the value of k. [1] (b) Sketch the curve. [2
June 2023, AS Paper 2, Q7 (4 marks): 2 7 (a) Use the factor theorem to show that ( x 2 ) is a factor of x 6 x x 30 . [1] - + - - 3 2 (b) Factorise x 6 x x 30 completely. [3] + - -
June 2023, AS Paper 2, Q11 (5 marks): In this question you must show detailed reasoning. 3 2 The equation of a curve is y 2 x 9 x 24 x - . 8 = + + Show that there are no stationary points on this cu
June 2023, AS Paper 2, Q15 (7 marks): A family is planning a holiday in Europe. They need to buy some euros before they go. The exchange rate, y, is the number of euros they can buy per pound. They
June 2022, Paper 1, Q2 (3 marks): x 13 - 2 Express ( in partial fractions. [3] x x 3 )( 2 ) - +
June 2022, Paper 2, Q16 (15 marks): The equation of a curve is 4 3 2 y x x x x 6 8 21 12 6 . = + - + - (a) In this question you must show detailed reasoning. Determine • The coordinates of the sta
June 2022, Paper 3, Q1 (2 marks): A curve for which y is inversely proportional to x is shown below. y 4 3 2 1 x –4 –3 –2 –1 1 2 3 4 5 6 0 –1 –2 –3 Find the equation of the curve. [2]
June 2022, Paper 3, Q2 (6 marks): The function ( ) f x x is defined on the domain x 0 . = H 2 The function ( ) g x 25 x is defined on the domain R. = - (a) Write down an expression for fg x . (
June 2022, Paper 3, Q7 (12 marks): 7 A student is trying to find the binomial expansion of 1 x . - 3 6 x x She gets the first three terms as 1 . - + 2 8 3 3 6 x x x 3 She draws the graphs of the
June 2022, Paper 3, Q8 (16 marks): 3 8 The curves y h ( ) x and y h - ( ) x , where ( ) h x x - , are shown below. 8 = = = The curve y h ( ) x crosses the x-axis at B and the y-axis at A. = 1 The
June 2022, Paper 3, Q12 (5 marks): a k. r 12 (a) Show that cos x sin x [2] = + 2 16 x ( x ) 2 2 r - 4 x r - (b) Hence show that sin x gives the approximation cos x , as stated . . 2 2 2 x x x 5 4
June 2022, AS Paper 1, Q1 (3 marks): n + 1 Rationalise the denominator of the fraction ,n where n is a positive integer. [3] 3 +
June 2022, AS Paper 1, Q4 (6 marks): 4 The quadratic function ( )x f is given by ( ) f x x 3 x 2 . = - + 2 (a) Write ( )x f in the form ( x a ) b , where a and b are constants. [2] + + (b) Write do
June 2022, AS Paper 1, Q5 (6 marks): Part of the graph of y f ( ) x is shown below. The graph is the image of y tan x ° after a stretch in = = the x-direction. y 15 10 5 x -60 0 60 -5 -10 -15 (a) F
June 2022, AS Paper 1, Q6 (8 marks): d y 2 6 x x The curve passes through the The gradient of a curve is given by the equation 6 20 6 . = - + d x point (2, 6). (a) Find the equation of the curve. [
June 2022, AS Paper 1, Q8 (7 marks): A team of volunteers donates cakes for sale at a charity stall. The number of cakes that can be sold y x where y cakes can be sold when the price depends on the
June 2022, AS Paper 2, Q2 (4 marks): - 2 (a) Factorise x 3 19 x 14 . [2] - 2 (b) Solve the inequality x 3 19 x 14 1 0 . [2] - -
June 2022, AS Paper 2, Q7 (7 marks): (a) On the pair of axes in the Printed Answer Booklet, sketch the graphs of • y 2 x 4 = + 2 • y [2] = x (b) Determine the x-coordinates of the points of interse
June 2022, AS Paper 2, Q9 (10 marks): 9 The equation of a curve is y 12 x 4 x . = - 2 (a) State the coordinates of the intersection of the curve with the y-axis. [1] (b) Find the value of y when x 9
June 2022, AS Paper 2, Q10 (9 marks): In this question you must show detailed reasoning. 3 2 The equation of a curve is y 12 x 24 x 60 x 72 . = - - + Determine the magnitude of the total area bounde
November 2021, Paper 1, Q3 (5 marks): 3 (a) The diagram shows the line y x + and the curve y 5 8 2 x x . The shaded region is the = = - - finite region between the line and the curve. The curved par
November 2021, Paper 2, Q1 (2 marks): 1 The equation of a curve is y 4 x 8 x + . 1 = + The curve is stretched parallel to the x-axis with scale factor 2. 2 Find the equation of the new curve, giving
November 2021, Paper 2, Q3 (3 marks): Draw a number line to show the values of x which belong to the set { : x x 2 } { : x x 1 7 } . [3] H +
November 2021, Paper 2, Q4 (3 marks): Sketch the graph of y 2 x 3 . [3] = -
November 2021, Paper 3, Q1 (5 marks): + 2 1 (a) Express x 8 x + in the form ( 2 x a ) + . b [2] + 2 (b) Write down the coordinates of the turning point of the curve y x 8 x + . 2 [1] = + x2 2 (c) St
November 2021, Paper 3, Q3 (7 marks): (a) Determine, in terms of k, the coordinates of the point where the lines with the following equations intersect. x y k + = [3] 2 x y 1 - = (b) Determine, in t
November 2021, Paper 3, Q6 (4 marks): In this question you must show detailed reasoning. 3 1 =/ Show that 1 . [4] = r r 1 + + r 1
November 2021, Paper 3, Q8 (3 marks): a 8 For a particular value of a, the curve y passes through the point (3, 1). = 2 x Find the coordinates of all the other points on the curve where both the x-c
November 2021, Paper 3, Q9 (11 marks): The diagram shows the curve y 3 x . = - y 5 4 3 2 1 x –1 0 1 2 3 4 5 6 7 8 –1 –2 (a) Draw the line y 5 x - on the copy of the diagram in the Printed Answer Book
November 2021, Paper 3, Q10 (9 marks): 10 (a) Express ( in partial fractions. [3] 4 x 1 )( x 1 ) + + (b) A curve passes through the point (0, 2) and satisfies the differential equation d y y , = d x
November 2021, AS Paper 1, Q5 (5 marks): The diagram shows the triangle ABC in which AC 13 cm and AB is the shortest side. The = 4 perimeter of the triangle is 32 cm. The area is 24cm2 and sinB . = 5 A
November 2021, AS Paper 1, Q8 (12 marks): In this question you must show detailed reasoning. (a) Use differentiation to find the coordinates of the stationary point on the curve with equation 2 y 2 x 3
November 2021, AS Paper 1, Q9 (9 marks): (a) Sketch both of the following on the axes provided in the Printed Answer Booklet. 12 (i) The curve y , stating the coordinates of at least one point on the c
November 2021, AS Paper 1, Q11 (10 marks): On the day that a new consumer product went on sale (day zero), a call centre received 1 call about it. On the 2nd day after day zero the call centre received 3
November 2021, AS Paper 2, Q13 (9 marks): In this question you must show detailed reasoning. 7 3 The equation of a curve is y 3 x . = + - x 2 x Determine the coordinates of the points on the curve where
November 2020, Paper 1, Q1 (2 marks): c m 4 2 c 27 m x 1 Simplify 3 . [2] # 9 9 x
November 2020, Paper 1, Q2 (3 marks): Express a 2 + 2 in the form p q 2 , giving p and q in terms of a. [3] + 3 2 - J N J N 3 1 -
November 2020, Paper 1, Q7 (6 marks): In this question you must show detailed reasoning. 3 2 The function ( )x f is defined by ( )x f x x 8 x 12 for all values of x. = + - - (a) Use the factor theor
November 2020, Paper 2, Q15 (7 marks): Functions f (x) and g (x) are defined as follows. 3 f ( )x x for x 2 0 and ( )x g x - - for x 2 2. x 6 = = The function h (x) is defined as h (x) = fg (x). (a)
November 2020, Paper 3, Q2 (4 marks): The graph of y 1 x - is shown in Fig. 2. 2 = - y x O Fig. 2 Determine the set of values of x for which 1 x 2 2 . [4] -
November 2020, Paper 3, Q7 (9 marks): 1 7 (a) Express x - as a single fraction. [1] + A x The population of fish in a lake is modelled by the differential equation d x x ( 400 x ) - d = t 400 where
November 2020, AS Paper 1, Q11 (9 marks): In this question you must show detailed reasoning. 1 1 (a) A student is asked to solve the inequality x 4 . 2 1 + The student argues that x 1 4 x 1 16 , so that
November 2020, AS Paper 2, Q1 (2 marks): Solve the inequality x 2 5 1 6 x - . 3 [2] +
November 2020, AS Paper 2, Q7 (8 marks): In this question you must show detailed reasoning. A circle has centre (2, - 1) and radius 5. A straight line passes through the points (1, 1) and (9, 5). Find
June 2019, Paper 1, Q10 (7 marks): 10 (a) Express cos 7 x 2 sin x in the form R cos ( x ) where R 2 0 and 0 1 1 r, giving the - + a a 2 exact value of R and the value of a correct to 3 significan
June 2019, Paper 2, Q7 (5 marks): 288cm2. The angle of the sector is i radians and the radius of 7 The area of a sector of a circle is . the circle is r cm. (a) Find an expression for i in terms
June 2019, Paper 2, Q9 (9 marks): You are given that f ( ) x 2 x 3 for x 1 0 and = + + 2 g ( ) x x 2 x 1 for x 2 1 . = - (a) Find gf ( )x , stating the domain. [3] (b) State the range of gf ( )x
June 2019, Paper 3, Q1 (6 marks): The function ( )x f is defined for all real x by f ( ) x 3 x 2 . = - 1 (a) Find an expression for f - ( )x . [2] 1 (b) Sketch the graphs of y f ( ) x and y f -
June 2019, Paper 3, Q2 (5 marks): x2 2 2 (a) Find the transformation which maps the curve y to the curve y x 8 x - . 7 [4] = = + 2 (b) Write down the coordinates of the turning point of y x 8 x
June 2019, Paper 3, Q3 (6 marks): 3 (a) Express ( in partial fractions. [3] x 2 )( x 3 ) + + < ^ h 1 (b) Find ( d x in the form ln f ( ) x c , where c is the constant of integration and ( ) f x
June 2019, Paper 3, Q4 (3 marks): In this question you must show detailed reasoning. 1 1 1 3 Show that 10 . [3] + + = 11 11 12 12 13 10 13 + + + +
June 2019, Paper 3, Q13 (6 marks): (a) (i) Show that the cross-sectional area in Fig. C3.2 is x ( 2 r x ) . [2] - r 2 r r 2 2 (ii) Hence show that the cross-sectional area is ( h y ), as given in
June 2019, AS Paper 1, Q1 (3 marks): In this question you must show detailed reasoning. 2 2 Show that the equation x 7 x has no real roots. [3] = +
June 2019, AS Paper 1, Q3 (4 marks): k 3 2 - in the form a 3 Given that k is an integer, express b 2 where a and b are rational + 8 1 + expressions in terms of k. [4]
June 2019, AS Paper 1, Q7 (11 marks): In this question you must show detailed reasoning. 3 - (a) Nigel is asked to determine whether ( x 7 ) is a factor of x 37 x 84 . He substitutes x 7 + + = 3 and
June 2019, AS Paper 1, Q11 (11 marks): David puts a block of ice into a cool-box. He wishes to model the mass m kg of the remaining block of ice at time t hours later. He finds that when t = 5, m = 2
June 2019, AS Paper 2, Q1 (3 marks): = 1 Solve the equation x 4 - 7 , giving your answer as a fraction in its lowest terms. [3] 2
June 2019, AS Paper 2, Q3 (3 marks): Without using a calculator, prove that 3 2 [3] 2 2 3 .
June 2018, Paper 1, Q1 (3 marks): 2 1 x is a factor of x x x [3] Show that ( 2 ) 3 8 3 + . 2 - - +
June 2018, Paper 2, Q1 (2 marks): Show that a b , where a and b are prime numbers to be determined. [2] 27 192 + =
June 2018, Paper 2, Q2 (3 marks): Solve the inequality x [3] 2 1 1 5 . +
June 2018, Paper 2, Q5 (3 marks): (i) (A) Sketch the graph of y = 3x. 5 [1] (B) Give the coordinates of any intercepts. [1] The curve y = f(x) is the reflection of the curve y = 3x in the line y
June 2018, Paper 2, Q16 (11 marks): In the first year of a course, an A-level student, Aaishah, has a mathematics test each week. The night before each test she revises for t hours. Over the cours
June 2018, Paper 2, Q17 (12 marks): ^ h in partial fractions. 2 (i) Express x 8 x 9 - + 17 [5] ^ ^h h 2 x 1 x 2 + - (ii) Express y in terms of x given that ^ h 2 d y y x 8 x 9 - + and y = 16 when
June 2018, Paper 3, Q2 (2 marks): c 1 m. Write down the equation of the translated curve. [2] 3 2 The curve y x 2 x is translated by the vector = - 4 -
June 2018, Paper 3, Q4 (10 marks): In this question you must show detailed reasoning. 1 A curve has equation y x 5 - . The curve is shown in Fig. 4. = - + x 2 y x O Fig. 4 (i) Determine the coord
June 2018, Paper 3, Q7 (8 marks): In this question you must show detailed reasoning. 2 Fig. 7 shows the curve y 5 x x . = - y x O Fig. 7 2 The line y kx crosses the curve y x x on the x-axis and
June 2018, Paper 3, Q9 (4 marks): x e 9 The function ( )x is defined on the domain x x f , 0 . R ! = d x 1 e - f 1 (i) Find ( )x [3] - . f 1 (ii) Write down the range of ( )x [1] - . a 4
June 2018, Paper 3, Q10 (10 marks): f p where a and b can vary, point B has position vector f p and point C has 10 b Point A has position vector 2 0 0 2 f p. ABC is an isosceles triangle with AC =
June 2018, AS Paper 1, Q1 (2 marks): 1 in the form a b 5 , where a and b are integers to be found. [2] Write 3 + 5 -
June 2018, AS Paper 1, Q6 (5 marks): In this question you must show detailed reasoning. ^ h 3 You are given that f x 4 x 3 x 1 . = - + ^ h is a factor of f x^ h. (i) Use the factor theorem to show
June 2018, AS Paper 1, Q8 (8 marks): In this question you must show detailed reasoning. Fig. 8 shows the graph of a quadratic function. The graph crosses the axes at the points (-1, 0), (0, -4) and
June 2018, AS Paper 1, Q9 (9 marks): ^ h maps onto the curve C1 following a stretch scale factor 2 1 2 1 in the x-direction. 9 The curve y x = - 2 (i) Show that the equation of C1 can be written as
June 2018, AS Paper 2, Q5 (3 marks): Find the set of values of a for which the equation 2 + ax x 8 2 0 + = [3] has no real roots.

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