Hits: 80

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/11) | Q#11

Hits: 80 Question The diagram shows a shaded region bounded by the y-axis, the line y = −1 and the part of the  curve  y = x2 + 4x + 3 for which x ≥ −2. i. Express y=x2+4x+3 in the form y=(x+a)2+b, where a and b are constants. Hence, for x ≥ −2,  express […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/11) | Q#10

Hits: 47 Question Relative to an origin O, the position vectors of points A, B, C and D, shown in the diagram, are given  by are given by and i.       Show that AB is perpendicular to BC. ii.       Show that ABCD is a trapezium. iii.       Find the area of ABCD, giving your answer correct to […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/11) | Q#9

Hits: 63 Question A curve for which passes through the point (2,3).      i.       Find the equation of the curve.     ii.      Find .  iii.      Find the coordinates of the stationary point on the curve and, showing all necessary working,  determine the nature of this stationary point. Solution i.   We […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/11) | Q#8

Hits: 87 Question The diagram shows a sector OAC of a circle with centre O. Tangents AB and CB to the circle meet  at B. The arc AC is of length 6 cm and angle  radians. i.       Find the length of OA correct to 4 significant figures.    ii.       Find the perimeter of the shaded […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/11) | Q#7

Hits: 76 Question The functions f and g are defined by  for  for . i.       Find the range of f and the range of g.    ii.       Find an expression for fg(x), giving your answer in the form  , where a, b and c are  integers.  iii.      Find an expression for , giving your answer […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/11) | Q#6

Hits: 44 Question A straight line has gradient  and passes through the point (0, −2). Find the two values of for  which the line is a tangent to the curve y = x2 − 2x + 7 and, for each value of , find the coordinates  of the point where the line touches the curve. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/11) | Q#5

Hits: 47   Question     i.      Given that , show, without using a calculator, that .    ii.       Hence, showing all necessary working, solve the equation  for Solution i.   We are given that; Since ; We have the trigonometric identity; From this we can write; Therefore; Let ; Now we have two options. Since […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/11) | Q#4

Hits: 43 Question A runner who is training for a long-distance race plans to run increasing distances each day for 21  days. She will run km on day 1, and on each subsequent day she will increase the distance by  10% of the previous day’s distance. On day 21 she will run 20 km.       […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/11) | Q#3

Hits: 39 Question The line y = ax + b is a tangent to the curve y = 2×3 − 5×2 − 3x + c at the point (2, 6). Find the  values of the constants a, b and c. Solution We are given equation of the line as; We are given equation of the […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/11) | Q#2

Hits: 34 Question An increasing function, , is defined for x > n, where n is an integer. It is given that . Find the least possible value of n.  Solution We are given derivative of the function as; We are also given that it is an increasing function. To test whether a function is […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2019 | Oct-Nov | (P1-9709/11) | Q#1

Hits: 63 Question Find the term independent of in the expansion of . Solution Expression for the general term in the Binomial expansion of is: In the given case: Hence; Since we are looking for the coefficient of the term independent of i.e. , so we can equate; Hence, substituting ; Becomes; Hence coefficient of […]