Edexcel Core Mathematics C1 May 2016
Questions and Worked Solutions for C1 Edexcel Core Mathematics May 2016.
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4. Figure 1 shows a sketch of part of the curve with equation y = f(x). The curve has a maximum point A at (–2, 4) and a minimum point B at (3, –8) and passes through the origin O.
On separate diagrams, sketch the curve with equation
(a) y = 3f(x)
(b) y = f(x) – 4
On each diagram, show clearly the coordinates of the maximum and the minimum points and the coordinates of the point where the curve crosses the y-axis.
5. Solve the simultaneous equations
y + 4x + 1 = 0
y2 + 5x2 + 2x = 0
8. The straight line with equation y = 3x – 7 does not cross or touch the curve with equation y = 2px2 – 6px + 4p, where p is a constant.
(a) Show that 4p2 – 20p + 9 < 0
(b) Hence find the set of possible values of p.
9. On John’s 10th birthday he received the first of an annual birthday gift of money from his uncle. This first gift was £60 and on each subsequent birthday the gift was £15 more than the year before. The amounts of these gifts form an arithmetic sequence.
(a) Show that, immediately after his 12th birthday, the total of these gifts was £225
(b) Find the amount that John received from his uncle as a birthday gift on his 18th birthday.
(c) Find the total of these birthday gifts that John had received from his uncle up to and including his 21st birthday.
When John had received n of these birthday gifts, the total money that he had received from these gifts was £3375
(d) Show that n2 + 7n = 25 × 18
(e) Find the value of n, when he had received £3375 in total, and so determine John’s age at this time.
10. The points P(0, 2) and Q(3, 7) lie on the line l1, as shown in Figure 2. The line l2 is perpendicular to l1, passes through Q and crosses the x-axis at the point R, as shown in Figure 2.
Find
(a) an equation for l2, giving your answer in the form ax + by + c = 0, where a, b and c are integers,
(b) the exact coordinates of R,
(c) the exact area of the quadrilateral ORQP, where O is the origin.
11. The curve C has equation y = 2x3 + kx2 + 5x + 6, where k is a constant.
(a) Find dy/dx
The point P, where x = –2, lies on C.
The tangent to C at the point P is parallel to the line with equation 2y – 17x – 1 = 0
Find
(b) the value of k,
(c) the value of the y coordinate of P,
(d) the equation of the tangent to C at P, giving your answer in the form ax + by + c = 0, where a, b and c are integers.
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Edexcel Core Mathematics C1 May 2016 Past Paper
2. Express 93x + 1 in the form 3y, giving y in the form ax + b, where a and b are constants.4. Figure 1 shows a sketch of part of the curve with equation y = f(x). The curve has a maximum point A at (–2, 4) and a minimum point B at (3, –8) and passes through the origin O.
On separate diagrams, sketch the curve with equation
(a) y = 3f(x)
(b) y = f(x) – 4
On each diagram, show clearly the coordinates of the maximum and the minimum points and the coordinates of the point where the curve crosses the y-axis.
5. Solve the simultaneous equations
y + 4x + 1 = 0
y2 + 5x2 + 2x = 0
8. The straight line with equation y = 3x – 7 does not cross or touch the curve with equation y = 2px2 – 6px + 4p, where p is a constant.
(a) Show that 4p2 – 20p + 9 < 0
(b) Hence find the set of possible values of p.
9. On John’s 10th birthday he received the first of an annual birthday gift of money from his uncle. This first gift was £60 and on each subsequent birthday the gift was £15 more than the year before. The amounts of these gifts form an arithmetic sequence.
(a) Show that, immediately after his 12th birthday, the total of these gifts was £225
(b) Find the amount that John received from his uncle as a birthday gift on his 18th birthday.
(c) Find the total of these birthday gifts that John had received from his uncle up to and including his 21st birthday.
When John had received n of these birthday gifts, the total money that he had received from these gifts was £3375
(d) Show that n2 + 7n = 25 × 18
(e) Find the value of n, when he had received £3375 in total, and so determine John’s age at this time.
10. The points P(0, 2) and Q(3, 7) lie on the line l1, as shown in Figure 2. The line l2 is perpendicular to l1, passes through Q and crosses the x-axis at the point R, as shown in Figure 2.
Find
(a) an equation for l2, giving your answer in the form ax + by + c = 0, where a, b and c are integers,
(b) the exact coordinates of R,
(c) the exact area of the quadrilateral ORQP, where O is the origin.
11. The curve C has equation y = 2x3 + kx2 + 5x + 6, where k is a constant.
(a) Find dy/dx
The point P, where x = –2, lies on C.
The tangent to C at the point P is parallel to the line with equation 2y – 17x – 1 = 0
Find
(b) the value of k,
(c) the value of the y coordinate of P,
(d) the equation of the tangent to C at P, giving your answer in the form ax + by + c = 0, where a, b and c are integers.
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