OCR MEI C1 2006 January — Question 3 4 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Year2006
SessionJanuary
Marks4
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Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeStandard binomial expansion
DifficultyEasy -1.8 This is a straightforward application of the binomial theorem with a small positive integer exponent (n=4), requiring only direct substitution into the formula and basic arithmetic. It's a routine drill exercise testing recall of the binomial expansion method with no problem-solving element, making it significantly easier than average A-level questions.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n
Find the binomial expansion of \((2 + x)^4\), writing each term as simply as possible. [4]
Question 3:
3
6- 3
PMT
4
11 (i) Write x2(cid:1)7x(cid:2)6 in the form (x(cid:1)a)2(cid:2)b. [3]
(ii) State the coordinates of the minimum point on the graph of y (cid:3) x2(cid:1)7x(cid:2)6. [2]
(iii) Find the coordinates of the points where the graph of y (cid:3) x2(cid:1)7x(cid:2)6 crosses the axes and
sketch the graph. [5]
(iv) Show that the graphs of y (cid:3) x2(cid:1)7x(cid:2)6 and y (cid:3) x2(cid:1)3x(cid:2)4 intersect only once. Find the
x-coordinate of the point of intersection. [3]
12 (i) Sketch the graph of y (cid:3) x(x(cid:1)3)2. [3]
(ii) Show that the equationx(x(cid:1)3)2 (cid:3) 2 can be expressed as x3(cid:1)6x2(cid:2)9x(cid:1)2 (cid:3) 0. [2]
(iii) Show that x (cid:3) 2 is one root of this equation and find the other two roots, expressing your
answers in surd form.
Show the location of these roots on your sketch graph in part (i). [8]
4751 January 2006
Question 3:
3
6- 3
PMT
4
11 (i) Write x2(cid:1)7x(cid:2)6 in the form (x(cid:1)a)2(cid:2)b. [3]
(ii) State the coordinates of the minimum point on the graph of y (cid:3) x2(cid:1)7x(cid:2)6. [2]
(iii) Find the coordinates of the points where the graph of y (cid:3) x2(cid:1)7x(cid:2)6 crosses the axes and
sketch the graph. [5]
(iv) Show that the graphs of y (cid:3) x2(cid:1)7x(cid:2)6 and y (cid:3) x2(cid:1)3x(cid:2)4 intersect only once. Find the
x-coordinate of the point of intersection. [3]
12 (i) Sketch the graph of y (cid:3) x(x(cid:1)3)2. [3]
(ii) Show that the equationx(x(cid:1)3)2 (cid:3) 2 can be expressed as x3(cid:1)6x2(cid:2)9x(cid:1)2 (cid:3) 0. [2]
(iii) Show that x (cid:3) 2 is one root of this equation and find the other two roots, expressing your
answers in surd form.
Show the location of these roots on your sketch graph in part (i). [8]
4751 January 2006
Find the binomial expansion of $(2 + x)^4$, writing each term as simply as possible. [4]

\hfill \mbox{\textit{OCR MEI C1 2006 Q3 [4]}}
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