[PDF] Level 2 Mathematics and Statistics (91261) 2020

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912610

2

SUPERVISOR"S USE ONLY

Level

Achievement

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You should attempt ALL the questions in this booklet.

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You are required to show algebraic working in this paper. Guess-and-check methods or correct YOU MUST HAND THIS BOOKLET TO THE SUPERVISOR AT THE END OF THE EXAMINATION.

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QUESTION ONE

(a)

Factorise 6

2 - 15. 2 + 22. () in completed square form, i.e. () = ( + ) , where and are integers.

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ASSESSOR'S

(c) In the 16th century, mathematicians were developing a formula to solve any cubic equation. y = x 3

Px + R, where P and R are positive constants.

y = x 3 Px + R, for some values of P and R, passes through the xy

Find an expression for P in terms of R.

4

ASSESSOR'S

(ii) At point B it is true that 3x 2

P = 0.

x = -2࣠ 0.5

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ASSESSOR'S

(iii) Consider again the curve with the equation y = x 3

Px + R. As the values of P and R vary, the

xy P P Some examples of the graphs obtained from various values of P and R are illustrated below. P and R, the curve can intersect the x-axis three times. This will happen

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Find the condition that P and R must satisfy for the graph to have three distinct x-intercepts.

P and R are both positive integers.

ASSESSOR'S

QUESTION TWO

(a) Write as a single logarithm in simplest form: log(9) + log(4) - log(3). (36) = 2. ) + log ) = 4. 8

ASSESSOR'S

(c) Solve the equation: 5+4 +4 34
+1 =2. 9

ASSESSOR'S

(d) Consider two parabolas: y = ax 2 bx + c and y = dx 2 ex + c, where a, b, c, d, and e are constants. a, b, c, d, and e that would ensure

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ASSESSOR'S

QUESTION THREE

(a)

Solve the equation 3

= 30.

W=(x+2)

2 5 , where is a whole number. the subject of the formula W=(x+2) 2 5 will the function have values less than 20?

Please turn over

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ASSESSOR'S

(c) Zahra sells zips. Zahra notices that the higher the price of a zip, the fewer zips are sold. As of zips sold each day started at 98 and is dropping by 3 each day.

Day, 1

Price of a zip ($) = 2d + 5

d 98

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ASSESSOR'S

(ii) Zahra realises that not every whole number is a possible turnover value for a given day. k must satisfy for it to be a

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ASSESSOR'S

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ASSESSOR'S

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ASSESSOR'S

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