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11 Mathematical Methods Models of Growth Test
Page 1 PLEASE TURN OVER
NAME: …………………………………
PART A: NO CALCULATOR
QUESTION 1 5 mark s
Solve algebraically to find the exact value for x:
(a)
(2 marks)
(b)
(3 marks)
11 Mathematical Methods Models of Growth Test
Page 2
QUESTION 2 9 marks
(a) Expand and simplify (where possible):
(i)
(2 marks)
(ii)
(2 marks)
(b) Fully factorise:
(i)
(2 marks)
(ii)
(3 marks)
11 Mathematical Methods Models of Growth Test
Page 3 PLEASE TURN OVER
QUESTION 3 11 marks
(a) Algebraically determine in simplest form:
(i)
(2 marks)
(ii)
(2 marks)
11 Mathematical Methods Models of Growth Test
Page 4
(b) Write the following as a single logarithm or integer:
(i)
(2 marks)
(ii)
(2 marks)
(iii)
(3 marks)
11 Mathematical Methods Models of Growth Test
Page 5 PLEASE TURN OVER
QUESTION 4 10 marks
(a) Show that .
(3 marks)
(b) (i) Simplify
(2 marks)
(ii) Simplify
(2 marks)
(iii) Explain with algebraic working why
(3 marks)
11 Mathematical Methods Models of Growth Test
Page 6
PART B: CALCULATOR ALLOWED
NAME: …………………………………
QUESTION 5 6 marks
Solve algebraically (show all working) for the unknown in the following, giving your answers
correct to 2 decimal places:
(a)
(2 marks)
(b)
(2 marks)
(c)
(2 marks)
11 Mathematical Methods Models of Growth Test
Page 7 PLEASE TURN OVER
QUESTION 6 5 marks
The weight, , grams of radioactive material remaining
after years is given by the formula .
Find:
(a) the initial weight present;
(1 mark)
(b) (i) the amount present after 15 years.
(1 mark)
(ii) the amount present after 30 years.
(1 mark)
(c) How long it would take to decay to a ‘safe level’ of 5% of its original value?
(2 marks)
11 Mathematical Methods Models of Growth Test
Page 8
NAME: …………………………………
PART A: NO CALCULATOR
QUESTION 1 5 mark s
Solve algebraically to find the exact value for x:
(a)
(2 marks)
(b)
(3 marks)
11 Mathematical Methods Models of Growth Test
Page 9 PLEASE TURN OVER
QUESTION 2 9 marks
(a) Expand and simplify (where possible):
(i)
(2 marks)
(ii)
(2 marks)
(b) Fully factorise:
(i)
(2 marks)
(ii)
(3 marks)
QUESTION 3 11 marks
(a) Algebraically determine in simplest form:
(i)
(2 marks)
(ii)
(2 marks)
(b) Write the following as a single logarithm or integer:
(i)
(2 marks)
(ii)
(2 marks)
11 Mathematical Methods Models of Growth Test
Page 10
(iii)
(3 marks)
QUESTION 4 10 marks
(a) Show that .
(3 marks)
(b) (i) Simplify
(2 marks)
(ii) Simplify
(2 marks)
(iii) Explain with algebraic working why
(3 marks)
11 Mathematical Methods Models of Growth Test
Page 11 PLEASE TURN OVER
PART B: CALCULATOR ALLOWED
NAME: …………………………………
QUESTION 5 6 marks
Solve algebraically (show all working) for the unknown in the following, giving your answers
correct to 2 decimal places:
(a)
(2 marks)
(b)
(2 marks)
(c)
(2 marks)
11 Mathematical Methods Models of Growth Test
Page 12
QUESTION 6 5 marks
The weight, , grams of radioactive material remaining
after years is given by the formula .
Find:
(a) the initial weight present;
(1 mark)
(b) (i) the amount present after 15 years.
(1 mark)
(ii) the amount present after 30 years.
(1 mark)
(c) How long it would take to decay to a ‘safe level’ of 5% of its original value?
(2 marks)
