Free Printable G11 AAHL Mixed Units 1 and 2 (Oxford)

1.

Write the explicit formula for the geometric sequence.

a)

a_n = 4(3)^n-1

b)

a_n = 3(4)^n-1

c)

a_n = -4(3)^n-1

d)

a_n = 3(-4)^n-1

2.

Given the sequence:

125, 25, 5, ....

Write the rule a_n using the geometric sequence formula:

a)

a_n = (125)(1/5)^(n-1)

b)

a_n = 625(1/5)^(n-1)

c)

a_n = 625(5)^(n-1)

d)

a_n = 125 + 5n

3.

Calculate the final sum/total of the series.

a)

6

b)

21

c)

9

d)

2

4.

Find the sum to infinity of $9,3,1,...$

a)

$\frac{27}{2}$

b)

$\frac{3}{7}$

c)

$0.45$

d)

$1.56$

5.

Let a_n be the nth term of a geometric sequence. If a₂ = 576 and a₄ = 324, which of the following must be true?

I. a₈ ÷ a₉ > 1

II. a₅ ÷ a₇ > 1

III. a₁ > 0

a)

I only

b)

II only

c)

I and III only

d)

II and III only

6.

Find the term containing $m^5$ in the expansion of $\left(2m+3\right)^7$

a)

$6048m^5$

b)

$288m^5$

c)

$2016m^5$

d)

$20412m^5$

7.

The term independent of x in the expansion of $\ \left(x^3+\frac{3}{x^2}\right)^{15}\$ is

a)

$\ ^{15}C_9\left(3\right)^9$

b)

$\ ^{15}C_6\left(3\right)^6$

c)

$\ ^{15}C_9\left(3\right)^4$

d)

$\ ^{15}C_9\left(3\right)^7$

8.

Which expression represents g(f(x)) if
f(x) = 2x - 8 and
g(x) = 4x

a)

8x - 32

b)

8x² - 32x

c)

8x - 8

d)

6x - 8

9.

a)

9 - √17

b)

4

c)

2

d)

√8

10.

$h\left(x\right)=-\frac{2}{x-1}-3$
Find the inverse of the function.

a)

$h^{-1}\left(x\right)=\frac{2}{-x-3}+1$

b)

$h^{-1}\left(x\right)=-\frac{2}{x+2}-1$

c)

$h^{-1}\left(x\right)=\frac{2}{-x+3}$

d)

$h^{-1}\left(x\right)=\frac{3}{-x-3}-2$

11.

What is the range of the graph?

a)

1 ≤ x ≤ 5

b)

1 < x < 5

c)

1 ≤ y ≤ 5

d)

1 < y < 5

12.

What is the RANGE of the function?

a)

(-∞, +∞)

b)

(-∞, -3) U (-3, +∞)

c)

(-∞, 2] U [3, +∞)

d)

(-∞, 3] U [3, +∞)

13.

The blue function is the original function f(x) = x³. Which of the following is the correct equation for the red function, g(x)?

a)

$g\left(x\right)=x^3+1$

b)

$g\left(x\right)=x^3-1$

c)

$g\left(x\right)=\left(x-1\right)^3$

d)

$g\left(x\right)=\left(x+1\right)^3$

14.

$3f\left(x-2\right)$ Identify the transformations.

a)

horizontal shift to the left 2 and vertical stretch by a factor of 3

b)

horizontal shift to the right 2 and vertical stretch by a factor of 3

c)

horizontal shift to the right 2 and vertical shrink by a factor of 3

d)

horizontal shift to the left 2 and vertical shrink by a factor of 3

15.

$f\left(x\right)$ is transformed so that it maps onto $g\left(x\right)$ . Which equation would correctly represent $g\left(x\right)$ ?

a)

$g(x)=2f(x)$

b)

$g(x)=\frac{1}{2}f(x)$

c)

$g(x)=f(x)+2$

d)

$g(x)=f(x+2)$

16.

Select the graph that show the corresponding vertical & horizontal asymptotes to this function

a)

b)

c)

d)

17.

What's the vertical asymptote of the function?

a)

x = -9

b)

x = 9

c)

x = 3 , x = -3

d)

x = 3

18.

What is the domain?

a)

x ≠ 3

b)

x ≠ -1

c)

x ≠ 3, -1

d)

x ≠ 3, 1

19.

What are the coordinates of the y-intercept, if one exists.

a)

(0, 0)

b)

(0, 1)

c)

(0, -1)

d)

there isn't one

20.

What assumption would you make to start the proof by contradiction of:

there can be only one 90 angle in a triangle

a)

here can be more than one 90 angle in a triangle

b)

<a+<b+<c=180

c)

<a+<b+<c≠180

d)

all the angles in a triangle add up to 180.

G11 AAHL Mixed Units 1 and 2 (Oxford)

Total questions: 20

Worksheet time: 47mins

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