Free Printable REVISION SET B (Matrices & Graph)

1.

Which of the following property of transpose is CORRECT?

a)

$\left(AB\right)^T=A^TB^T$

b)

$\left(AB\right)^T=\left(BA\right)^T$

c)

$A^T=\frac{1}{A}$

d)

$\left(A^T\right)^T=A$

2.

Find the product of the two matrices.

a)

undefined

b)

-3 16
17 12
8 -10

c)

3 12
-15 -8
-1 -3

3.

a)

$1-2b$

b)

$2b-1$

c)

$a-8$

d)

$8-a$

4.

a)

$4$

b)

$-4$

c)

$\frac{1}{4}$

d)

$-\frac{1}{4}$

5.

a)

A

b)

B

c)

C

d)

D

6.

Find $m_{13}$ (minor) and $c_{13}$ (cofactor).

a)

$m_{13}=16,\ \ c_{13}=16$

b)

$m_{13}=16,\ \ c_{13}=-16$

c)

$m_{13}=8,\ \ c_{13}=8$

d)

$m_{13}=8,\ \ c_{13}=-8$

7.

a)

$-\frac{46}{15}$

b)

$-\frac{46}{7}$

c)

$-14$

d)

$14$

8.

Given $B^2-4B=5I$ , where $I$ is $3\times3$ identity matrix. Deduce the inverse of $B$ .

a)

$\frac{1}{4}\left(B-5I\right)$

b)

$\frac{1}{4}\left(5I-B\right)$

c)

$\frac{1}{5}\left(B-4I\right)$

d)

$\frac{1}{5}\left(5I-B\right)$

9.

a)

$2$

b)

$4$

c)

$6$

d)

$8$

10.

a)

A

b)

B

c)

C

d)

D

11.

Which set of values is not a function?

a)

(9,5) (10,5) (4,-5) (8,-5)

b)

(3,4) (4,-3) (7,4) (3, 8)

c)

(6,-5) (7, -3) (8, -1) (9, 1)

d)

(2, -2) (5, 9) (-5, -7) (1, 4)

12.

Given f(x)= -3x+7 and g(x)=2x² - 8, find f(g(x)).

a)

f(g(x))= -6x²+31

b)

f(g(x))= -6x²+24

c)

f(g(x))=18x²-84x+6

d)

f(g(x))=9x²-42x-1

13.

Find the domain and range of the function
Hint: Use a scratch graph to help you visualize things.

a)

Domain: (-∞, ∞) Range: [-∞, 4]

b)

Domain: [1, ∞) Range: (-∞, 4]

c)

Domain: [-1. ∞) Range: [4, ∞)

d)

Domain: [4, ∞) Range: [-1,∞)

14.

Given
$f\left(n\right)=-4-\frac{2}{5}n$ . What is the value of $f^{-1}\left(1\right)$ ?

a)

$-\frac{11}{2}$

b)

$-1$

c)

$-\frac{25}{2}$

d)

$-\frac{6}{5}$

15.

In which of the following graphs is each input not paired with a unique output?

a)

b)

c)

d)

16.

Given $f\left(x\right)=2x+1$ .Find $g\left(x\right)$ if $\left(g\ \circ\ f\right)\left(x\right)=\frac{1+2x}{2+x}$

a)

$\frac{x-1}{2}$

b)

$\frac{2x}{2+x}$

c)

$\frac{1+x}{4+x}$

d)

$\frac{2+x}{x-1}$

17.

Which graph shows inverse functions?

a)

b)

c)

d)

18.

Given $f\left(x\right)=x^2+x+2$ and $g\left(x\right)=\ln\left(x+1\right)$ .Find $\left(g\ \circ\ f\right)\left(1\right)$ .

a)

$0$

b)

$4$

c)

$\ln5$

d)

$\ln7$

19.

Find the range for $f\left(x\right)=x+3\ ,\ \ -1<x\le5$ .

a)

$\left(-\infty,\infty\right)$

b)

$\left(3,\infty\right)$

c)

$\left(2,8\right)$

d)

$\left(2,8\right]$

20.

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

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

21.

What is the domain and range of the function y=2^x?
Use the graph to help!

a)

Domain: All Real Numbers
Range: y>0

b)

Domain: All Real Numbers
Range: y>1

c)

Domain: −2<x<∞
Range: y>0

d)

Domain: −∞<x<∞
Range: y>0

REVISION SET B (Matrices & Graph)

Total questions: 21

Worksheet time: 52mins

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