Free Printable AM Final Revision

1.

Is $\frac{x+4}{2x+7}$ a proper fraction or an improper fraction?

a)

Proper

b)

Improper

2.

$a^3+b^3=\ ?$

a)

$\left(a+b\right)\left(a^2+ab+b^2\right)$

b)

$\left(a+b\right)\left(a^2-ab+b^2\right)$

c)

$\left(a+b\right)\left(a^2+2ab+b^2\right)$

d)

$\left(a+b\right)\left(a^2-2ab+b^2\right)$

3.

$a^3-b^3=\ ?$

a)

$\left(a-b\right)\left(a^2+ab+b^2\right)$

b)

$\left(a-b\right)\left(a^2-ab+b^2\right)$

c)

$\left(a-b\right)\left(a^2+2ab+b^2\right)$

d)

$\left(a-b\right)\left(a^2-2ab+b^2\right)$

4.

For a quadratic function, f(x), to lie completely above the x-axis (assume coefficient of x² > 0),

a)

discriminant < 0

b)

discriminant = 0

c)

discriminant > 0

d)

discriminant $\ge0$

5.

For a quadratic function, f(x), to lie completely below/above the x-axis,

a)

discriminant < 0

b)

discriminant = 0

c)

discriminant > 0

d)

discriminant $\ge0$

6.

If a curve and a line intersect at only one point,

a)

discriminant < 0

b)

discriminant = 0

c)

discriminant > 0

d)

discriminant $\ge0$

7.

If a curve $y=\left(x-3\right)^2+5$ and a straight line intersect at only one point, but the line is not a tangent to the curve,

a)

the line is a horizontal line

b)

the line is a vertical line

c)

the line has gradient = 0

d)

the line has gradient = 1

8.

Solve the inequality $x^2-4<0$

a)

x = -2 or x = 2

b)

x < -2 or x < 2

c)

x < -2 or x > 2

d)

-2 < x < 2

9.

y = |x|-1 and y = 0 intersect at

a)

0 points

b)

1 point

c)

2 points

d)

3 points

10.

y = |x - 1| and y = 0 intersect at

a)

0 points

b)

1 point

c)

2 points

d)

3 points

11.

$9C_2=\ ?$ (Read as 9 Choose 2)

a)

$9C_7$

b)

$9C_0+9C_1$

c)

$9C_0\times9C_1$

d)

$2C_9$

12.

$\sqrt{12}\times\sqrt{3}\div\sqrt{4}=\ ?$

a)

3

b)

$\sqrt{3}$

c)

$\sqrt{4}$

d)

4

13.

$\log_2\left(x-11\right)$ can have __ value(s) when x is negative

a)

negative

b)

positive

c)

negative and positive

d)

no real

14.

$\log_2\left(7x\right)$ can have __ value(s) when x is positive

a)

negative

b)

positive

c)

negative and positive

d)

no real

15.

Differentiate tan x = ?

a)

$\frac{1}{\cos^2x}$

b)

$\sin x\cos x$

c)

$-\sin x\cos x$

d)

$\frac{1}{\operatorname{cosec}^2x}$

16.

Differentiate x(ln x) = ?

a)

ln x + 1

b)

ln x - 1

c)

1/x + 1

d)

1/x - 1

17.

Integrate 3 (with respect to x) = ?

a)

0

b)

c

c)

3x

d)

3x + c

18.

Integrate 2x (with respect to x) = ?

a)

2 + c

b)

x + c

c)

x² + c

d)

2x² + c

19.

A point P(1,0) lies on a function, f(x). d²y/dx² = 0 means that

a)

stationary point exists at (1,0)

b)

point of inflexion exists at (1,0)

c)

line of symmetry exists at (1,0)

d)

no conclusion can be made

20.

y²=2x is drawn on the same Cartesian plane as y=2^x . How many points of intersection are there?

a)

0

b)

1

c)

2

d)

3

AM Final Revision

Total questions: 20

Worksheet time: 11mins

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