Diagnostic Quiz Level 3

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Name and Surname

Level

Intermediate 2 or A'Level 2

Email Address

If f(x) = x^3 + 3x - 4, give a factor for f(x)

x - 2

x + 4

x -1

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Give the sum of roots for the polynomial: 2x^2 - 3x + 4

2/3

3/2

-3/2

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Simplify to a single log: 2 log a + 4 log b - 3 log b

log (a^2 b)

log (2a + 4b) / 3b

(2a * 4b )/ b^3

2 (log a + 2 log b) - 3 log b

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Solve e^2x + 3 e^x - 4 = 0

x = 1, x = 0

x = 0, x = -4

x = 0

x = e, x = 0

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Rationalize: [8 - sqrt(5)] / [3 + sqrt (5)]

sqrt(5) means square root of 5

29/4 - 11/4 (sqrt(5)

8/3 sqrt (5)

5 sqrt (5)

10 - 1/3 sqrt (5)

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By using pascal's triangle, give the coefficient of x^2 in the expansion: (x + 2) ^4

-24

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Find the possible values of the constant k, if the quadratic equation x^2 + k^2 = (k+1)x has equal roots

k = 0, 1

k = 1/3 , -1

k = 1/3, 0

k = -1/3, 1

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The function f(x) is defined by f(x) = x^2 + 8x + 23. Find the value of the constants a and b if f(x) = (x + a) ^2 + b

4, 7

2, 4

4, 0

-7, 0

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Find the range of the function f(x) = x^2 + 1

f(x) < -1

f(x) > 0

f(x) > 1

f(x) < 1

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Solve the inequality: [ (4 - x) / x ] > -2

x < 0 x > -4

x > 0 x > - 4

x < 1 x < -4

x > 0 x < -4

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A, B and C are three points with coordinates (2,5) (8, -1) and (5, 2) respectively. Find the equation of the line that passes through C and is perpendicular to AB

y = x + 3

y = x - 3

y = -x + 3

y = 2x

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Solve the equation: 4 Sec^2 (x) = 3 tan (x) + 5 for x between 0 and 2pi

pi = 3.142....

pi/ 4 5pi / 4, 4.567, 1.345

2.897, 6.038 and pi / 4

pi/ 4, 5pi / 4, 3.897 and 2.897

pi/ 4, 5pi/4, 2.897 and 6.038

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if sin^2 (x) = 8/9 and x is obtuse, find without using a calculator, cos (x)

1/2

9/8

-1/3

1/3

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Find the Area of a sector if its radius is 20cm and the perimeter is 110cm

700

7/2

900

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Find the perpendicular distance between the point (3, -4) and the line 3y = 2x - 12

sqrt (13)

6 * sqrt (13)

12/ sqrt (13)

6/ sqrt (13)

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Find the area of triangle ABC where AC = 10 BC = 7 and angle C is 25 degrees

14.8

13.5

10.9

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If tan (x) = a find a^2 Cosec^2 (x) in terms of a

1 + a^2

1/a^2

[a^2 + 1 ]/ a^2

1 - 1/a^2

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Simplify the expression: tan^2 (x) - sin ^2 (x)

2 sin (x)

cos (x) sin (x)

sin ^2 (x) tan ^2 (x)

tan (x)

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Find the intersection of the lines: 3x + y = 7 and 2x - y = 3

(4, 5)

(2, 1)

(1, 5)

(5, 4)

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Find the intersection point of the line y = 2x + 3 and the curve x^2 + 3x + 1

(1, 5) ( 0,3)

(0,1) (1, 3)

(-2, -1)

(1, 5) ( -2, -1)

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Differentiate 2x^3 + x^2 + 4

6x^3 + 2x^2

6x^2 + 2x + 4x

6x^2 + 2x

2x^2 + x

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Differentiate 2 Cos (x)

2 Sin (x)

-2 SIn (x)

Cos (x)

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Differentiate e ^ (4x + 2)

4e^ (4x + 2)

4 e

4x + 2 e ^ (4x + 1)

4x + 2

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Differentiate 4x Sin (3x)

4x Sin x

4 Cos 3x

4 Sin 3x + 12x Cos 3x

4x Sin 3x + 4 Cos 3x

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Differentiate Tan (x)

Sin (x) / Cos (x)

Sec ^2 (x)

Cot (x)

2 Tan ^2 (x)

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What is the gradient of the curve y = x^4 + x^2 + 4 at the point x = 0

4x^3 + 2x

-1

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What are the coordinates of the turning points of the curve: [(x^3) / 3] - 2x^2 + 3x

x^2 - 4x + 3

(3, 0 ) (1, 4/3 )

(1, 3)

(0,0) (3,0)

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One of the turning Points of 4x^3 + 2x^2 is (0,0). Find the nature of this turning point

Minima

Maxima

Point of Inflection

None of the above

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Find the maximum Area of a rectangle if its perimeter is to be 400 mm

100

20000

30000000

10000

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Find the equation of the normal at the point (1,3) on the curve y = x^2 + 2x

y = x - 2

y = x + 2

4y = 13 - x

y = 2x + 2

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