sat-25-May

In the figure below, AB and GE are parallel. Triangle ACD is isosceles with the lengths of CA and CD equal. The measures of angles FDE and GDH are 60° and 65° respectively. What is the measure of angle CAB?

• 55°

• 6°

• 10°

• 15°

• 5°

If a, b and y are positive real numbers such that none of them is equal to 1 and b ^{2a + 6} = y ², which of these must be true?

• y = b ^{a + 3}

• 2a + 6 = 2

• b = y

• b = 2

• b(2a + 6) = 2y

A number x is divided by 0.71 and the result decreased by 0.2. If the fifth root of the final result equals -0.15, what is the value of x rounded to the nearest thousandth?

• 0.141

• 0.71

• 0.143

• 0.142

• 0.036

Forty students are each registered to study one or more of three courses. 23 students are registered in one course only and 14 students are registered in two courses only. How many are registered in all 3 courses?

• 3

• 11

• 37

• 17

• 26

If the perimeter of a regular hexagon is equal to 6 a, then the area of this hexagon if given by

• 6 a ²

• 3 a ²

• 0.5 √ 3 a ²

• √ 3 a ²

• 1.5 √ 3 a ²

AB is a diameter to the circle in the figure below and point C is on the circle. The measure of the diameter is 10 units and side AC has a length of 5 units. Find the measure of angle CBA

• 28

• 30

• 40

• 45

• 43

For what value of positive k does the equation have one solution only?

(x + k) x = - 4

• 1

• 3/2

• 3

• 4

• 5

The average of the roots of a quadratic equation is equal to 3 and the difference of the roots is equal to 2. Which of these could be the equation?

• x ² - 5x + 6 = 0

• x ² + 5x + 6 = 0

• x ² - 6x + 8 = 0

• x ² + 6x + 8 = 0

The volume of a rectangular solid is equal to 1000 m 3. If the length, width and height are increased by 50%, the volume of the new rectangular solid is equal to

• 3375 m³

• 3500 m³

• 1500 m³

• 5000 m³

• 50000 m³

In the figure below angle ADE is right and BC and DE are parallel. The length of AC is 5 and the length of BC is 4. Find tan(angle CED).

• 5/4

• 4/5

• 4/3

• 1

• 3/4