Solutions with detailed explanations to compass math test practice questions in sample 11.

What is the value of 2(x^{3}  y^{2}) + 2(x^{3} + y^{2}) for x = 2 and y = 4?
Solution
Substitute x and y by their values and simplify
2(2^{3}  (4)^{2}) + 2(2^{3} + (4)^{2})
= 2(8  16) + 2(8 + 16)
= 16 + 48 = 32

If x = 3, what is the value of 6 / x + 4x  20?
Solution
Substitute x by its value and simplify
6 / x + 4x  20
= 6/3 + 4(3)  20
= 2 + 12  20 = 6

The surface area A of a cylindrical container is given by the formula
A = 2 pi r^{2} + 2 pi r h
where r is the radius, h is the height of the container and h its height and pi is a constant which can be approximeted by 3.14. Which of the values below is closeset to the area of a container whose radius is 10 cm and its height 5 cm?
A) 628
B) 1256
C) 314
D) 3140
E) 942
Solution
Substitute r, h and pi by their values in the formula for the area.
A = 2(3.14)(10)^{2} + 2(3.14)(10)(5)
= 628 + 314 = 942

If x =  2 and y = 3, what is the value of  x^{ y}?
Solution
Substitute x and y by their values and simplify
 x^{ y}
=  (2)^{(3)}
=  1 / (2)^{3}
=  1 / 8 = 1 / 8

If y = 3, what is the value of (y^{3}  3) / ( y + 3)?
Solution
Substitute y by its values and simplify
(y^{3}  3) / ( y + 3)
= ((3)^{3}  3) / ( (3) + 3)
simplify
= (27  3) / (3 + 3)
= 30 / 6 =  5

What is the value of 3 x^{3}  2 x^{2} + 2 for x =  2?
Solution
Substitute x by its values in the given expression
3 x^{3}  2 x^{2} + 2
= 3 (2)^{3}  2 (2)^{2} + 2
Simplify
= 3(8)  2(4) + 2
= 24 8 + 2 = 30

If x = 2.7, what is the value of x + 0.75(x  1.5) + 1.2?
Solution
Substitute x by its values in the given expression and simplify
x + 0.75(x  1.5) + 1.2
= 2.7 + 0.75(2.7  1.5) + 1.2
= 4.8

If x =  0.07 and y = 1.2, what is the value of x y  0.2 (y  x)?
A) 0.338
B)  0.338
C) 0.3
D)  0.3
E) 0.338

At normal resting heart rates, the mean arterial pressure MAP can be approximated by the simple formula
MAP = DP + (1/3)( SP  DP )
where DP is the diastolic pressure and SP systolic pressure. Find the mean arterial pressure MAP, rounded to the nearest unit, for a person with systolic pressure SP of 101 mmHg and a diastolic pressure DP of 72 mmHg.
A) 85
B) 100
C) 90
D) 80
E) 82

What is the value of 3 / (x  4 y) + 2 / (0.5 x + 8 y) for x =  2 and y =  0.25?
A) 11 / 3
B) 3 / 11
C)  3 / 11
D)  11/3
E) 3

