Solutions 2008 Part A

Part A:

1) Consider function g represented in the Cartesian plane below:

Which of the following statements is true?

soln: A) is true: the sum of the zeros is equal to – 2. Zeros are 2 and – 4.

2) If p > 1, which of the following expressions is equivalent to ?

soln: D) is correct. Since square root x = x ½ so, ( p16 )½ = p 8.

3) The rule of function f is f (x) = a (x + 7)² + k , with a > 0 and k < 0.

Of these 3 statements:

1. Function f has two zeros.
2. Function f has a minimum.
3. Function f is decreasing over the interval [ – , 7].

which ones are true?

soln: A) 1 and 2 only are true. The 3rd statement would be if the 7 were – 7.

4) The slope of a line in the Cartesian plane is equal to zero. Point P(5, 16) is on this line.

What is the equation of the line?

soln: D) y = 16.

5) Two perpendicular lines l1 and l2 intersect at a point on the y-axis.

The equation for l1 is
What is the equation for l2 ?

soln: C) y = – 3x + 6 because the slope of l1 is – 6/ – 18 = 1/3. Perpendicular: slope = – 3.

6) Area of right triangle GHI is 420 cm². GI = 74 cm. In right triangle JKL, JL = 20 cm. Given that angle I = angle L (as shown), what is the area of triangle JKL to the nearest cm²?

soln: A) 31 cm² is true: k = 20/74 = 10/37 so k² = ( 10/ 37)² -- A = ( 10/ 37)² × 420 = 30.679

7) Triangle MNO has these characteristics:

- angle MNO = 35°, ......... - angle NMO = 45° , ......... - NO = 10 m
which of these triangles must be congruent to triangle MNO?

soln: B) is correct. angle N = 35° = Q, and angle M = 45° = P, so O = R, NO = QR = 10 m.

8) What must be the value of s, t, and u so that the 2 prisms are equivalent?

soln: B) s = 8 cm, t = 4 cm, u = 18 cm. since s×t×u must equal 9 × 4 × 16 = 576.

9) Patricia entered a javelin throwing competition. Her throw was in the 65th percentile of the distribution of the lengths of throws for all the competitors.

Which of these statements must be true?

soln: C) is true since Q 2 = 50% and Q 3 = 75% and 65% is between them.

10) The table shows the distribution of the employees of a factory according to different strata.

 Annual Salary Women Men Total [20,000 - 40, 000[ 42 56 98 [40,000 - 60, 000[ 35 35 70 [60,000 - 80, 000[ 49 21 70 80, 000 or more 14 63 77 Total 140 175 315
We need a representative sample of 180 employees.
Which of these statements is true?

soln: C) The sample must include 44 women between 20 and 60 thousand.

Yes because
A) The sample must include 72 women. No, should be 80 women from proportion.
B) The sample must include 12 men \$80, 000 or more. No, should be 36
D) The sample should have 20 people between 40 and 60 thousand. No, should be 40