1. 6 pints of a 20 percent solution of alcohol in water are mixed with 4 pints of a 10 percent alcohol in water solution. The percentage alcohol in the new solution is
2. ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS = 6. What is the length of the arc AQB ?
3. If x ¤ y = (x + y)2 - (x - y)2
Then √5 ¤ √5 =
4. Which of the following describes the relationship between A and B as shown in the pairs of numbers in the table above?
A. B = A + 4
B. B = 2A + 1
C. B = 3A - 1
D. B = A2 + 1
E. B = A2 - 1
5. The total weight of a tin and the cookies it contains is 2 pounds. After ? of the cookies are eaten, the tin and the remaining cookies weigh 0.8 pounds. What is the weight of the empty tin in pounds?
6. Which of the following pairs of angles must be equal?
A. a and e only
B. a and e, and c and d only
C. c and d only
D. d and e only
E. c and d and d and e only
7. The average bonus per employee was
8. Refer to the chart from the previous question.
If median bonus amount = m, mean bonus amount = n, and modal bonus amount = p, which of the following represents the correct ordering of m, n and p?
A. m < n < p
B. m < n = p
C. m = p
D. p < m < n
E. p = n < m
9. Which of the following is the equation of a line passing through the origin and parallel to the line 2x – y = 5?
A. 5x – y = 0
B. 2x – y = 0
C. 2x + y = 5
D. 2x + y = 0
E. x + 2y = 0
10. The graph shows a quadratic function with a minimum at (-1,1)
If f(a) = f(1), which if the following could be the value of a?
1.Correct Answer: A
Total new volume is 10 pints. The first solution contributes 0.2 x 6 pints alcohol, and the second contributes 0.1 x 4. Total alcohol = 1.6. Percentage alcohol = (1.6 / 10) x 100 = 16
2.Correct Answer: A
Arc AQB is one quarter the perimeter of the circle (because angle S is a right angle).
To find the radius we need to see that the diagonal SQ of the rectangle= radius.
Now use Pythagoras to find the diagonal; 82 + 62 = r2
So r = 10 (You could have spotted that this is a 3-4-5 triangle and so saved this part of the calculation)
The length of the arc = ? 20 π = 5π
3.Correct Answer: E
The strange symbol tells us what to do to x and y. We then follow these directions for the actual values for x and y given in the problem.
Hence, (2 √5)2 - (0)2 = 4.5 =20
4.Correct Answer: D
You can try out the relationships using at least two pairs from the table to see whether the relationship holds. But it is relatively easy to spot that the first number squared + 1 gives the second number in each case
5.Correct Answer: C
Let the weight of the empty tin = w
(2 - w) = weight of the cookies; and one quarter of the cookies weigh (2 - w)/4
One quarter of the cookies + tin = 0.8 = w + (2 - w)/4
Multiply through by 4; 3.2 = 4w + 2 - w
1.2 = 3w; w = 0.4
6.Correct Answer: B
This question is testing that you know that the angle between a tangent to a circle and a chord (angle c is such an angle) is equal to the angle in the opposite segment (angle d is in the segment opposite to c in this case). Similarly, angle a is equal to angle e for the same reason.
7.Correct Answer: D
To calculate the total spent in bonuses we have to multiply the bonus by the number of employees for each bonus amount: (50 x 7)+ (100 x 37)+ (150 x 4)+ (200 x 2) = 5050. Now divide by the total number of employees to find the average = 5050/50 = 101
8.Correct Answer: C
The median is the middle term in the ranked series. There are 50 terms and so the median is the average of the middle two terms. Both middle terms will be 100.
Mean is 101 and mode is the most common term which is 100. Hence median and mode are equal and less than the mean.
9.Correct Answer: B
First rearrange the equation into the form y = mx + c; y = 2x – 5
From this we know the slope is 2 and so the equation we are looking for must have the ‘m’ value = 2. We are also told that the equation must pass through the origin; this means that the ‘c’ value must be 0.
In B we can rearrange to get y = 2x which fulfills both requirements.
10.Correct Answer: E
We can see that f(1) will be the y-coordinate of the point on the graph where the x coordinate is 1. Reading from the graph this is 3
If f(a) is also 3, the value of a will be the x-coordinate of the other point on the graph where y = 3. Reading from the graph we get -3