Although much care was given in solving these problems, the solver is only human. If you found any errors in the solution, please comment in the box below.
Note: If you have old MTAP questions, you can send them to email@example.com and I will solve them for you and post it here.
21.) When is divided by , the quotient and remainder are both . What is ?
If we divide 5 by 3, then we get a quotient of 1 and a remainder of 2. If we generalize latex the dividend, as the divisor, as the quotient and as the remainder, we can form the equation
In the given, we can see that , , and .
Substituting in *,
22.) If two more than twice p is four less than twice q, express q in terms of p.
23.) If x is nonnegative and 3x – 4 ≤ x, what is the least value of x?
3x – 4 ≤ x
3x – x ≤ 4
2x ≤ 4
x ≤ 2
So the lowest non-negative value is x = 0.
Answer: x = 0
24.) In Item 23, what is the maximum value of x?
Answer: x = 2 (Obvious!)
25.) Solve for in the equation .
26.) Solve for in the equation .
There are two values for :
Answer: -1 and 4
27.) If ∠B is the complement of ∠A, and the supplement of ∠A is 138°, what is ∠B – ∠A?
Complementary angles add up to 90° and supplementary angles add up to 180°. So,
∠A + 138 = 180
∠A = 42.
Now since ∠A and ∠B are complementary,
∠A + ∠B = 90
42 + ∠B = 90
∠B = 90 – 42
∠B = 48.
Now, ∠B – ∠A = 48 – 42 = 6
28.) If the diagonals of rectangle ABCD meet E and ∠AEB = 140°, what is ∠EBC?
∠A + ∠B + ∠E = 180°
∠A + ∠B + 140 = 180°
∠A + ∠B = 40°
Since ABE is an isosceles triangle, ∠A = ∠B. This means that ∠A = ∠B = 20°.
Clearly, ∠ABC = 90°. So,
∠ABE + ∠EBC = 90°
20° + ∠EBC = 90°
∠EBC = 90 – 20°
∠EBC = 70°
29.) If two exterior angles of a triangle measures 80° and 130°, what is its smallest interior angle?
The adjacent interior and exterior angles of a triangle are supplementary. Therefore, the largest exterior angle has the smallest adjacent interior angle.
The sum of the exterior angle of any polygon is 360°so,
Among the three angles, 150° is the largest and its adjacent interior angle is 30°.
30.) In a grouped data, if 100 – 200 forms one class, what is the class interval of the data?
The class interval is the difference between the upper class limit and the lower class limit of a class. Here, the upper class limit is 200 and the lower class limit is 100. So, the class interval is 200 – 100 = 100.