Sample Math Questions
1. Simplify the following expression
(6x88 ÷ x2 )+ x3
A. 6x7
B. 6x9
C. 6x4 + x3
D. 6x6 + x3
2. What is the value of the following expression if m = -3 3m + 2m2 - 36
A. -63
B. -45
C. -27
D. -9
3. Solve for p using the following system of equations.
2p - 5k = 20
3p - 20k = 75
A. p = -1
B. p = 1
C. p = 5
D. p = -5
4. What is the midpoint of points D (5, -2) and E (26, 9)?
A. (1, 17.5)
B. (3.5, 15.5)
C. (17.5, 1)
D. (15.5, 3.5)
5. A square has a perimeter of 24cm. If a diagonal line is drawn through the square in such a way that two identical right triangles are produced, what is the length of the diagonal line?
A. 3.46 cm
B. 6 cm
C. 8.49 cm
D. 24 cm
Answer Key:
1. Correct Answer: D
Explanation: To solve this problem, it is necessary to observe the law of exponents which states that xm/xn = xm-n.
Therefore, 6x8/x2 = 6x8-2, or 6x6
Since we cannot add x3 to this value, the expression cannot be simplified any further.
2. Correct Answer: C
Explanation: To solve this problem, it is necessary to substitute the provided value of m (-3) into the expression where m is used to represent the number:
3 (-3) + 2 (-3)2 - 36
Keep in mind that when negative numbers are squared, they become positive.
-9 + 2*9 - 36
-9 + 18 - 36
-27
3. Correct Answer: B
Explanation:
2p - 5k = 20
3p - 20k = 75
To solve for a variable using a system of equations, one of the variables must be cancelled out. To eliminate k from these equations, first multiply the top equation by -4.
-4(2p - 5k = 20)
-8p + 20k = -80
Then, add the two equations to eliminate k.
-8p + 20k = -80
+3p - 20k = 75
-5p = -5
Solve for p.
-5p = -5
p = -5/-5
p = 1
4. Correct Answer: C
Explanation: To find a midpoint, simply calculate the average of the two sets of points.
For x, the midpoint is calculated in the following manner:
(5 + 26)/2 = 15.5
For y, the midpoint is calculated in the following manner:
(-2 + 9)/2 = 3.5
The midpoint is (15.5, 3.5)
5. Correct Answer: D
Explanation: We know the figure is a square, meaning each of its sides is the same length. To find the length of each side, simply divide the perimeter by 4: 24 / 4 = 6cm
When a diagonal line is drawn through the square, two right triangles are formed.
Since we know the length of two of the triangle's sides (6cm), we can find the length of the third side by using the Pythagorean Theorem.
a2 + b2 = c2
62 + 62 = c2
36 + 36 = c2
72 = c2
v72 = vc2
8.49 = c
The length of the diagonal line is 8.49cm.