AFOQT PRACTICE TEST (MATH SECTION) QUESTIONS AND ANSWERS 2023

AFOQT PRACTICE TEST (MATH SECTION) QUESTIONS AND ANSWERS 2023 if the volume of a cube is 8cm^3, what is the length of the cube? a. 1 cm b. 2 cm c. 3 cm d. 4 cm e. 8 cm B. 2 cm Simplify the following expression: (2x2 + 3) (2x - 1) a. 4x3 - 2x2 +6x - 3 b. 2x2 +6x - 3 c. 4x3 - 2x2 +6x + 3 d. 4x3 - 2x2 - 6x - 3 e. 2x2 - 6x + 3 A. 4x3 - 2x2 +6x - 3 Simplify the following expression: (2x4y7m2z) * (5x2y3m8) a. 10x6y9m10z b. 7x6y10m10z c. 10x5y10m10z d. 10x6y10m10z e. 7x5y9m10z D. 10x6y10m10z A classroom contains 13 boys and 18 girls. If a student's name is chosen randomly, what is the probability it will be a girl's name? a. 36% b. 42% c. 58% d. 72% e. 84% c. 58% If x - 9 = 2x + 10, what is the value of x? a. -19 b. 19 c. 6.3 d. -6.3 e. none of the above a. -19 A rectangle has a width of 7 cm and a length of 9 cm. What is its perimeter? a. 16 cm b. 32 cm c. 48 cm d. 62 cm e . 63 cm b. 32 The perimeter of a figure is the sum of all of its sides. Since a rectangle's width and length will be the same on opposite sides, the perimeter of a rectangle can be calculated by using the following formula: perimeter = 2(width) + 2(length) Using the numbers given in the question: perimeter = 2(7cm) + 2(9cm) perimeter = 14cm + 18cm perimeter = 32cm In the following inequality, solve for q. -3q + 12 ≥ 4q - 30 a. q ≥ 6 b. q = 6 c. q ≠ 6 d. q ≤ 6 e. q does not exist D: First, gather the like terms on opposite sides of the equation to make it easier to solve: -3q - 4q ≥ -30 - 12 -7q ≥ -42 Then, divide both sides by -7 to solve for q: -7q/-7 ≥ -42/-7 q ≥ 6 Finally, when both sides are divided by a negative number, the direction of the sign must be reversed: q ≤ 6 If x - 6 = 0, then x is equal to a. 0 b. 3 c. 6 d. 9 e. 12 C: To solve for x, it is necessary to add 6 to both sides to isolate the variable: x - 6 + 6 = 0 + 6 x = 6 If x = -3, calculate the value of the following expression: 3x3 + (3x + 4) - 2x2 a. -104 b. -58 c. 58 d. 104 e. 0 A: To calculate the value of this expression, substitute -3 for x each time it appears in the expression: 3(-3)3 + (3(-3)+ 4) - 2(-3)2 According to the order of operations, any operations inside of brackets must be done first: 3(-3)3 + (-9+ 4) - 2(-3)2 3(-3)3 + -5 - 2(-3)2 Then, the value of the expression can be calculated: 3(-27) + -5 - 2(9) -81 + -5 - 18 -104 If 3x - 30 = 45 - 2x, what is the value of x? a. 5 b. 10 c. 15 d. 20 e. 25 C: First, combine like terms to make the equation easier to solve: 3x + 2x = 45 + 30 5x = 75 Then, divide both sides by 5 to solve for x: 5x/5 = 75/5 x = 15 Solve for x in the following inequality: 1/4x - 25 ≥ 75 a. x ≥ 400 b. x ≤ 400 c. x ≥ 25 d. x ≤ 25 e. x ≥ 50 A: First, add 25 to both sides to isolate x: 1/4x - 25 + 25 ≥ 75 + 25 1/4x ≥ 100 Then, multiply both sides by 4 to solve for x: 1/4x * 4 ≥ 100 * 4 x ≥ 400 If x2 - 5 = 20, what is possible value of x? a. 5 b. 10 c. 12.5 d. 15 e. 25 A: First, add 5 to both sides to isolate x: x2 - 5 + 5 = 20 + 5 x2 = 25 Then, take the square root of both sides to solve for x v√x² = √25 x = 5 What is the area of a square that has a perimeter of 8 cm? a. 2 cm2 b. 4 cm2 c. 32 cm2 d. 64 cm2 e. 160 cm2 B: First, we must calculate the length of one side of the square. Since we know the perimeter is 8cm, and that a square has 4 equal sides, the length of each side can be calculated by dividing the perimeter (8cm) by 4: 8cm / 4 = 2cm The formula for the area of a square is length2 Therefore, to calculate the area of this square: 2cm2 or 2cm * 2cm Area = 4cm2 If x = 4 and y = 2, what is the value of the following expression: 3xy - 12y + 5x a. -4 b. 10 c. 12 d. 20 e. 24 D: To find the value of this expression, substitute the given values for x and y into the expression: 3(4)(2) - 12(2) + 5(4) Then, calculate the value of the expression: 3*8 - 12*2 + 5*4 24 - 24 + 20 20 If 0.65x + 10 = 15, what is the value of x? a. 4.92 b. 5.78 c. 6.45 d. 7.69 e. 8.12 D: First, subtract 10 from both sides to isolate x: 0.65x + 10 - 10 = 15 - 10 0.65x = 5 Then, divide both sides by 0.65 to solve for x: 0.65x/0.65 = 5/0.65 x = 7.69 Simplify the following: (3x + 5) (4x - 6) a. 12x2 -38x -30 b. 12x2 + 2x -30 c. 12x2 -2x -1 d. 12x2 +2x + 30 e. 12x2 + 7x - 30 B: Use the FOIL method (first, outside, inside, and last) to get rid of the brackets: 12x2 -18x + 20x -30 Then, combine like terms to simplify the expression: 12x2 -18x + 20x -30 12x2 + 2x -30 Simplify the following expression: 50x^18t^6w^3z^20/5x^5t^2w^2z^19 a. 10x13t3wz b. 10x13t4wz c. 10x12t4wz d. 10x13t4wz2 e. 10x12t3w2z2 B: To simplify this expression, it is necessary to follow the law of exponents that states: xn/xm = xn-m First, the 50 can be divided by 5: 50/5 = 10 Then, it is simply a matter of using the law of exponents described above to simplify the expression: 10x18-5t6-2w3-2z20-19 10x13t4wz 4! = a. 4 b. 12 c. 16 d. 20 e. 24 E: To calculate the value of this permutation, it is necessary to multiply each number between one and 4: 1 * 2 * 3 * 4 = 24 If a cube is 5 cm long, what is the volume of the cube? a. 15 cm3 b. 65 cm3 c. 105 cm3 d. 125 cm3 e. 225 cm3 D: Because it is a cube, it is known that the width and the height of the cube is also 5cm. Therefore, to find the volume of the cube, we must cube 5cm: 5cm3 This is the same as: 5 * 5 * 5 = 125 The volume of the cube is 125cm3. Solve for x by factoring: x2 -13x + 42 = 0 a. x = 6, 7 b. x = -6, -7 c. x = 6, -7 d. x = -6, 7 e. x = 7 only A: First, factor this equation to make solving for x easier: (x - 6) (x - 7) = 0 Then, solve for both values of x: 1) x - 6 = 0 x = 6 2) x - 7 = 0 x = 7 A triangle has a base measuring 12 cm and a height of 12 cm. What is its area? a. 24 cm2 b. 56 cm2 c. 72 cm2 d. 144 cm2 e. 288 cm2 C: The area of a triangle can be calculated by using the following formula: A = 1/2b*h Therefore, by using the values given in the question: A = 1/2(12cm) * 12cm A = 6cm * 12cm A = 72cm2 Simplify the following expression: (3x2 7x7)+ (2y3 9y12) a. 21x14 + 18y26 b. 10x9 + 11y15 c. 21x14 + 18y15 d. 21x9 + 18y15 e. 10x14 + 11y26 D: To simplify this expression, it is necessary to observe the law of exponents that states: xn * xm = xn+m Therefore: 3*7x7+2 + 2*9y12+3 21x9 + 18y15 If x/3 + 27 = 30, what is the value of x? a. 3 b. 6 c. 9 d. 12 e. 27 C: First, subtract 27 from both sides to isolate x: x/3 + 27 - 27 = 30 - 27 x/3 = 3 Then, both sides must be multiplied by 3 to solve for x: 3(x/3) = 3 * 3 x = 9 What is the slope of a line with points A (4,1) and B (-13,8)? a. 7/17 b. -7/17 c. -17/7 d. 17/7 e. none of the above B: To find the slope of a line, it is necessary to calculate the change in y and the change in x: Change in y: 1 - 8 = -7 Change in x: 4 - (-13) = 17 The slope of a line is expressed as change in y over change in x: -7/17