MATH PLACEMENT EXAMS SET 2025/2026 QUESTIONS
WITH ANSWERS TAGGED A+
✔✔(8 - 3x^2)(2x^2 + 6) = - ✔✔-6x^4 - 2x^2 + 48
✔✔(x^2 + x - 6)(x^2 - 6) = - ✔✔x^4 + x^3 - 12x^2 -6x + 36
✔✔Solve for x: 5x(x + 8) = 0 - ✔✔x = -8 , 0
✔✔Solve for x: (x - 4)(x + 2) = 7 - ✔✔x = 5 , -3
✔✔Sketch the graph of: y=x^2 + 4x + 6 - ✔✔
✔✔Sketch the graph of: y = 5 - 2x^2 - ✔✔
✔✔Solve for x and y:
x+y=3
2x + 5y = 12 - ✔✔(1 , 2)
✔✔Find the point of intersection:
x - 2y = 5
2x + 3y = 10 - ✔✔(5 , 0)
✔✔A machine packs 180 boxes of cereal in a half-hour. How long does it take to pack
330 boxes? - ✔✔55 minutes
✔✔75% of the students are boys. There are 24 boys. What is the total number of
students? - ✔✔32
✔✔(6/x) = (3/8) - ✔✔x = 16
✔✔Simplify the ratio: 4:26 - ✔✔2:13
✔✔20% of a number is 60. What is the number? - ✔✔300
✔✔The two legs of a right-angle triangle are 3 inches and 4 inches long, how long is the
hypoteneuse? - ✔✔5
✔✔If the legs of a right triangle are 10 and 24, then the hypotenuse is: - ✔✔26
✔✔Use the Pythagorean Theorem. Round to the nearest tenth when necessary: a = 5,
b = 7, c = ? - ✔✔8.6
, ✔✔(4 - 5i)(12 + 11i) = - ✔✔103 - 16i
✔✔(3-4i)^2 = - ✔✔-7 - 24i
✔✔Simplify: sqrt(-16) = - ✔✔4i
✔✔What is the slop and y-intercept of:
y=2x - 4 - ✔✔slope = 2
y-intercept = -4
✔✔Change the equation to slope-intercept form:
x - 2y = 9 - ✔✔y = (1/2)x - (9/2)
✔✔What is the y-intercept of the following equation:
3x + 6y = 2 - ✔✔1/3
✔✔Solve by completing the square:
x^2 + 15x + 56 = 0 - ✔✔x = -7, -8
✔✔Solve by completing the square:
x^2 - 9x - 5 = 23 - ✔✔x = (9/2) +- (sqrt(193)/2)
✔✔Simplify:
(5-x)/(x^2 - x - 20) - ✔✔-(1/(x+4))
✔✔Simplify:
(6p^2 - 150)/(p^2 - 3x - 40) - ✔✔(6(p-5))/(p-8)
✔✔2sqrt(2) + 3sqrt(2) = - ✔✔5sqrt(2)
✔✔Solve:
10/sqrt(12) = - ✔✔2.89
✔✔Solve:
5sqrt(144) = - ✔✔60
✔✔Simplify:
sqrt(108) = - ✔✔6sqrt(3)
✔✔Simplify:
(x^2 + 5x - 24)/(x^2 + 6x + 8) * (x^2 + 4x + 4)/(x^2 - 3x) = - ✔✔(x + 8)/(x + 4) * (x + 2)/x
WITH ANSWERS TAGGED A+
✔✔(8 - 3x^2)(2x^2 + 6) = - ✔✔-6x^4 - 2x^2 + 48
✔✔(x^2 + x - 6)(x^2 - 6) = - ✔✔x^4 + x^3 - 12x^2 -6x + 36
✔✔Solve for x: 5x(x + 8) = 0 - ✔✔x = -8 , 0
✔✔Solve for x: (x - 4)(x + 2) = 7 - ✔✔x = 5 , -3
✔✔Sketch the graph of: y=x^2 + 4x + 6 - ✔✔
✔✔Sketch the graph of: y = 5 - 2x^2 - ✔✔
✔✔Solve for x and y:
x+y=3
2x + 5y = 12 - ✔✔(1 , 2)
✔✔Find the point of intersection:
x - 2y = 5
2x + 3y = 10 - ✔✔(5 , 0)
✔✔A machine packs 180 boxes of cereal in a half-hour. How long does it take to pack
330 boxes? - ✔✔55 minutes
✔✔75% of the students are boys. There are 24 boys. What is the total number of
students? - ✔✔32
✔✔(6/x) = (3/8) - ✔✔x = 16
✔✔Simplify the ratio: 4:26 - ✔✔2:13
✔✔20% of a number is 60. What is the number? - ✔✔300
✔✔The two legs of a right-angle triangle are 3 inches and 4 inches long, how long is the
hypoteneuse? - ✔✔5
✔✔If the legs of a right triangle are 10 and 24, then the hypotenuse is: - ✔✔26
✔✔Use the Pythagorean Theorem. Round to the nearest tenth when necessary: a = 5,
b = 7, c = ? - ✔✔8.6
, ✔✔(4 - 5i)(12 + 11i) = - ✔✔103 - 16i
✔✔(3-4i)^2 = - ✔✔-7 - 24i
✔✔Simplify: sqrt(-16) = - ✔✔4i
✔✔What is the slop and y-intercept of:
y=2x - 4 - ✔✔slope = 2
y-intercept = -4
✔✔Change the equation to slope-intercept form:
x - 2y = 9 - ✔✔y = (1/2)x - (9/2)
✔✔What is the y-intercept of the following equation:
3x + 6y = 2 - ✔✔1/3
✔✔Solve by completing the square:
x^2 + 15x + 56 = 0 - ✔✔x = -7, -8
✔✔Solve by completing the square:
x^2 - 9x - 5 = 23 - ✔✔x = (9/2) +- (sqrt(193)/2)
✔✔Simplify:
(5-x)/(x^2 - x - 20) - ✔✔-(1/(x+4))
✔✔Simplify:
(6p^2 - 150)/(p^2 - 3x - 40) - ✔✔(6(p-5))/(p-8)
✔✔2sqrt(2) + 3sqrt(2) = - ✔✔5sqrt(2)
✔✔Solve:
10/sqrt(12) = - ✔✔2.89
✔✔Solve:
5sqrt(144) = - ✔✔60
✔✔Simplify:
sqrt(108) = - ✔✔6sqrt(3)
✔✔Simplify:
(x^2 + 5x - 24)/(x^2 + 6x + 8) * (x^2 + 4x + 4)/(x^2 - 3x) = - ✔✔(x + 8)/(x + 4) * (x + 2)/x
