Algebra
(30 seconds) Solve for x: 2(x − 4) + 5 = 3x − 9
Answer: x=6
(30 seconds) Two angles are supplementary. One angle measures 67°. What is the measure of the other angle?
Answer: 113°
(30 seconds) Find the exact value: sin(π/6)
Answer: 1/2
(1 min 30 sec) If f(x) = (x2+1)3ex, then find its derivative, f'(x).
Answer: f'(x) = ex[6x(x2+1)2 + (x2+1)3]
(45 seconds) Factor by grouping: x3+4x2+3x+12
Answer: (x2+3)(x+4)
(45 seconds) A triangle has a base of 14 cm and a height of 9 cm. Find the area of the triangle.
Answer: 63 cm2
(30 seconds) Simplify completely: tan(x)/sin(x)
Answer: sin(x)
(1 minute) If f(x)= sin(cos(x)), then find its derivative, f'(x). Afterward, evaluate at f'(π/2).
Answer: f'(x) = -sin(x)cos(cos(x)), f'(π/2) = -1
(1 min 30 secs) Solve the system: x² + y² = 25 and
x − y = 1
Answer: x = 4 or x = −3, then y = 3 or y = −4
(1 minute) Two triangles are similar. The corresponding sides of the triangles are 8 cm and 12 cm. If another side of the smaller triangle is 10 cm, what is the corresponding side of the larger triangle?
Answer: 15 cm
(1 min) Solve for x on 0 less than or equal to x less than or equal to 2π: sin(x) = √3 / 2
Answer: x = π/3 , 2π/3
(1 minute) Let h(x) = (ex-1-x)/x, x not equal to 0. Evaluate lim as x-->0 of h(x).
Answer: lim as x-->0 of h(x) = 1/2
Solve for x: √(x + 6) = x
Answer: x = 3, but not x = -2 because it’s extraneous
(1 minute 30 seconds) A rectangle has a diagonal of 13 in and a width of 5 in. What is the area of the rectangle?
Answer: 60 in2
(1 min) Simplify completely: (sin2(x)+cos2(x))/cos(x)
Answer: sec(x)
(45 secs) Let f(x,y) = ax2y+bxy2, where a,b are constants. Find the sum of fx(x,y) + fy(x,y).
Answer: fx(x,y) + fy(x,y) = 2axy+by2+ax2+2bxy
(2 mins) Factor completely: x6 − 64
Answer: (x − 2)(x + 2)(x² + 2x + 4)(x² − 2x + 4)
(2 minutes) A circle has a radius of 6cm. A square is inscribed in the circle. Find the area of the square.
Answer: 72 cm2
(2 mins) Find the exact value of: sin(π/12) in radians
Answer: (√6 - √2)/4
(2 min and 30 sec) Evaluate the integral: ∫x2exdx
Answer: x2ex - 2(xex-ex) + C