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This flashcards contain Multi-Step Equations, Two Step Variables, Inequalities, Functions, Geometry, Trigonometry, Pre-Calculus and Calculus

Question: Solve for x: 3x + 5 = 2x + 12

Solution: 3x + 5 = 2x + 12 → 3x - 2x = 12 - 5 → x = 7

Question: Solve: 4(x - 3) = 2x + 6

Solution: 4x - 12 = 2x + 6 → 4x - 2x = 6 + 12 → 2x = 18 → x = 9

Question: Solve: 5x - 7 = 2(2x + 1)

Solution: 5x - 7 = 4x + 2 → 5x - 4x = 2 + 7 → x = 9

Question: Solve: (3x+1)/2 = 7

Solution: 3x + 1 = 14 → 3x = 13 → x = 13/3

Question: Solve: 2(3x - 4) - 5 = x + 6

Solution: 6x - 8 - 5 = x + 6 → 6x - 13 = x + 6 → 5x = 19 → x = 19/5

Question: Solve: 2x + 5 = 11

Solution: 2x = 11 - 5 → 2x = 6 → x = 3

Question: Solve: 3x - 7 = 8

Solution: 3x = 8 + 7 → 3x = 15 → x = 5

Question: Solve: x/4 + 3 = 7

Solution: x/4 = 7 - 3 → x/4 = 4 → x = 16

Question: Solve: 5 - 2x = 1

Solution: -2x = 1 - 5 → -2x = -4 → x = 2

Question: Solve: 7x + 2 = 30

Solution: 7x = 30 - 2 → 7x = 28 → x = 4

Question: Solve: 3x + 4 > 10

Solution: 3x > 10 - 4 → 3x > 6 → x > 2

Question: Solve: 5 - 2x ≤ 1

Solution: -2x ≤ 1 - 5 → -2x ≤ -4 → x ≥ 2

Question: Solve: (x - 3)/2 ≥ 5

Solution: x - 3 ≥ 10 → x ≥ 13

Question: Solve: 4x - 7 < 9

Solution: 4x < 16 → x < 4

Question: Solve: 2(3x - 1) > 10

Solution: 6x - 2 > 10 → 6x > 12 → x > 2

Question: Solve: -3x + 5 ≥ 8

Solution: -3x ≥ 8 - 5 → -3x ≥ 3 → x ≤ -1

Question: Solve: 7x + 2 < 16

Solution: 7x < 14 → x < 2

Question: If f(x) = 2x + 3, find f(4)

Solution: f(4) = 2(4) + 3 = 11

Question: If g(x) = x^2 - 5, find g(3)

Solution: g(3) = 3^2 - 5 = 4

Question: Evaluate: h(x) = 3x - 7, find h(0)

Solution: h(0) = 3(0) - 7 = -7

Question: If f(x) = x^2 + 2x, find f(-2)

Solution: f(-2) = (-2)^2 + 2(-2) = 4 - 4 = 0

Question: Find the slope of f(x) = 5x + 1

Solution: slope = coefficient of x = 5

Question: Determine if f(x) = x^2 is linear or nonlinear

Solution: degree of x is 2 → quadratic → nonlinear

Question: If f(x) = -3x + 4, solve f(x) = 10

Solution: -3x + 4 = 10 → -3x = 6 → x = -2

Question: Area of triangle with base 6 and height 4

Solution: A = 1/2 * b * h = 1/2 * 6 * 4 = 12

Question: Circumference of circle with r = 5

Solution: C = 2πr = 2π*5 = 10π

Question: Volume of rectangular prism l=3, w=4, h=5

Solution: V = lwh = 345 = 60

Question: Area of circle with r = 7

Solution: A = π r^2 = π * 7^2 = 49π

Question: Right triangle legs 3 and 4, find hypotenuse

Solution: c = √(3^2 + 4^2) = √(9+16) = 5

Question: Volume of cylinder r=2, h=6

Solution: V = π r^2 h = π * 2^2 * 6 = 24π

Question: Perimeter of rectangle l=8, w=3

Solution: P = 2(l+w) = 2*(8+3) = 22

Question: sin 30°

Solution: 1/2

Question: cos 60°

Solution: 1/2

Question: tan 45°