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Ultimate AS Pure True False Quiz (Set 4)

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  • d²y/dx² > 0 indicates concave down
    False It indicates concave up.
  • ∫sin(2x) dx = ½cos(2x) + c
    False Correct is −½cos(2x) + c.
  • ∫cos(2x) dx = ½ sin(2x) + c
    True Chain rule in reverse.
  • cos(90°) = 1
    False It equals 0.
  • ln(1) = 0
    True Because e⁰ = 1.
  • y = −f(x) reflects graph in x-axis
    True y-values are negated.
  • ∫sec(x) dx = ln|sec(x) + tan(x)| + c
    True Standard integral.
  • d/dx(sin(x)) = cos(x)
    True Standard derivative.
  • d/dx(√x) = 1/(2√x)
    True Rewrite as x^(1/2) and differentiate.
  • ∫x² dx = ½x³ + c
    False Correct is x³/3 + c.
  • log₅(25) = 2
    True Since 5² = 25.
  • y = 3f(x) is a horizontal stretch
    False It’s a vertical stretch.
  • tan(180°) = 1
    False tan(180°) = 0.
  • x² + 2x + 2 = 0 has real solutions
    False Discriminant 2² − 8 = −4, no real roots.
  • d/dx(1/x) = −1/x²
    True Power rule with exponent −1.
  • ln(e⁵) = 5
    True Log cancels exponential.
  • e^(ln(7)) = 7
    True Exponential cancels log.
  • y = f(x) + 3 is a translation 3 units upwards
    True Adding moves graph up.
  • The gradient of y = x³ at x = 2 is 8
    False Derivative 3x² = 12.
  • The gradient of y = x² at x = 4 is 8
    True Derivative 2x = 8.
  • d²y/dx² of y = x³ is 6x
    True Differentiate twice.
  • ∫cosec(x) dx = ln|cosec(x) − cot(x)| + c
    True Another standard integral.
  • d/dx(tan(x)) = sec²(x)
    True Standard result.
  • y = f(−x) reflects graph in y-axis
    True x-values are negated.
  • cos(180°) = −1
    True Unit circle fact.
  • tan(90°) is undefined
    True Because cos(90°) = 0.
  • sin(0°) = 0
    True Standard trig fact.
  • d²y/dx² of y = x² is 2
    True Second derivative is constant.
  • d²y/dx² < 0 indicates concave up
    False It indicates concave down.
  • sin²(x) + cos²(x) = 1
    True Fundamental identity.
  • log(1000) = 2
    False log(1000) = 3.
  • f(x) = x² is one-to-one
    False f(2) = f(−2), so not one-to-one.
  • d/dx(cos(x)) = cos(x)
    False It equals −sin(x).
  • log₂(8) = 2
    False It equals 3, since 2³ = 8.
  • 1 + tan²(x) = cos²(x)
    False It equals sec²(x).
  • d/dx(x⁴) = 4x³
    True Apply power rule.
  • sin(180°) = 0
    True Standard trig fact.
  • ∫e^(−x) dx = −e^(−x) + c
    True Differentiate −e^(−x) to check.
  • x² − 9 = 0 has roots x = 3 and x = −3
    True Factorises as (x − 3)(x + 3).
  • f(x) = 2x + 1 has inverse f⁻¹(x) = (x − 1)/2
    True Rearrange for x.
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