AP Physics · Practice Sheet 6

1. 1.

   Mathematics

   Find the distance between the points (-5, -1) and (0, -6).

   Formula:Distance Between Two Points

   $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

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2. 2.

   Mathematics

   Find the binomial coefficient C(6, 3) — the coefficient of x^3 in (1 + x)^6.

   Formula:Binomial Coefficient

   $\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$

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3. 3.

   Mathematics

   Find term number 3 of a geometric progression with first term 5 and common ratio 3.

   Formula:GP nth Term

   $a_n = a\,r^{\,n-1}$

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4. 4.

   Mathematics

   For the quadratic 1x² + 7x − 6 = 0, find the sum and product of its roots.

   Formula:Vieta's Formulas (roots)

   $\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$

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5. 5.

   Physics

   A body moving at 12 m/s accelerates at 3 m/s² for 2 s. Find the distance travelled.

   Formula:Equation of Motion (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^{2}$

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6. 6.

   Physics

   Find the force required to accelerate a 24 kg mass at 17 m/s².

   Formula:Newton's Second Law (F = ma)

   $F = ma$

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7. 7.

   Mathematics

   Evaluate log base 5 of 15,625.

   Formula:Logarithm Evaluation

   $\log_{b}(b^{k}) = k$

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8. 8.

   Mathematics

   Find term number 7 of a geometric progression with first term 4 and common ratio 2.

   Formula:GP nth Term

   $a_n = a\,r^{\,n-1}$

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9. 9.

   Physics

   A constant force of 129 N moves an object 48 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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10. 10.

    Mathematics

    If f(x) = 2x³ + 4x² + 8x, find f′(2).

    Formula:Derivative of a Polynomial

    $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

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11. 11.

    Mathematics

    Find the distance between the points (6, -8) and (-8, -2).

    Formula:Distance Between Two Points

    $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

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12. 12.

    Physics

    A projectile is launched at 22 m/s at 30° to the horizontal. Find its range (g = 9.8 m/s²).

    Formula:Projectile Range

    $R = \dfrac{u^{2}\sin 2\theta}{g}$

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13. 13.

    Mathematics

    Find the binomial coefficient C(10, 3) — the coefficient of x^3 in (1 + x)^10.

    Formula:Binomial Coefficient

    $\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$

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14. 14.

    Physics

    Find the electrical power when 186 V drives a current of 17 A.

    Formula:Electrical Power

    $P = VI$

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15. 15.

    Physics

    If 4,480 J of work is done in 30 s, find the power.

    Formula:Power

    $P = \dfrac{W}{t}$

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16. 16.

    Mathematics

    Find term number 3 of a geometric progression with first term 2 and common ratio 3.

    Formula:GP nth Term

    $a_n = a\,r^{\,n-1}$

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17. 17.

    Physics

    Find the kinetic energy of a 5 kg object moving at 8 m/s.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2}mv^{2}$

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18. 18.

    Physics

    Find the force required to accelerate a 39 kg mass at 2 m/s².

    Formula:Newton's Second Law (F = ma)

    $F = ma$

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19. 19.

    Mathematics

    For the quadratic 1x² + 1x + 7 = 0, find the sum and product of its roots.

    Formula:Vieta's Formulas (roots)

    $\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$

    View formula →
20. 20.

    Mathematics

    If f(x) = 4x³ + 2x² + 8x, find f′(2).

    Formula:Derivative of a Polynomial

    $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

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