AP Physics · Practice Sheet 16

1. 1.

   Mathematics

   Find the sum of the first 12 terms of an AP with first term 7 and common difference 4.

   Formula:AP Sum of n Terms

   $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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2. 2.

   Physics

   Calculate the potential energy of a 4 kg object at a height of 47 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   Physics

   A projectile is launched at 31 m/s at 60° 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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4. 4.

   Mathematics

   For the quadratic 4x² − 6x + 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

   If 2,766 J of work is done in 48 s, find the power.

   Formula:Power

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

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6. 6.

   Physics

   Find the voltage across a 29 Ω resistor carrying a current of 12 A.

   Formula:Ohm's Law

   $V = IR$

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7. 7.

   Mathematics

   For the quadratic 3x² + 8x − 1 = 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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8. 8.

   Mathematics

   Find the distance between the points (3, -7) and (5, -6).

   Formula:Distance Between Two Points

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

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9. 9.

   Physics

   A projectile is launched at 47 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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10. 10.

    Mathematics

    Find the sum of the first 24 terms of an AP with first term 4 and common difference 7.

    Formula:AP Sum of n Terms

    $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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11. 11.

    Mathematics

    Evaluate log base 10 of 10,000.

    Formula:Logarithm Evaluation

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

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12. 12.

    Physics

    Find the kinetic energy of a 2 kg object moving at 24 m/s.

    Formula:Kinetic Energy

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

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13. 13.

    Mathematics

    Find the slope of the line through (-6, 5) and (8, 3).

    Formula:Slope of a Line

    $m = \dfrac{y_2-y_1}{x_2-x_1}$

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14. 14.

    Mathematics

    Evaluate ∫ from 2 to 3 of 4x^2 dx.

    Formula:Definite Integral of a Power

    $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

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15. 15.

    Mathematics

    Find the sum of the first 3 terms of a GP with first term 1 and common ratio 3.

    Formula:GP Sum of n Terms

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

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16. 16.

    Mathematics

    For the quadratic 4x² + 5x + 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 →
17. 17.

    Mathematics

    In an arithmetic progression with first term 7 and common difference 10, find term number 11.

    Formula:AP nth Term

    $a_n = a + (n-1)d$

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18. 18.

    Physics

    Find the kinetic energy of a 8 kg object moving at 16 m/s.

    Formula:Kinetic Energy

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

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19. 19.

    Mathematics

    In an arithmetic progression with first term 18 and common difference 8, find term number 14.

    Formula:AP nth Term

    $a_n = a + (n-1)d$

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20. 20.

    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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