AP Physics · Practice Sheet 8

1. 1.

   Mathematics

   Find the sum of the first 11 terms of an AP with first term 7 and common difference 1.

   Formula:AP Sum of n Terms

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

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2. 2.

   Physics

   Find the density of an object with mass 436 g and volume 8 cm³.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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3. 3.

   Mathematics

   For the quadratic 2x² + 2x − 2 = 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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4. 4.

   Physics

   Find the voltage across a 34 Ω resistor carrying a current of 7 A.

   Formula:Ohm's Law

   $V = IR$

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5. 5.

   Mathematics

   Evaluate ∫ from 1 to 3 of 1x^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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6. 6.

   Physics

   An object starts at 9 m/s and accelerates at 10 m/s² for 9 s. Find its final velocity.

   Formula:Equation of Motion (v = u + at)

   $v = u + at$

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7. 7.

   Mathematics

   In an arithmetic progression with first term 5 and common difference 4, find term number 12.

   Formula:AP nth Term

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

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8. 8.

   Mathematics

   For the quadratic 3x² − 1x − 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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9. 9.

   Mathematics

   Find the binomial coefficient C(10, 4) — the coefficient of x^4 in (1 + x)^10.

   Formula:Binomial Coefficient

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

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10. 10.

    Mathematics

    Find term number 4 of a geometric progression with first term 3 and common ratio 2.

    Formula:GP nth Term

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

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11. 11.

    Mathematics

    In an arithmetic progression with first term 19 and common difference 7, find term number 16.

    Formula:AP nth Term

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

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12. 12.

    Physics

    A force of 965 N acts on an area of 48 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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13. 13.

    Physics

    Find the voltage across a 15 Ω resistor carrying a current of 11 A.

    Formula:Ohm's Law

    $V = IR$

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14. 14.

    Mathematics

    Find the slope of the line through (7, 5) and (0, -2).

    Formula:Slope of a Line

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

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15. 15.

    Mathematics

    Find the sum of the first 15 terms of an AP with first term 15 and common difference 2.

    Formula:AP Sum of n Terms

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

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16. 16.

    Mathematics

    Find the slope of the line through (0, -1) and (8, 8).

    Formula:Slope of a Line

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

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17. 17.

    Physics

    If 2,852 J of work is done in 12 s, find the power.

    Formula:Power

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

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18. 18.

    Mathematics

    Find the sum of the first 6 terms of a GP with first term 4 and common ratio 3.

    Formula:GP Sum of n Terms

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

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19. 19.

    Mathematics

    Find term number 7 of a geometric progression with first term 4 and common ratio 3.

    Formula:GP nth Term

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

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20. 20.

    Physics

    Find the force required to accelerate a 43 kg mass at 6 m/s².

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

    $F = ma$

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