AP Physics · Practice Sheet 47

1. 1.

   Mathematics

   Find term number 7 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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2. 2.

   Mathematics

   For the quadratic 1x² − 5x − 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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3. 3.

   Physics

   A projectile is launched at 26 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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4. 4.

   Physics

   If 4,077 J of work is done in 39 s, find the power.

   Formula:Power

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

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5. 5.

   Mathematics

   For the quadratic 3x² − 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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6. 6.

   Mathematics

   Find the sum of the first 14 terms of an AP with first term 20 and common difference 1.

   Formula:AP Sum of n Terms

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

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7. 7.

   Physics

   Find the density of an object with mass 33 g and volume 32 cm³.

   Formula:Density

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

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8. 8.

   Physics

   If 2,003 J of work is done in 10 s, find the power.

   Formula:Power

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

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9. 9.

   Physics

   Find the voltage across a 3 Ω resistor carrying a current of 12 A.

   Formula:Ohm's Law

   $V = IR$

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10. 10.

    Mathematics

    Evaluate log base 10 of 1,000.

    Formula:Logarithm Evaluation

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

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11. 11.

    Mathematics

    Find the sum of the first 6 terms of a GP with first term 2 and common ratio 3.

    Formula:GP Sum of n Terms

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

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12. 12.

    Physics

    A body moving at 15 m/s accelerates at 6 m/s² for 3 s. Find the distance travelled.

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

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

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13. 13.

    Physics

    Find the force required to accelerate a 46 kg mass at 1 m/s².

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

    $F = ma$

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14. 14.

    Mathematics

    For the quadratic 4x² + 8x − 2 = 0, find the sum and product of its roots.

    Formula:Vieta's Formulas (roots)

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

    View formula →
15. 15.

    Mathematics

    Evaluate ∫ from 0 to 5 of 1x^1 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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16. 16.

    Physics

    A projectile is launched at 44 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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17. 17.

    Mathematics

    In an arithmetic progression with first term 9 and common difference 3, find term number 16.

    Formula:AP nth Term

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

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18. 18.

    Mathematics

    Find the distance between the points (-2, -3) and (3, 4).

    Formula:Distance Between Two Points

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

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19. 19.

    Mathematics

    For the quadratic 4x² + 7x + 9 = 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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20. 20.

    Physics

    Find the momentum of a 8 kg body moving at 15 m/s.

    Formula:Linear Momentum

    $p = mv$

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