AP Physics · Practice Sheet 26

1. 1.

   Mathematics

   Find the sum of the first 12 terms of an AP with first term 6 and common difference 3.

   Formula:AP Sum of n Terms

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

   View formula →
2. 2.

   Mathematics

   Find term number 5 of a geometric progression with first term 2 and common ratio 3.

   Formula:GP nth Term

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

   View formula →
3. 3.

   Physics

   A body moving at 10 m/s accelerates at 2 m/s² for 10 s. Find the distance travelled.

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

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

   View formula →
4. 4.

   Physics

   An object starts at 13 m/s and accelerates at 9 m/s² for 5 s. Find its final velocity.

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

   $v = u + at$

   View formula →
5. 5.

   Mathematics

   Evaluate log base 3 of 27.

   Formula:Logarithm Evaluation

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

   View formula →
6. 6.

   Mathematics

   For the quadratic 4x² − 6x − 4 = 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 →
7. 7.

   Mathematics

   Find the slope of the line through (1, 3) and (0, -6).

   Formula:Slope of a Line

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

   View formula →
8. 8.

   Mathematics

   If f(x) = 4x³ + 6x² + 1x, find f′(3).

   Formula:Derivative of a Polynomial

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

   View formula →
9. 9.

   Physics

   Find the force required to accelerate a 28 kg mass at 1 m/s².

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

   $F = ma$

   View formula →
10. 10.

    Physics

    A projectile is launched at 18 m/s at 60° to the horizontal. Find its range (g = 9.8 m/s²).

    Formula:Projectile Range

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

    View formula →
11. 11.

    Mathematics

    Find the sum of the first 5 terms of a GP with first term 2 and common ratio 2.

    Formula:GP Sum of n Terms

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

    View formula →
12. 12.

    Mathematics

    In an arithmetic progression with first term 8 and common difference 1, find term number 19.

    Formula:AP nth Term

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

    View formula →
13. 13.

    Mathematics

    Find the sum of the first 10 terms of an AP with first term 20 and common difference 6.

    Formula:AP Sum of n Terms

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

    View formula →
14. 14.

    Physics

    Find the density of an object with mass 307 g and volume 34 cm³.

    Formula:Density

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

    View formula →
15. 15.

    Mathematics

    Find the sum of the first 7 terms of a GP with first term 3 and common ratio 2.

    Formula:GP Sum of n Terms

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

    View formula →
16. 16.

    Physics

    Find the electrical power when 28 V drives a current of 14 A.

    Formula:Electrical Power

    $P = VI$

    View formula →
17. 17.

    Mathematics

    For the quadratic 4x² − 5x + 8 = 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 →
18. 18.

    Physics

    A constant force of 90 N moves an object 14 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

    View formula →
19. 19.

    Mathematics

    In an arithmetic progression with first term 1 and common difference 4, find term number 13.

    Formula:AP nth Term

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

    View formula →
20. 20.

    Mathematics

    Find the sum of the first 7 terms of a GP with first term 4 and common ratio 3.

    Formula:GP Sum of n Terms

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

    View formula →

© FormulaWon — formulawon.app · Answers & step-by-step working available on the solutions sheet.