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Placement Test Practice — Calculus
Placement Test Practice — Calculus
This set reviews core first-calculus ideas in a placement-style format.
Practice Test — 20 Questions
1. $$\lim_{x \to 2}(x^2+1)$$
2. $$\lim_{x \to 4} \frac{x^2-16}{x-4}$$
3. Differentiate $x^5$.
4. Differentiate $3x^2-7x+1$.
5. Differentiate $\sin x$.
6. Differentiate $e^x$.
7. Find the critical point of $x^2-2x$.
8. Is that point a max or min?
9. If $s(t)=t^2+4t$, find $v(t)$.
10. If $v(t)=9t-2$, find $a(t)$.
11. $$\int x^2\,dx$$
12. $$\int (4x+3)\,dx$$
13. $$\int_0^1 x\,dx$$
14. $$\int_1^2 3\,dx$$
15. State the meaning of continuity at a point.
16. Which rectangle of fixed perimeter has maximum area?
17. Differentiate $x^2\cos x$ using the product rule.
18. $$\lim_{x \to -1}(2x^3)$$
19. Find an antiderivative of $\cos x$.
20. What theorem connects derivatives and definite integrals?
Show Answer Key
1. $5$
2. $8$
3. $5x^4$
4. $6x-7$
5. $\cos x$
6. $e^x$
7. $x=1$
8. Minimum
9. $2t+4$
10. $9$
11. $\frac{x^3}{3}+C$
12. $2x^2+3x+C$
13. $\frac{1}{2}$
14. $3$
15. Function value exists, the limit exists, and they are equal.
16. A square
17. $2x\cos x-x^2\sin x$
18. $-2$
19. $\sin x+C$
20. The Fundamental Theorem of Calculus