Wazari Exam (Iraq Baccalaureate) - Scientific Branch · Mathematics

Calculus, Complex Numbers, Vectors and Probability

29 practice questions, each with the answer and an explanation.

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All 29 questions

Differentiate $f (x) = 5 x^{4} - 3 x^{2} + 7$ with respect to $x$ .
Find $\int (6 x^{2} + 4) d x$ .
Differentiate $y = x^{2} e^{3 x}$ .
Differentiate $y = ln (x^{2} + 1)$ .
Evaluate $\int_{0}^{2} (3 x^{2} - 2 x) d x$ .
Simplify $(2 + 3 i) (1 - i)$ , where $i^{2} = - 1$ .
What is the modulus of the complex number $3 - 4 i$ ?
Let $z = 1 + i$ . Find $z^{8}$ .
Find the dot product of $a = (2, - 1, 3)$ and $b = (1, 4, 2)$ .
For $a = (3, 4)$ and $b = (4, 3)$ , find $cos θ$ for the angle between them.
An arithmetic sequence has first term $7$ and common difference $4$ . Find the sum of the first $20$ terms.
A geometric series has first term $12$ and common ratio $\frac{1}{3}$ . What is its sum to infinity?
Two fair dice are rolled. What is the probability that the sum is $8$ ?
Bag A holds 2 red and 3 blue balls; bag B holds 4 red and 1 blue. A bag is chosen at random and one ball drawn. It is red. What is the probability it came from bag A?
A farmer has $120$ m of fencing for a rectangular pen with one side against an existing wall, so only three sides need fencing. What is the greatest possible area?
Find the equation of the tangent to $y = x^{2}$ at the point where $x = 3$ .
The function $f (x) = x^{3} - 6 x^{2} + 9 x + 1$ has a local maximum. What is its value?
The area of the triangle with vertices $A (1, 0, 0)$ , $B (0, 2, 0)$ , $C (0, 0, 3)$ is:
Solve $lo g_{2} x + lo g_{2} (x - 2) = 3$ .
Evaluate $lo g_{3} 81$ .
What is $i^{7}$ ?
Solve $2^{x + 1} = 32$ .
Find the gradient of the line through $(1, 2)$ and $(3, 8)$ .
Differentiate $y = sin 2 x$ .
A vector is $(2, 3, 6)$ . What is its magnitude?
Find $\int cos 3 x d x$ .
Find the coefficient of $x^{2}$ in the expansion of $(x + 2)^{4}$ .
For what value of $k$ does $x^{2} - 6 x + k = 0$ have exactly one repeated real root?
A quadratic with real coefficients has $3 + 2 i$ as one root. Which quadratic is it, if the leading coefficient is $1$ ?

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