Math Foundations: 17 MCQs with answers

$\sqrt{2}$

$\sqrt{2}$ cannot be expressed as a fraction of two integers, so it is irrational. The others are rational.

$2^6$

Using the power of a power rule: $(a^m)^n = a^{m \times n}$, so $(2^3)^2 = 2^{3 \times 2} = 2^6$.

y-axis

A point with x-coordinate 0 lies on the y-axis. Here, $(0, -4)$ is on the negative y-axis.

$2x + 3y = 6$

A linear equation in two variables has the form $ax + by + c = 0$ where $a$ and $b$ are not both zero. $2x + 3y = 6$ fits this form.

$20$ cm$^2$

Area of a triangle = $\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 5 = 20$ cm$^2$.

$6$

Mean = $\frac{2+4+6+8+10}{5} = \frac{30}{5} = 6$.

$x^2 + 2xy + y^2$

Using the identity: $(x + y)^2 = x^2 + 2xy + y^2$.

$\frac{1}{2}$

A fair coin has two equally likely outcomes: head or tail. So, probability of head = $\frac{1}{2}$.

$360^\circ$

The sum of interior angles of a quadrilateral is always $360^\circ$.

True

Any integer $n$ can be written as $\frac{n}{1}$, so it is rational.

False

The degree of a non-zero constant polynomial is 0, not 1.

$3$

Substitute $x=2$: $p(2) = 2(2)^2 - 3(2) + 1 = 8 - 6 + 1 = 3$.

$\angle B = \angle C$

In an isosceles triangle, angles opposite equal sides are equal. Since $AB = AC$, the angles opposite them, $\angle C$ and $\angle B$, are equal.

$x^2 + 2x + 1$

A polynomial has non-negative integer exponents. $x^2 + 2x + 1$ is a polynomial; the others involve division by a variable or fractional exponents.

Equal

Parallel lines have the same slope. Perpendicular lines have slopes that are negative reciprocals.

$x^2 - 5x + 6$

A quadratic polynomial has degree 2. $x^2 - 5x + 6$ has degree 2.

$a > c$

By transitivity of inequality, if $a > b$ and $b > c$, then $a > c$.