##### 代数工具: 基础能力测试

LIVE课程将用最简单的语言将最复杂的数学概念去芜存菁。在开始上课前，让我们来确认你已经掌握了我们将在本课程中使用的基本概念。如果您在此测试中答出 80%以上的题目，同时在 place-out test 中得到低于 70%的分数，那么就从这个模块开始学习吧！ 这个测试对你来说应该很容易，因为它只是基础能力测试。

10:00

1.

What is $10\%$ of $894?$

$8940$

$8.94$

$89.4$

$\displaystyle \frac{10}{894}$

$\displaystyle \frac{894}{100}$

2.

Which of these choices is the biggest?

$\displaystyle \frac{2}{3}$

$0.\overline{333}$

$\displaystyle \frac{2}{5}$

$\displaystyle \frac{4}{6}$

$\displaystyle \frac{5}{7}$

3.

Simplify:

$\frac{5}{x+1} + \frac{5x^2}{x^2 + x}$

$5$

$x$

$\displaystyle \frac{5x^2 + x}{x^2 + x + 1}$

$5 + x$

$\displaystyle \frac{5}{x+1}$

4.

What is the average of $x+5$ and $x-9?$

$x - 2$

$-2$

$-4$

$x$

$x - 4$

5.

Solve this equation for $x:$

$3x^3 - 1 = 374$

$x = 25$

$x = 5$

$x = 5 \sqrt{5}$

$x = 125$

$x = \sqrt[3]{375}$

6.

Simplify:

$(6x + 2y) (0.5y - 1.5x)$

$3y^2 + 9x + x^2$

$2.5y + 4.5x$

$4.5y + 2.5x$

$-9x^2 + xy + y^2$

$y^2 - 9x^2$

7.

Which of the following is equivalent to

$\frac{(3x + 1)(6x + 1)}{3} ?$

Choose all of the following that apply.

$\displaystyle \left(x + \frac{1}{3}\right)(6x + 1)$

$\displaystyle (3x+1)\left(2x + \frac{1}{3}\right)$

$\displaystyle \left(x + \frac{1}{3}\right)\left(2x + \frac{1}{3}\right)$

$(x+1)(2x+1)$

$\displaystyle 6x^2 + 3x + \frac{1}{3}$

8.

A root, or solution, of the equation

$10x^2 - 15x + 7 = 0$

is which of the following?

$x = 0$

$x = 1$

A value of $x$ that makes $10x^2 - 15x = 7$ true

A value of $x$ that makes $10x^2 - 15x + 7$ equal to zero

The square root of $10x^2 - 15x + 7$

9.

Which of the following are terms in the expansion of

$(ay + 3) (by + 3)?$

Choose all of the following that apply.

$3ya$

$3by$

$9ab$

$ay$

$3x$