##### 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。

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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.

$$3ya$$

$$3by$$

$$9ab$$

$$ay$$

$$3x$$