代数工具 的图标
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。

考试时间还剩下:

10:00

1.

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

89408940

8.948.94

89.489.4

10894\displaystyle \frac{10}{894}

894100\displaystyle \frac{894}{100}

2.

Which of these choices is the biggest?

23\displaystyle \frac{2}{3}

0.3330.\overline{333}

25\displaystyle \frac{2}{5}

46\displaystyle \frac{4}{6}

57\displaystyle \frac{5}{7}

3.

Simplify:

5x+1+5x2x2+x \frac{5}{x+1} + \frac{5x^2}{x^2 + x}

55

xx

5x2+xx2+x+1\displaystyle \frac{5x^2 + x}{x^2 + x + 1}

5+x5 + x

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

4.

What is the average of x+5x+5 and x9?x-9?

x2x - 2

2-2

4-4

xx

x4x - 4

5.

Solve this equation for x:x:

3x31=374 3x^3 - 1 = 374

x=25x = 25

x=5x = 5

x=55x = 5 \sqrt{5}

x=125x = 125

x=3753x = \sqrt[3]{375}

6.

Simplify:

(6x+2y)(0.5y1.5x) (6x + 2y) (0.5y - 1.5x)

3y2+9x+x23y^2 + 9x + x^2

2.5y+4.5x2.5y + 4.5x

4.5y+2.5x4.5y + 2.5x

9x2+xy+y2-9x^2 + xy + y^2

y29x2y^2 - 9x^2

7.

Which of the following is equivalent to

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

Choose all of the following that apply.

(x+13)(6x+1)\displaystyle \left(x + \frac{1}{3}\right)(6x + 1)

(3x+1)(2x+13)\displaystyle (3x+1)\left(2x + \frac{1}{3}\right)

(x+13)(2x+13)\displaystyle \left(x + \frac{1}{3}\right)\left(2x + \frac{1}{3}\right)

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

6x2+3x+13\displaystyle 6x^2 + 3x + \frac{1}{3}

8.

A root, or solution, of the equation

10x215x+7=0 10x^2 - 15x + 7 = 0

is which of the following?

x=0x = 0

x=1x = 1

A value of xx that makes 10x215x=710x^2 - 15x = 7 true

A value of xx that makes 10x215x+710x^2 - 15x + 7 equal to zero

The square root of 10x215x+710x^2 - 15x + 7

9.

Which of the following are terms in the expansion of

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

Choose all of the following that apply.

3ya3ya

3by3by

9ab9ab

ayay

3x3x