Advanced Quizzes — Quiz 4
Hard SAT Math Quiz 4: Expert-Level Practice for the Digital SAT
Challenge yourself with Hard SAT Math Quiz 4, a high-level practice quiz created for students who want to excel on the Digital SAT Math section. Featuring difficult SAT-style questions that require logical reasoning, mathematical precision, and efficient problem-solving, this quiz is ideal for students working toward 700–800 SAT Math scores.
The questions are carefully designed to reflect the variety and complexity of the Digital SAT, covering Algebra, Advanced Math, Problem-Solving and Data Analysis, Geometry, and Trigonometry. Rather than focusing on memorization, this quiz encourages you to analyze unfamiliar situations, connect multiple mathematical concepts, and choose the most efficient solution under timed conditions.
Every problem is accompanied by a detailed step-by-step explanation that helps you understand the underlying concepts, identify common errors, and develop effective test-taking strategies. Whether you're preparing for your first Digital SAT or refining your skills before test day, Hard SAT Math Quiz 4 offers realistic practice that builds confidence, strengthens mathematical reasoning, and prepares you for the most challenging questions on the exam.
Questions in this quiz (10)
$$x^2(x^3-4)=4^x$$If $$x$$ is an integer, what is one possible solution to the equation above?
- 2
$$20-\sqrt{x}=\frac{2}{3}\sqrt{x}+10$$If $$x$$ > $$0$$, for what value of $$x$$ is the equation above true?
- 36
The volume of a sphere is increased by a factor of $$8$$. Approximately by what percent must the radius have increased?
- $$50\%$$
- $$75\%$$
- $$100\%$$
- $$200\%$$
Lena walks at a constant rate of $$2$$ meters per second. Marcus runs $$5$$ times as fast. If Marcus gives Lena a head start of $$60$$ meters in a race, how many meters must Marcus run to catch Lena?
- $$60$$
- $$75$$
- $$90$$
- $$150$$
Use the information below. $$1$$ gallon $$=128$$ fluid ounces $$1$$ fluid ounce $$=30$$ milliliters A science lab has $$4$$ gallons of liquid available. Each student needs $$240$$ milliliters for an experiment. What is the maximum number of students who can participate?
- $$60$$
- $$64$$
- $$72$$
- $$80$$
Which of the following is equivalent to $$25x^4-10x^2y^2+y^4$$?
- $$(5x^2-y^2)^2$$
- $$(5x-y)^4$$
- $$(5x^2+y^2)^2$$
- $$(25x^2-y^2)^2$$
If $$x$$ > $$2$$, which of the following is equivalent to $$\frac{x}{\frac{1}{x-2}+\frac{1}{x+2}}$$
- $$\frac{x^2-4}{2}$$
- $$\frac{2}{x^2-4}$$
- $$\frac{x(x-2)(x+2)}{2}$$
- $$\frac{x^2+4}{2}$$
If $$a$$ > $$0$$ and $$b$$ > $$0$$, the equation $$\sqrt{ab}=a+b$$ is equivalent to which of the following?
- $$ab=a^2+b^2$$
- $$ab=a^2+2ab+b^2$$
- $$0=a^2+ab+b^2$$
- $$2ab=a^2+b^2$$
If $$x^2+x=\frac{x\sqrt{x+1}}{m(x-1)}$$ which of the following gives $$m$$ in terms of $$x$$?
- $$\frac{x\sqrt{x+1}}{(x^2+x)(x-1)}$$
- $$\frac{(x^2+x)(x-1)}{x\sqrt{x+1}}$$
- $$\frac{x\sqrt{x+1}}{x^2+x-1}$$
- $$\frac{x-1}{x\sqrt{x+1}}$$
$$(x-2)^2+7(x-2)-18=0$$If $$x$$ > $$0$$, for what real value of $$x$$ is the equation above true?
- $$2$$
- $$5$$
- $$8$$
- $$4$$
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Frequently asked questions
How many questions are in Advanced Quizzes — Quiz 4?
This practice set includes 10 questions. Finish in one sitting when possible, then review incorrect answers before retaking.
What topic does Advanced Quizzes — Quiz 4 cover?
Advanced Quizzes — Quiz 4 focuses on Advanced Quizzes. Questions follow exam-style wording and difficulty so you can practice the skills tested on major Advanced Quizzes assessments. These are practice materials, not official exam questions.
How is Advanced Quizzes — Quiz 4 scored?
Your score is the percentage of correct answers. A typical passing score is 70%. After you finish, review each miss with the available explanations on The School of Mathematics.
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