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High School SAT Prep Math — Advanced

SAT Math — Advanced Math & Data Analysis

Practise quadratics, exponential growth, ratios and percentages, and data/statistics questions — the Advanced Math and Problem-Solving & Data Analysis domains.

Exam Tips for Advanced Math

1. Factor quadratics by finding two numbers that multiply to the constant and add to the middle coefficient.
2. For percent problems, write the relationship as an equation before solving — don't try to do it all in your head.
3. For data questions, sort the values first if they aren't already in order — median and range both depend on order.
4. Use your calculator freely here — these questions reward careful setup more than mental arithmetic.

What This Test Covers

Quadratic Equations

Factoring and solving for the roots of a quadratic.

Exponential Growth

Modeling repeated doubling or scaling over time.

Ratios & Percentages

Working backward from a percent change to an original value.

Statistics

Mean, median, and interpreting rates from a scatterplot.

Probability

Calculating the likelihood of a single event from a set.

Function Evaluation

Substituting values into nonlinear functions like g(x) = x² - 4.

Knowledge Check

SAT Style

Answer all 10 questions. A calculator is allowed, just like the real digital SAT.

Score: 0 / 0

Question 1 — Quadratic equations

What are the solutions to x² - 5x + 6 = 0?

Question 2 — Exponential growth

A population of bacteria doubles every hour, starting at 100. How many bacteria are there after 3 hours?

Question 3 — Percentages

A jacket's price is reduced by 20% to a sale price of $64. What was the original price?

Question 4 — Ratios

A recipe uses flour and sugar in a ratio of 5:2. If 10 cups of flour are used, how much sugar is needed?

Question 5 — Statistics

A data set is: 4, 8, 15, 16, 23, 42. What is the median?

Question 6 — Data interpretation

A scatterplot shows a company's revenue rising steadily over 5 years, from $2 million to $7 million. What is the approximate average rate of increase per year?

Question 7 — Probability

A bag contains 5 red, 3 blue, and 2 green marbles. What is the probability of drawing a blue marble?

Question 8 — Function evaluation

If g(x) = x² - 4, what is g(-3)?

Question 9 — Percentages

A stock priced at $50 rises to $65. What is the percent increase?

Question 10 — Statistics

Test scores were: 62, 75, 88, 91, 95. What is the range?

Key Concepts Summary