New SAT Maths Practice Questions with Solutions
Sample 1

A set of 30 Maths questions, with detailed solutions similar to the questions in the NEW SAT math test. Another set of 28 new sat maths questions, with detailed solutions may be used to practice.
Some of the questions could be challenging which makes these questions suitable for a good preparation for the new maths sat test.

  1. Which positive real number is equal to the quarter of its cube root?
  2. If the points with coordinates \((a , b)\) and \((c , d)\) lie on the line with equation \(2y + 3x = 4\) and \(a - c = 3\), then what is the value of \(d - b\)?
  3. Given the system of equations \[ \frac{1}{3}x^2 - \frac{1}{3}y^2 = 7, \qquad 0.01x + 0.01y = 0.05. \] What is \(x - y\)?
  4. Function \(f\) is given by \(f(x) = x^2 + a x + b\), where \(a\) and \(b\) are real numbers. What are the values of \(a\) and \(b\) if the division of \(f(x)\) by \(x - 1\) gives a remainder equal to \(-2\) and the division of \(f(x)\) by \(x + 2\) gives a remainder equal to \(-5\)?
  5. What are the values of the real numbers \(a, b, c\) if the equation \[ -4x(x+5) - 3(4x+2) = a x^2 + b x + c \] is true for all values of \(x\)?
  6. What is the simplified form of the expression \(|x - 10| + |x - 12|\) for values of \(x\) such that \(10 < x < 12\)?
  7. A function is defined by the formula \(y = \dfrac{2x - 1}{x + 3}\). What is the value of \(x\) for \(y = -\dfrac{1}{4}\)?
  8. Which of the graphs below may be that of equation \(-3x + 3y = 3\)?
    Graphs of lines for SAT question
  9. Which of the graphs below may be that of equation \(2y - 2(x-2)^2 - 2 = 0\)?
    Graphs of parabolas for SAT question
  10. What is the solution set for the equation \(|x - 3| = \sqrt{x + 17}\)?
  11. Find the solution set for the equations \(x^2 = 7|x| - 10\).
  12. Write the inequality \(\frac{3}{2} \le x \le \frac{5}{2}\) using one inequality symbol only.
  13. What is the solution set for the equations \((x - 2)(x^2 - 7x + 13) - x + 2 = 0\)?
  14. If \(f\) is a function, which of the functions defined below must have a graph symmetric with respect to the \(y\)-axis?
    a) \(g(x) = (f(x))^2\)    b) \(h(x) = |f(x)|\)    c) \(i(x) = f(x^2)\)    d) \(j(x) = f(-x)\)
  15. Find all values of \(k\) for which the equation \(-2|x - 4| - 2 = k + 1\) has two solutions.
  16. Find the value of \(x\) if \((x+2)^2 + 2(x+2) + y = -2\) and \(y - 2 = x\).
  17. Find the ratio \(r = \dfrac{f(x+h) - f(x)}{h}\) in terms of \(m\) if \(f(x) = m x + b\), where \(m\) and \(b\) are constant real numbers.
  18. What is the solution set for the equations \(\dfrac{2}{w + 2} = \dfrac{4}{w+3} - \dfrac{1}{3}\)?
  19. The equations of the two parabolas shown below are of the form: \(y = x^2 + A x + B\) and \(y = -x^2 + M x + N\). The two parabolas are tangent (touch at one point) and \(A - M = 2\). What is the value of \(B - N\)?
    Two tangent parabolas
  20. If the lines with equations \(A x + B y = C\) and \(M x + N y = P\) are perpendicular and \(\dfrac{M}{N} = 5\), what is the value of \(\dfrac{A}{B}\)?
  21. Solve for \(x\) in terms of \(K, L, M, N, P\) the equation \[ -\dfrac{K x - L}{M x - N} = P. \]
  22. The square root of a real number plus twice the same number is equal to \(10\). What is the number?
  23. The graph of \(f(x) = -x^2 + a\) and the line \(y = x - 2\) are shown. The two graphs intersect at a point that is on the \(x\)-axis. Find \(a\).
    Parabola and line intersecting on x-axis
  24. For what values of \(x\) is the function \[ f(x) = \dfrac{x+2}{\sqrt{|x-2|-4}} \] not a real number?
  25. What is the value of \(0.25x + 0.15y\) if \(5x + 3y = 2\)?
  26. If the complex number \(\dfrac{8 - 16i}{2 - 2i}\) is written in the form \(a + ib\), where \(i = \sqrt{-1}\), then what is the value of \(b\)?
  27. Given the system of equations \(0.2(x+y)^2 = 4\) and \(0.5(x-y)^2 = 3\), find the value of the product \(xy\).
  28. There are \(200\) liters of water in a tank which started leaking at the rate of \(0.25\) liters per minute for about one hour. Then the rate at which water is leaking from the tank increases to \(0.4\) liter per minute. What is the quantity \(q\) of water left in the tank \(t\) hours after the tank started leaking with \(t > 1\)?
  29. Zoe has to write an essay of \(30\) pages. On average, she writes \(11\) pages every \(2\) hours and \(35\) minutes. How many hours would it take Zoe to finish the essay? Round answer to the nearest hour.
  30. A new car was bought at \(\$50{,}000\). The price of the car decreased at a rate of \(\$4000\) a year for the first two years and it has been decreasing continuously at a constant rate of \(\$6000\) since. Write a formula for the price \(P\) in dollars as a function of time \(t\) in years with \(t = 0\) corresponding to \(2\) years after the car was bought.

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