SAT-aligned practice

Print the practice set

The whole practice set for paper. Answers are at the end, shown only if you ask for them.

To save a PDF, choose “Save as PDF” in the print dialog.

  1. A phone plan costs 37 dollars a month plus 15 cents per text. Maya wants a model for her monthly bill. Which is the best definition of the variable?
    1. Let n be the number of texts Maya sends in one month
    2. Let n be texts
    3. Let n be the cost of one text
  2. Solve 3x+3=−183x + 3 = -18. x=  ?x = \;?
  3. A survey asked 145 people whether they exercise weekly. Under 30: 22 yes, 43 no. Age 30 or over: 27 yes, 53 no. What proportion of the under-30s exercise weekly?
  4. f(x)=2x2+3f(x) = 2x^2 + 3. Find f(−3)f(-3).
  5. A table gives x=0,1,2,3x = 0, 1, 2, 3 and y=4,12,36,108y = 4, 12, 36, 108. What kind of relationship is it?
    1. Exponential: yy is multiplied by 3 at each step
    2. Linear: yy goes up by 8 at each step
    3. Neither
  6. A tile pattern has 6, 9, 14 and 21 tiles in steps 1 to 4 (a square of tiles plus 5 extra). How many tiles are in step 10?
  7. Solve x2=100x^2 = 100. Enter all solutions.
  8. Put the steps for constructing the perpendicular bisector of a segment AB of length 7 cm in order.
    • With the compass point on A, draw an arc with a radius of more than half of AB
    • Keep the same opening; with the point on B, draw an arc that crosses the first one twice
    • Label the two crossing points P and Q
    • Draw the line through P and Q with the straightedge
  9. △ABC≅△DEF\triangle ABC \cong \triangle DEF with AB=3AB = 3, BC=11BC = 11 and CA=18CA = 18. Find DEDE.
  10. Dilate A(3,1)A(3, 1) about the origin with scale factor 2. Tap its image.
  11. An isosceles right triangle has legs of length 8. Find the hypotenuse (exact).
  12. A cylinder of radius 4 is sliced by a plane parallel to its base. What shape is the cross section?
    1. A circle of radius 4
    2. A rectangle
    3. An ellipse
  13. Find the distance between (−1,−3)(-1, -3) and (2,1)(2, 1).
  14. A central angle measures 49∘49^\circ. Find an inscribed angle that intercepts the same arc (degrees).
  15. Two fair dice are rolled. Find the probability that the sum is 2.
  16. a1=3a_1 = 3 and an+1=2an−7a_{n+1} = 2a_n - 7. Find a3a_3.
  17. Expand (x+6)(x+9)(x + 6)(x + 9). What is the coefficient of xx?
  18. Evaluate 365236^{ \frac{ 5 }{2} }.
  19. A culture starts with 7 grams of algae. Each week, the amount is multiplied by 3. How many grams are there after 3 weeks?
  20. Evaluate log⁡1020+log⁡105\log_{ 10 } 20 + \log_{ 10 } 5 without a calculator.
  21. f(x)={x+3if x<53xif x≥5f(x) = \begin{cases} x + 3 & \text{if } x < 5 \\ 3x & \text{if } x \ge 5 \end{cases}. Find f(5)f(5).