SAT Math warmups

Five warmups of three questions each, 15 questions in total, with worked answers on separate pages. Each set takes about six minutes and leaves space to calculate.

The warmups reuse questions from the free 1600.now worksheet library, so the wording and explanations match the worksheets students can print afterwards. Every question here is original 1600.now material, not an official College Board item.

Download the warmups

Two PDFs, each with the five warmups and the worked answers. Print at actual size in black and white.

US Letter PDF A4 PDF

US Letter: 7 pages. Warmups on pages 1–5, one set per page; worked answers on pages 6–7.
A4: 7 pages. Warmups on pages 1–5, one set per page; worked answers on pages 6–7.

The five warmups

Give the page out, run the six minutes, and collect answers before students open the worked answers. Answers stay collapsed below until you expand them.

Warmup 1: Percent discount and percent change

Problem Solving and Data Analysis / Percentages / 6 minutes

Three questions on the two percent moves that cost points: taking a discount off the original price, and judging a percent change against the right base.

A jacket originally costs $80 and is discounted by 25%. What is the sale price?
1. $65
2. $20
3. $100
4. $60
A store's revenue rises from $240,000 to $300,000. What is the percent increase?
1. 20%
2. 25%
3. 60%
4. 125%
The price of an item rises by 25%. By what percent must the new price decrease to return to the original price?
1. 20%
2. 25%
3. 30%
4. 75%

Show answers and explanations

D. The remaining price is 75% of $80: $0.75 (80) = $60$ . The $20 discount is not the sale price.
B. The increase is $60,000. Divide by the original $240,000: $\frac{60000}{240000} = 0.25$ , or 25%.
A. If the original price is 100, the new price is 125. A decrease of 25 from 125 is $\frac{25}{125} = 20%$ .

Warmup 2: Solve linear equations in one variable

Algebra / Linear equations in one variable / 6 minutes

Distribution, a fixed-fee cost model, and one equation that asks for an expression built from x instead of x itself.

If $3 (2 x - 5) = 21$ , what is $x$ ?
1. 9
2. 6
3. 3
4. 12
A repair costs a fixed fee of $$35$ plus $$18$ per hour. A customer pays $$107$ before tax. How many hours of work are charged?
1. 2
2. 3
3. 4
4. 5
If $7 x - 4 = 3 x + 20$ , what is $2 x + 1$ ?
1. 6
2. 11
3. 12
4. 13

Show answers and explanations

B. Distribute: $6 x - 15 = 21$ . Add 15 to get $6 x = 36$ , so $x = 6$ . Checking gives $3 (12 - 5) = 21$ .
C. Set $35 + 18 h = 107$ . Then $18 h = 72$ , so $h = 4$ hours. The fixed fee is paid once.
D. First solve $4 x = 24$ , giving $x = 6$ . The question asks for $2 x + 1$ , which is $12 + 1 = 13$ .

Warmup 3: Slope, intercepts, and rate models

Algebra / Linear functions / 6 minutes

Read a slope from two points, turn a described rate into a model, and find an x-intercept without graphing.

A line passes through (2, 5) and (6, 17). What is its slope?
1. 2
2. 3
3. 4
4. 12
A tank contains 90 liters at time $t = 0$ and 66 liters at $t = 4$ minutes. If the rate is constant, which model gives the remaining liters?
1. $V (t) = 90 - 6 t$
2. $V (t) = 90 - 24 t$
3. $V (t) = 66 - 6 t$
4. $V (t) = 6 t + 90$
What is the $x$ -intercept of $y = 3 x - 12$ ?
1. (-12, 0)
2. (0, -12)
3. (3, 0)
4. (4, 0)

Show answers and explanations

B. Slope is change in $y$ divided by change in $x$ : $\frac{17 - 5}{6 - 2} = \frac{12}{4} = 3$ .
A. The volume drops 24 liters in 4 minutes, a rate of $- 6$ liters per minute. With initial volume 90, $V (t) = 90 - 6 t$ .
D. At an $x$ -intercept, $y = 0$ . Solving $0 = 3 x - 12$ gives $x = 4$ , so the point is $(4, 0)$ .

Warmup 4: Ratios, rates, and unit conversion

Problem Solving and Data Analysis / Ratios, rates, and proportions / 6 minutes

Share a total by a ratio, scale a production rate, and convert units so the unwanted unit cancels.

The ratio of red beads to blue beads is $3 : 5$ . If there are 40 beads altogether, how many are red?
1. 8
2. 15
3. 24
4. 25
A machine produces 150 parts in 6 minutes. At the same rate, how many parts does it produce in 10 minutes?
1. 200
2. 225
3. 250
4. 300
How many inches are in $3.5$ feet? Use $12 inches = 1 foot$ .
1. 24
2. 36
3. 42
4. 45

Show answers and explanations

B. There are $3 + 5 = 8$ equal parts. Each part contains $\frac{40}{8} = 5$ beads, so red beads total $3 (5) = 15$ .
C. The rate is $\frac{150}{6} = 25$ parts per minute. In 10 minutes, the machine produces $25 (10) = 250$ parts.
C. Multiply 3.5 feet by 12 inches per foot. The feet cancel, leaving 42 inches.

Warmup 5: Right triangles and trigonometry

Geometry and Trigonometry / Right triangles and trigonometry / 6 minutes

Use one Pythagorean triple, one sine ratio, and the complementary-angle identity that turns $sin (A)$ into $cos (B)$ .

A right triangle has legs of lengths 6 and 8. What is the hypotenuse length?
1. 7
2. 10
3. 12
4. 14
For an acute angle $A$ in a right triangle, the opposite side is 3 and the hypotenuse is 5. What is $sin (A)$ ?
1. $\frac{3}{5}$
2. $\frac{4}{5}$
3. $\frac{3}{4}$
4. $\frac{5}{3}$
The acute angles $A$ and $B$ of a right triangle are complementary. If $sin (A) = \frac{7}{25}$ , what is $cos (B)$ ?
1. $\frac{7}{25}$
2. $\frac{24}{25}$
3. $\frac{7}{24}$
4. $\frac{25}{7}$

Show answers and explanations

B. The Pythagorean theorem gives $c^{2} = 6^{2} + 8^{2} = 100$ . Taking the positive square root gives $c = 10$ .
A. Sine is opposite divided by hypotenuse. The specified side lengths give $sin (A) = \frac{3}{5}$ .
A. For complementary angles, $sin (A) = cos (B)$ . Therefore $cos (B)$ has the same value, $\frac{7}{25}$ .

Where each warmup comes from

Every set is drawn from one worksheet, so a student who misses two of three has a longer version to take home.

SAT Percentages Worksheet — 3 questions from this sheet are in warmup 1.
SAT Linear Equations Worksheet — 3 questions from this sheet are in warmup 2.
SAT Linear Functions Worksheet — 3 questions from this sheet are in warmup 3.
SAT Ratios and Rates Worksheet — 3 questions from this sheet are in warmup 4.
SAT Right Triangles and Trigonometry Worksheet — 3 questions from this sheet are in warmup 5.

All printable SAT worksheets

Printing and classroom use

Choose the paper size that matches your printer. Pages 1–5 contain the five student sets. Print pages 6–7 separately for the worked answers. The answer pages are safe to print separately for a substitute or a study hall.

Students may use a calculator. The blank space under each question is intentional: when a student writes the setup, a wrong method is visible in the work, not only in the answer.

After the warmup

Move the same skills into mixed practice with explanations after every question. The question bank is free and ad-free, and it needs no account.

Practice these skills